Introduction to general chemistry. Questions for self-control Examples of problem solving

Properties of dilute solutions that depend only on the amount of nonvolatile solute are called colligative properties. These include a decrease in the vapor pressure of the solvent above the solution, an increase in the boiling point and a decrease in the freezing point of the solution, as well as osmotic pressure.

Decreasing the freezing point and increasing the boiling point of a solution compared to a pure solvent:

T deputy = = K TO. m 2 ,

T kip. = = K E. m 2 .

Where m 2 – molality of the solution, K K and K E – cryoscopic and ebullioscopic solvent constants, X 2 – mole fraction of solute, H pl. And H Spanish – enthalpy of melting and evaporation of the solvent, T pl. And T kip. – melting and boiling points of the solvent, M 1 – molar mass of the solvent.

Osmotic pressure in dilute solutions can be calculated using the equation

Where X 2 is the molar fraction of the dissolved substance, and is the molar volume of the solvent. In very dilute solutions this equation becomes van't Hoff equation:

Where C– molarity of the solution.

Equations that describe the colligative properties of nonelectrolytes can also be applied to describe the properties of electrolyte solutions by introducing the Van't Hoff correction factor i, For example:

= iCRT or T deputy = iK TO. m 2 .

The isotonic coefficient is related to the degree of electrolyte dissociation:

i = 1 + ( – 1),

where is the number of ions formed during the dissociation of one molecule.

Solubility of a solid in an ideal solution at temperature T described Schroeder equation:

Where X– mole fraction of solute in solution, T pl. – melting temperature and H pl. – enthalpy of melting of the solute.

EXAMPLES

Example 8-1. Calculate the solubility of bismuth in cadmium at 150 and 200 o C. The enthalpy of fusion of bismuth at the melting temperature (273 o C) is 10.5 kJ. mol –1 . Assume that an ideal solution is formed and the enthalpy of fusion does not depend on temperature.

Solution. Let's use the formula .

At 150 o C , where X = 0.510

At 200 o C , where X = 0.700

Solubility increases with temperature, which is characteristic of an endothermic process.

Example 8-2. A solution of 20 g of hemoglobin in 1 liter of water has an osmotic pressure of 7.52 10 –3 atm at 25 o C. Determine the molar mass of hemoglobin.

65 kg. mol –1 .

TASKS

Calculate the minimum osmotic work performed by the kidneys to excrete urea at 36.6 o C, if the concentration of urea in plasma is 0.005 mol. l –1, and in urine 0.333 mol. l –1.
10 g of polystyrene is dissolved in 1 liter of benzene. The height of the solution column (density 0.88 g cm–3) in the osmometer at 25 o C is 11.6 cm. Calculate the molar mass of polystyrene.
Human serum albumin protein has a molar mass of 69 kg. mol –1 . Calculate the osmotic pressure of a solution of 2 g of protein in 100 cm 3 of water at 25 o C in Pa and in mm of the solution column. Assume the density of the solution to be 1.0 g cm–3.
At 30 o C, the vapor pressure of an aqueous solution of sucrose is 31.207 mm Hg. Art. The vapor pressure of pure water at 30 o C is 31.824 mm Hg. Art. The density of the solution is 0.99564 g cm–3. What is the osmotic pressure of this solution?
Human blood plasma freezes at -0.56 o C. What is its osmotic pressure at 37 o C, measured using a membrane permeable only to water?
*The molar mass of the enzyme was determined by dissolving it in water and measuring the height of the solution column in an osmometer at 20 o C, and then extrapolating the data to zero concentration. The following data was received:

