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17.11: Worksheets for Chapter 17

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Concentration by Percent Mass Worksheet

CK-12 Foundation Chemistry

Name______________________ Date_________

The definition of percent mass concentration is the ratio of the mass of solute divided by the total mass of the solution and multiplied by 100 to convert to a percentage.

 percent \ by \ mass = \frac {mass \ of \ solute} {mass \ of \ solution} \times \ 100

Example: What is the percent concentration by mass of a solution formed by dissolving 100. \ grams of ethanol, C_2H_5OH, in 100. \ grams of water?

Solution: percent by mass = \frac {mass \ of \ solute} {mass \ of \ solution}  \times 100 =  \frac {100. \ g} {200. \ g} \times  100 = 50.0 \%

Example: If the density of a 10.0\% by mass KNO_3 solution in water is 1.19 \ g/mL, how many grams of KNO_3 are present in 100. \ mL of the solution?

Solution: We can multiply the volume times the density to the mass of the 100. \ mL of solution and then take 10.0\% of the mass of the solution to get the mass of the potassium nitrate.

grams \ of \ solution &= (100. \ mL)(1.19 \ g/mL) = 119 \  grams\\grams \ of \ KNO_3 &= (0.10)(119 \ grams) = 11.9 \ grams

Exercises

  1. If 30.0 \ grams of AgNO_3 are dissolved in 275 \ grams of water, what is the concentration of the silver nitrate by mass percent?
  2. How many grams of MgF_2 are present in 100.0 \ g of a 20.0\% MgF_2 in water solution?
  3. How many grams of water are present in the solution in question #2?
  4. The density of a 30.0\% by mass solution of NaOH in water is 1.33 \ g/mL. How many grams of NaOH are required to prepare 500. \ mL of this solution?
  5. The density of pure water is 1.00 \ g/mL. What is the concentration gy percent mass of a solution prepared by dissolving 85.0 \ grams of NaOH in 750. \ mL of water?
  6. A solution is prepared by dissolving 66.0 \ grams of acetone, C_3H_6O, in 146.0 \ grams of water. The density of the solution is 0.926 \ g/mL. What is the percent concentration of acetone by mass?
  7. A 35.4\% solution of H_3PO_4 in water has a density of 1.20 \ g/mL. How many grams of phosphoric acid are present in 300. \ mL of this solution?

Mole Fraction and Molality Worksheet

CK-12 Foundation Chemistry

Name______________________ Date_________

Mole Fraction

The definition of mole fraction is the ratio of the moles of solute divided by the total moles of the solution.

 mole \ fraction =  \frac {moles \ of \ solute} {moles \ of \ solution}

Example: What is the mole fraction of ethanol in a solution prepared by dissolving 100. \ g of ethanol, C_2H_5OH, in 100. \ g of water?

Solution:

moles \ ethanol &=  \frac {100. \ g} {46.0  \ g/mol} = 2.17 \ moles\\moles \ water &=  \frac {100. \ g} {18.0 \ g/mol} = 5.56 \ moles\\mole \ fraction \ of \ ethanol &=  \frac {2.17 \ mols} {7.73 \ mols} = 0.281

Molality

The definition of molality is the ratio of the moles of solute divided by the kilograms of solvent.

 molality =  \frac {moles  \ of \ solute} {kilograms \ of \ solvent}

Example: What is the molality of a solution prepared by dissolving 100. \ g of ethanol, C_2H_5OH, in 100. \ g of water?

moles \ ethanol &=  \frac {100. \ g} {46.0 \ g/mol} = 2.17 \ moles\\molality \ of \ ethanol & = \frac {2.17 \ mols} {0.100 \ kg} = 21.7 \ m

Example: A 35.4\% solution of H_3PO_4 in water has a density of 1.20 \ g/mL. What is the mole fraction of