C, mg. cm –3
h, cm

The molar mass of a lipid is determined by the increase in boiling point. The lipid can be dissolved in methanol or chloroform. The boiling point of methanol is 64.7 o C, the heat of evaporation is 262.8 cal. g –1 . The boiling point of chloroform is 61.5 o C, the heat of evaporation is 59.0 cal. g –1 . Calculate the ebullioscopic constants of methanol and chloroform. Which solvent is best to use to determine molar mass with maximum accuracy?
Calculate the freezing point of an aqueous solution containing 50.0 g of ethylene glycol in 500 g of water.
A solution containing 0.217 g of sulfur and 19.18 g of CS 2 boils at 319.304 K. The boiling point of pure CS 2 is 319.2 K. The ebullioscopic constant of CS 2 is 2.37 K. kg. mol –1 . How many sulfur atoms are there in a sulfur molecule dissolved in CS 2?
68.4 g of sucrose dissolved in 1000 g of water. Calculate: a) vapor pressure, b) osmotic pressure, c) freezing point, d) boiling point of the solution. The vapor pressure of pure water at 20 o C is 2314.9 Pa. Cryoscopic and ebullioscopic constant waters are 1.86 and 0.52 K. kg. mol –1 respectively.
A solution containing 0.81 g of hydrocarbon H(CH 2) nH and 190 g of ethyl bromide freezes at 9.47 o C. The freezing point of ethyl bromide is 10.00 o C, the cryoscopic constant is 12.5 K. kg. mol –1 . Calculate n.
When 1.4511 g of dichloroacetic acid is dissolved in 56.87 g of carbon tetrachloride, the boiling point increases by 0.518 degrees. Boiling point CCl 4 76.75 o C, heat of evaporation 46.5 cal. g –1 . What is the apparent molar mass of the acid? What explains the discrepancy with the true molar mass?
A certain amount of a substance dissolved in 100 g of benzene lowers its freezing point by 1.28 o C. The same amount of a substance dissolved in 100 g of water lowers its freezing point by 1.395 o C. The substance has a normal molar mass in benzene, and in water completely dissociated. How many ions does a substance dissociate into in an aqueous solution? The cryoscopic constants for benzene and water are 5.12 and 1.86 K. kg. mol –1 .
Calculate the ideal solubility of anthracene in benzene at 25 o C in molality units. The melting enthalpy of anthracene at the melting point (217 o C) is 28.8 kJ. mol –1 .
Calculate solubility n-dibromobenzene in benzene at 20 and 40 o C, assuming that an ideal solution is formed. Melting enthalpy n-dibromobenzene at its melting point (86.9 o C) is 13.22 kJ. mol –1 .
Calculate the solubility of naphthalene in benzene at 25 o C, assuming that an ideal solution is formed. The melting enthalpy of naphthalene at its melting temperature (80.0 o C) is 19.29 kJ. mol –1 .
Calculate the solubility of anthracene in toluene at 25 o C, assuming that an ideal solution is formed. The melting enthalpy of anthracene at the melting point (217 o C) is 28.8 kJ. mol –1 .
Calculate the temperature at which pure cadmium is in equilibrium with a Cd – Bi solution, the mole fraction of Cd in which is 0.846. The melting enthalpy of cadmium at the melting point (321.1 o C) is 6.23 kJ. mol –1 .

What are solutions and what characteristics of chemical compounds and mechanical mixtures do they have?

What determines the thermal effect of dissolution?

What is solubility and what does it depend on?

What is the concentration of a solution called? Define percentage, molar, molar equivalent and molal concentrations, and mole fraction.

Define Raoult's law.

What are the consequences of Raoult's law?

What are cryoscopic and ebullioscopic solvent constants?

Literature.

Korovin N.V. General chemistry.- M.: Higher. school, 2002. Ch. 8, § 8.1.

Glinka N.L. General chemistry. - M.: Integral-Press, 2002, Ch. 7,

1.6. Examples of problem solving

Example 1. When 10 g of potassium nitrate (KNO 3) was dissolved in 240 g of water, the temperature of the solution decreased by 3.4 degrees. Determine the heat of solution of the salt. The specific heat capacity (sp) of the solution is 4.18 J/g. TO.

Solution:

1. Find the mass of the resulting solution (m):

m = 10 + 240 = 250 (g).

2. Let’s determine the amount of heat absorbed by the solution:

Q = m. court. T

Q = 250. 4.18. (-3.4) = - 3556.4 J = - 3.56 kJ.

3. We calculate the amount of heat absorbed when dissolving one mole of KNO 3, i.e. its heat of dissolution (molar mass of KNO 3 is 101 g/mol):

when 10 g of salt is dissolved, 3.56 kJ is absorbed

when dissolving 101 g of salt --------- x,

x = = 35.96 kJ

Answer: the heat of solution of KNO 3 is 35.96 kJ/mol.

Solution:

1. Find the weight amount of sulfuric acid contained in 1 liter of 17.5% solution:

a) find the mass of a liter (1000 ml) of solution:

m =  . V = 1.12 . 1000 = 1120 g;

b) find the weight amount of sulfuric acid:

100 g of solution contains 17.5 g of H 2 SO 4;

in 1120 g of solution - x,

2. Find the titer of the solution; To do this, it is necessary to divide the weight amount of acid contained in a known volume of solution by the volume of solution expressed in milliliters:

T = = 0.196 g/ml.

3. Find the molar concentration of the solution; To do this, it is necessary to divide the weight amount of acid contained in 1 liter of solution by the molar mass (MH 2 SO 4), 98 g/mol:

2 mol/l.

4. Find the molar concentration of the solution equivalent; To do this, it is necessary to divide the weight of the acid contained in 1 liter of solution (196 g) by the equivalent mass (EH 2 SO 4).

The equivalent mass of H 2 SO 4 is equal to its molar mass divided by the number of hydrogen atoms:

Therefore, C eq = = 4 mol equiv/l.

The molar concentration equivalent can also be calculated using the formula

5.Calculate the molality of the solution; To do this, you need to find the number of moles of acid contained in 1000 g of solvent (water).

From previous calculations (see point 3) it is known that 1120 g (1 l) of solution contains 196 g or 2 moles of H2SO4, therefore, water in such a solution:

1120 - 196 = 924 g.

Let's make a proportion:

per 924 g of water there are 2 moles of H 2 SO 4

per 1000 g of water - x.

With m = x = = 2.16 mol/1000 g of water.

Answer: T = 0.196 g/ml; = 2 mol/l; C eq = 4 mol equiv/l;

With m = 2.16 mol/1000 g of water.

Example 3. How many milliliters of a 96% solution of H 2 SO 4 ( = 1.84 g/cm 3) will be required to prepare 1 liter of its solution with a molar equivalent concentration of 0.5?

Solution.

1. We calculate the weight amount of H 2 SO 4 required to prepare 1 liter of solution with a molar equivalent concentration of 0.5 (the equivalent of sulfuric acid is 49 g):

1000 ml of 0.5 N solution contains 49. 0.5 = 24.5 g H 2 SO 4.

2. Determine the weight amount of the original (96%) solution containing 24.5 g of H 2 SO 4:

100 g of solution contains 96 g of H 2 SO 4,

in x g of solution - 24.5 g of H 2 SO 4.

x = = 25.52 g

3. Find the required volume of the original solution by dividing the weight amount of the solution by its density ():

V = = 13.87 ml.

Answer: to prepare 1 liter of sulfuric acid solution with a molar concentration equivalent of 0.5, 13.87 ml of a 96% solution of H 2 SO 4 is required.

Example 4. A solution prepared from 2 kg (m) of ethyl alcohol and 8 kg (g) of water was poured into the car radiator. Calculate the freezing point of the solution. The cryoscopic water constant Kk is 1.86.

Solution.

1. Find the decrease in the freezing temperature of the solution using a corollary from Raoult’s law:

т з = K к С m = K к .

The molar mass of C 2 H 5 OH is 46 g/mol, therefore,

Т з = 1.86 = 10.1 о С.

2. Find the freezing temperature of the solution:

T s = 0 - 10.1 = - 10.1 o C.

Answer: the solution freezes at a temperature of -10.1 o C.

Example 1. Calculate the osmotic pressure of a solution containing 135 g of glucose C 6 H 12 O 6 in 1.5 liters at 0 0 C.

Solution: Osmotic pressure is determined by Van't Hoff's law:

See RT

We find the molar concentration of the solution using the formula:

Substituting the value of the molar concentration into the expression of Van't Hoff's law, we calculate the osmotic pressure:

π = C m RT= 0.5 mol/l ∙ 8.314 Pa∙m 3 /mol∙K∙273=1134.86 ∙10 3 Pa

Example 2.Determine the boiling point of a solution containing 1.84 g of nitrobenzene C 6 H 5 NO 2 in 10 g of benzene. The boiling point of pure benzene is 80.2 0 C.

Solution: The boiling point of the solution will be ∆t kip higher than the boiling point of pure benzene: t bale (solution) = t bale (solvent) + ∆t bale;

According to Raoult's law: ∆t kip = E∙ C m ,

Where E -ebullioscopic solvent constant (tabular value),

With m– molal concentration of solution, mol/kg

∆t kip = E∙ C m = 1.5 ∙ 2.53=3.8 0 C.

t bale (solution) = t bale (solvent) + ∆t bale = 80.2 0 C +3.8 0 C = 84 0 C.

901. A solution containing 57 g of sugar C 12 H 22 O 11 in 500 g of water boils at 100.72 0 C. Determine the ebullioscopic constant of water.

902. A solution containing 4.6 g of glycerol C 3 H 8 O 3 in 71 g of acetone boils at 56.73 0 C. Determine the ebullioscopic constant of acetone if the boiling point of acetone is 56 0 C.

903. Calculate the boiling point of a solution containing 2 g of naphthalene C 10 H 8 in 20 g of ether, if the boiling point of ether is 35.6 0 C, and its ebullioscopic constant is 2.16.

904. 4 g of a substance are dissolved in 100 g of water. The resulting solution freezes at -0.93 0 C. Determine the molecular mass of the dissolved substance.

905. Determine the relative molecular weight of benzoic acid if its 10% solution boils at 37.57 0 C. The boiling point of the ester is 35.6 0 C, and its ebullioscopic constant is 2.16.

906. The decrease in the freezing point of a solution containing 12.3 g of nitrobenzene C 6 H 5 NO 2 in 500 g of benzene is 1.02 0 C. Determine the cryoscopic constant of benzene.

907. The freezing point of acetic acid is 17 0 C, the cryoscopic constant is 3.9. Determine the freezing point of a solution containing 0.1 mol of a solute in 500 g of acetic acid CH 3 COOH.

908. A solution containing 2.175 g of solute in 56.25 g of water freezes at -1.2 0 C. Determine the relative molecular weight of the solute.

909. At what temperature does a solution containing 90 g of glucose C 6 H 12 O 6 in 1000 g of water boil?

910. 5 g of a substance are dissolved in 200 g of alcohol. The solution boils at 79.2 0 C. Determine the relative molecular weight of the substance if the ebullioscopic constant of alcohol is 1.22. The boiling point of alcohol is 78.3 0 C.

911. An aqueous solution of sugar freezes at -1.1 0 C. Determine the mass fraction (%) of sugar C 12 H 22 O 11 in the solution.

912. In what mass of water should 46 g of glycerol C 3 H 8 O 3 be dissolved to obtain a solution with a boiling point of 100.104 0 C?

913. A solution containing 27 g of a substance in 1 kg of water boils at 100.078 0 C. Determine the relative molecular weight of the dissolved substance.

914. Calculate the mass of water in which 300 g of glycerol C 3 H 8 O 3 should be dissolved to obtain a solution that freezes at – 2 0 C.

915. A solution of glucose in water shows an increase in boiling point of 0.416 0 C. Clean out the decrease in the freezing point of this solution.

916. Calculate the freezing point of a 20% solution of glycerol C 3 H 8 O 3 in water.

917. 1.6 g of a substance are dissolved in 250 g of water. The solution freezes at -0.2 0 C. Calculate the relative molecular mass of the solute.

918. A solution containing 0.5 g of acetone (CH 3) 2 CO in 100 g of acetic acid lowers the freezing point by 0.34 0 C. Determine the cryoscopic constant of acetic acid.

919. Calculate the mass fraction (%) of glycerol in an aqueous solution whose boiling point is 100.39 0 C.

920. How many grams of ethylene glycol C 2 H 4 (OH) 2 are required to be added for each kilogram of water to prepare antifreeze with a freezing point of -9.3 0 C?

921. A solution containing 565 g of acetone and 11.5 g of glycerol C 3 H 5 (OH) 3 boils at 56.38 0 C. Pure acetone boils at 56 0 C. Calculate the ebullioscopic constant of acetone.

922. At what temperature does a 4% solution of ethyl alcohol C 2 H 5 OH in water freeze?

923. Determine the mass fraction (%) of sugar C 12 H 22 O 11 in an aqueous solution if the solution boils at 101.04 0 C.

924. Which solution will freeze at a lower temperature: a 10% glucose solution C 6 H 12 O 6 or a 10% sugar solution C 12 H 22 O 11?

925. Calculate the freezing point of a 12% aqueous (by mass) solution of glycerol C 3 H 8 O 3.

926. Calculate the boiling point of a solution containing 100 g of sucrose C 12 H 22 O 11 in 750 g of water.

927. A solution containing 8.535 g of NaNO 3 in 100 g of water crystallizes at t = -2.8 0 C. Determine the cryoscopic constant of water.

928. To prepare a coolant, 6 g of glycerin ( = 1.26 g/ml) are taken per 20 liters of water. What will be the freezing point of the prepared antifreeze?

929. Determine the amount of ethylene glycol C 2 H 4 (OH) 2 that must be added to 1 kg of water to prepare a solution with a crystallization temperature of –15 0 C.

930. Determine the crystallization temperature of a solution containing 54 g of glucose C 6 H 12 O 6 in 250 g of water.

931. A solution containing 80 g of naphthalene C 10 H 8 in 200 g of diethyl ether boils at t = 37.5 0 C, and pure ether boils at t = 35 0 C. Determine the ebullioscopic constant of the ether.

932. When 3.24 g of sulfur was added to 40 g of benzene C 6 H 6, the boiling point increased by 0.91 0 C. How many atoms do sulfur particles in solution consist of, if the ebullioscopic constant of benzene is 2.57 0 C.

933. A solution containing 3.04 g of camphor C 10 H 16 O in 100 g of benzene C 6 H 6 boils at t = 80.714 0 C. (The boiling point of benzene is 80.20 0 C). Determine the ebullioscopic constant of benzene.

934. How many grams of carbamide (urea) CO(NH 2) 2 must be dissolved in 125 g of water so that the boiling point increases by 0.26 0 C. The ebullioscopic constant of water is 0.52 0 C.

935. Calculate the boiling point of a 6% (by mass) aqueous solution of glycerol C 3 H 8 O 3.

936. Calculate the mass fraction of sucrose C 12 H 22 O 11 in an aqueous solution whose crystallization temperature is 0.41 0 C.

937. When 0.4 g of a certain substance is dissolved in 10 g of water, the crystallization temperature of the solution decreases by 1.24 0 C. Calculate the molar mass of the dissolved substance.

938. Calculate the freezing point of a 5% (by mass) solution of sugar C 12 H 22 O 11 in water.

939. How many grams of glucose C 6 H 12 O 6 should be dissolved in 300 g of water to obtain a solution with a boiling point of 100.5 0 C?

940. A solution containing 8.5 g of some non-electrolyte in 400 g of water boils at a temperature of 100.78 0 C. Calculate the molar mass of the dissolved substance.

941. When 0.4 g of a certain substance is dissolved in 10 g of water, the crystallization temperature of the solution becomes –1.24 0 C. Determine the molar mass of the dissolved substance.

942. Calculate the mass fraction of sugar C 12 H 22 O 11 in a solution whose boiling point is 100.13 0 C.

943. Calculate the crystallization temperature of a 25% (by mass) solution of glycerol C 3 H 8 O 3 in water.

944. Crystallization temperature of benzene C 6 H 6 5.5 0 C, cryoscopic constant 5.12. Calculate the molar mass of nitrobenzene if a solution containing 6.15 g of nitrobenzene in 400 g of benzene crystallizes at 4.86 0 C.

945. A solution of glycerol C 3 H 8 O 3 in water shows an increase in boiling point by 0.5 0 C. Calculate the crystallization temperature of this solution.

946. Calculate the mass fraction of urea CO(NH 2) 2 in an aqueous solution whose crystallization temperature is –5 0 C.

947. In what amount of water should 300 g of benzene C 6 H 6 be dissolved to obtain a solution with a crystallization temperature of –20 0 C?

948. Calculate the boiling point of a 15% (by mass) solution of glycerol C 3 H 8 O 3 in acetone, if the boiling point of acetone is 56.1 0 C and the ebullioscopic constant is 1.73.

949. Calculate the osmotic pressure of a solution at 17 0 C if 1 liter of it contains 18.4 g of glycerol C 3 H 5 (OH) 3.

950. 1 ml of solution contains 10 15 molecules of dissolved substance. Calculate the osmotic pressure of the solution at 0 0 C. What volume contains 1 mole of dissolved substance?

951. How many molecules of a dissolved substance are contained in 1 ml of a solution whose osmotic pressure at 54 0 C is equal to 6065 Pa?

952. Calculate the osmotic pressure of a 25% (by mass) sucrose solution C 12 H 22 O 11 at 15 0 C (ρ = 1.105 g/ml).

953. At what temperature will the osmotic pressure of a solution containing 45 g of glucose C 6 H 12 O 6 in 1 liter of water reach 607.8 kPa?

954. Calculate the osmotic pressure of a 0.25 M sugar solution C 12 H 22 O 11 at 38 0 C.

955. At what temperature will the osmotic pressure of a solution containing 60 g of glucose C 6 H 12 O 6 in 1 liter reach 3 atm?

956. The osmotic pressure of a solution with a volume of 5 liters at 27 0 C is 1.2 ∙ 10 5 Pa. What is the molar concentration of this solution?

957. How many grams of ethyl alcohol C 2 H 5 OH must 1 liter of solution contain so that its osmotic pressure is the same as that of a solution containing 4.5 g of formaldehyde CH 2 O in 1 liter at the same temperature.

958. How many grams of ethyl alcohol C 2 H 5 OH must be dissolved in 500 ml of water so that the osmotic pressure of this solution at 20 0 C is equal to 4.052 ∙ 10 5 Pa?

959. 200 ml of solution contain 1 g of dissolved substance and at 20 0 C have an osmotic pressure of 0.43 ∙ 10 5 Pa. Determine the molar mass of the solute.

960. Determine the molar mass of the solute if a solution containing 6 g of the substance in 0.5 liters at 17 0 C has an osmotic pressure of 4.82 ∙ 10 5 Pa.

961. How many grams of glucose C 6 H 12 O 6 should 1 liter of solution contain so that its osmotic pressure is the same as that of a solution containing 34.2 g of sugar C 12 H 22 O 11 in 1 liter at the same temperature?

962. 400 ml of solution contain 2 g of dissolved substance at 27 0 C. The osmotic pressure of the solution is 1.216 ∙ 10 5 Pa. Determine the molar mass of the solute.

963. A sugar solution C 12 H 22 O 11 at 0 0 C exerts an osmotic pressure of 7.1 ∙ 10 5 Pa. How many grams of sugar are contained in 250 ml of this solution?

964. 2.45 g of urea are contained in 7 liters of solution. The osmotic pressure of the solution at 0 0 C is 1.317 ∙ 10 5 Pa. Calculate the molar mass of urea.

965. Determine the osmotic pressure of a solution, 1 liter of which contains 3.01 ∙ 10 23 molecules at 0 0 C.

966. Aqueous solutions of phenol C 6 H 5 OH and glucose C 6 H 12 O 6 contain equal masses of dissolved substances in 1 liter. In which solution is the osmotic pressure greater at the same temperature? How many times?

967. A solution containing 3 g of a non-electrolyte in 250 ml of water freezes at a temperature of – 0.348 0 C. Calculate the molar mass of the non-electrolyte.

968. A solution containing 7.4 g of glucose C 6 H 12 O 6 in 1 liter at a temperature of 27 0 C has the same osmotic pressure as a solution of urea CO (NH 2) 2. How many g of urea are contained in 500 ml of solution?

969. The osmotic pressure of a solution, 1 liter of which contains 4.65 g of aniline C 6 H 5 NH 2, at a temperature of 21 0 C is 122.2 kPa. Calculate the molar mass of aniline.

970. Calculate the osmotic pressure at a temperature of 20 0 C of a 4% sugar solution C 12 H 22 O 11, the density of which is 1.014 g/ml.

971. Determine the osmotic pressure of a solution containing 90.08 g of glucose C 6 H 12 O 6 in 4 liters at a temperature of 27 0 C.

972. A solution with a volume of 4 liters contains 36.8 g of glycerol (C 3 H 8 O 3) at a temperature of 0 0 C. What is the osmotic pressure of this solution?

973. At 0 0 C, the osmotic pressure of a sucrose solution C 12 H 22 O 11 is 3.55∙10 5 Pa. What mass of sucrose is contained in 1 liter of solution?

974. Determine the size of the osmotic solution, in 1 liter of which With contains 0.4 mol of non-electrolyte at a temperature of 17 0 C.

975. What is the osmotic pressure of a solution containing 6.2 g of aniline (C 6 H 5 NH 2) in 2.5 liters of solution at a temperature of 21 0 C.

976. At 0 0 C, the osmotic pressure of a sucrose solution C 12 H 22 O 11 is 3.55∙10 5 Pa. What mass of sucrose is contained in 1 liter of solution?

977. At what temperature will an aqueous solution of ethyl alcohol freeze if the mass fraction of C 2 H 5 OH is 25%?

978. A solution containing 0.162 g of sulfur in 20 g of benzene boils at a temperature 0.081 0 C higher than pure benzene. Calculate the molecular weight of sulfur in solution. How many atoms are there in one sulfur molecule?

979. 300 ml of water was added to 100 ml of a 0.5 mol/l aqueous solution of sucrose C 12 H 22 O 11. What is the osmotic pressure of the resulting solution at 25 0 C?

980. Determine the boiling and freezing temperatures of a solution containing 1 g of nitrobenzene C 6 H 5 NO 2 in 10 g of benzene. The ebuloscopic and cryoscopic constants of benzene are respectively 2.57 and 5.1 K∙kg/mol. The boiling point of pure benzene is 80.2 0 C, the freezing point is -5.4 0 C.

981. What is the freezing point of a non-electrolyte solution containing 3.01∙10 23 molecules in one liter of water?

982. Solutions of camphor weighing 0.522 g in 17 g of ether boil at a temperature 0.461 0 C higher than pure ether. The ebullioscopic constant of the ether is 2.16 K∙kg/mol. Determine the molecular weight of camphor.

983. The boiling point of an aqueous solution of sucrose is 101.4 0 C. Calculate the molal concentration and mass fraction of sucrose in the solution. At what temperature does this solution freeze?

984. The molecular weight of the nonelectrolyte is 123.11 g/mol. What mass of non-electrolyte must be contained in 1 liter of solution so that the solution at 20 0 C has an osmotic pressure equal to 4.56∙10 5 Pa?

985. When 13.0 nonelectrolyte was dissolved in 400 g of diethyl ether (C 2 H 5) 2 O, the boiling point increased by 0.453 K. Determine the molecular weight of the dissolved substance.

986. Determine the boiling point of an aqueous solution of glucose if the mass fraction of C 6 H 12 O 6 is equal to 20% (for water K e = 0.516 K∙kg/mol).

987. A solution consisting of 9.2 g of iodine and 100 g of methyl alcohol (CH 3 OH) boils at 65.0 0 C. How many atoms are included in the iodine molecule in a dissolved state? The boiling point of alcohol is 64.7 0 C, and its ebullioscopic constant K e = 0.84.

988. How many grams of sucrose C 12 H 22 O 11 must be dissolved in 100 g of water in order to: a) lower the crystallization temperature by 1 0 C; b) increase the boiling point by 1 0 C?

989. 2.09 of a certain substance is dissolved in 60 g of benzene. The solution crystallizes at 4.25 0 C. Establish the molecular weight of the substance. Pure benzene crystallizes at 5.5 0 C. The cryoscopic constant of benzene is 5.12 K∙kg/mol.

990. At 20 0 C, the osmotic pressure of a solution, 100 ml of which contains 6.33 g of blood coloring matter - hematin, is 243.4 kPa. Determine the molecular weight of hematin.

991. A solution consisting of 9.2 g of glycerol C 3 H 5 (OH) 3 and 400 g of acetone boils at 56.38 0 C. Pure acetone boils at 56.0 0 C. Calculate the ebullioscopic constant of acetone.

992. The vapor pressure of water at 30 0 C is 4245.2 Pa. What mass of sugar C 12 H 22 O 11 should be dissolved in 800 g of water to obtain a solution whose vapor pressure is 33.3 Pa less than the vapor pressure of water? Calculate the mass fraction (%) of sugar in the solution.

993. The vapor pressure of ether at 30 0 C is 8.64∙10 4 Pa. What amount of non-electrolyte must be dissolved in 50 mol of ether to reduce the vapor pressure at a given temperature by 2666 Pa?

994. The decrease in vapor pressure over a solution containing 0.4 mol of aniline in 3.04 kg of carbon disulfide at a certain temperature is 1003.7 Pa. The vapor pressure of carbon disulfide at the same temperature is 1.0133∙10 5 Pa. Calculate the molecular mass of carbon disulfide.

995. At a certain temperature, the vapor pressure over a solution containing 62 g of phenol C 6 H 5 O in 60 mol of ether is 0.507∙10 5 Pa. Find the vapor pressure of ether at this temperature.

996. The vapor pressure of water at 50 0 C is 12334 Pa. Calculate the vapor pressure of a solution containing 50 g of ethylene glycol C 2 H 4 (OH) 2 in 900 g of water.

997. The pressure of water vapor at 65 0 C is 25003 Pa. Determine the water vapor pressure over a solution containing 34.2 g of sugar C 12 H 22 O 12 in 90 g of water at the same temperature.

998. The vapor pressure of water at 10 0 C is 1227.8 Pa. In what volume of water should 16 g of methyl alcohol be dissolved to obtain a solution whose vapor pressure is 1200 Pa at the same temperature? Calculate the mass fraction of alcohol in the solution (%).

999. At what temperature will an aqueous solution in which the mass fraction of methyl alcohol is 45% crystallize?

1000. An aqueous-alcohol solution containing 15% alcohol crystallizes at – 10.26 0 C. Determine the molar mass of the alcohol.

Problem 427.
Calculate the mole fractions of alcohol and water in a 96% (by weight) solution of ethyl alcohol.
Solution:
Mole fraction(N i) – the ratio of the amount of dissolved substance (or solvent) to the sum of the amounts of all
substances in solution. In a system consisting of alcohol and water, the mole fraction of water (N 1) is equal to

And the mole fraction of alcohol , where n 1 is the amount of alcohol; n 2 - amount of water.

Let's calculate the mass of alcohol and water contained in 1 liter of solution, provided that their densities are equal to one of the proportions:

a) mass of alcohol:

b) mass of water:

We find the amount of substances using the formula: , where m(B) and M(B) are the mass and amount of the substance.

Now let's calculate the mole fractions of substances:

Answer: 0,904; 0,096.

Problem 428.
666 g of KOH dissolved in 1 kg of water; the density of the solution is 1.395 g/ml. Find: a) mass fraction of KOH; b) molarity; c) molality; d) mole fractions of alkali and water.
Solution:
A) Mass fraction– the percentage of the mass of the dissolved substance to the total mass of the solution is determined by the formula:

Where

m (solution) = m(H 2 O) + m(KOH) = 1000 + 666 = 1666 g.

b) Molar (volume-molar) concentration shows the number of moles of solute contained in 1 liter of solution.

Let's find the mass of KOH per 100 ml of solution using the formula: formula: m = p V, where p is the density of the solution, V is the volume of the solution.

m(KOH) = 1.395 . 1000 = 1395 g

Now let's calculate the molarity of the solution:

We find how many grams of HNO 3 are per 1000 g of water by making up the proportion:

d) Mole fraction (Ni) – the ratio of the amount of dissolved substance (or solvent) to the sum of the amounts of all substances in the solution. In a system consisting of alcohol and water, the mole fraction of water (N 1) is equal to the mole fraction of alcohol, where n 1 is the amount of alkali; n 2 - amount of water.

100g of this solution contains 40g KOH and 60g H2O.

Answer: a) 40%; b) 9.95 mol/l; c) 11.88 mol/kg; d) 0.176; 0.824.

Problem 429.
The density of a 15% (by mass) H 2 SO 4 solution is 1.105 g/ml. Calculate: a) normality; b) molarity; c) molality of the solution.
Solution:
Let's find the mass of the solution using the formula: m = p V, where p- density of the solution, V - volume of the solution.

m(H 2 SO 4) = 1.105 . 1000 = 1105 g.

The mass of H 2 SO 4 contained in 1000 ml of solution is found from the proportion:

Let us determine the molar mass of the equivalent of H 2 SO 4 from the relationship:

ME (V) - molar mass of acid equivalent, g/mol; M(B) is the molar mass of the acid; Z(B) - equivalent number; Z (acids) is equal to the number of H+ ions in H 2 SO 4 → 2.

a) Molar equivalent concentration (or normality) shows the number of equivalents of a solute contained in 1 liter of solution.

b) Molal concentration

Now let's calculate the molality of the solution:

c) Molal concentration (or molality) shows the number of moles of solute contained in 1000 g of solvent.

We find how many grams of H 2 SO 4 are contained in 1000 g of water, making up the proportion:

Now let's calculate the molality of the solution:

Answer: a) 3.38n; b) 1.69 mol/l; 1.80 mol/kg.

Problem 430.
The density of a 9% (by weight) sucrose solution C 12 H 22 O 11 is 1.035 g/ml. Calculate: a) the concentration of sucrose in g/l; b) molarity; c) molality of the solution.
Solution:
M(C 12 H 22 O 11) = 342 g/mol. Let's find the mass of the solution using the formula: m = p V, where p is the density of the solution, V is the volume of the solution.

m(C 12 H 22 O 11) = 1.035. 1000 = 1035 g.

a) We calculate the mass of C 12 H 22 O 11 contained in the solution using the formula:

Where
- mass fraction of dissolved substance; m (in-va) - mass of dissolved substance; m (solution) - mass of solution.

The concentration of a substance in g/l shows the number of grams (units of mass) contained in 1 liter of solution. Therefore, the concentration of sucrose is 93.15 g/l.

b) Molar (volume-molar) concentration (CM) shows the number of moles of a dissolved substance contained in 1 liter of solution.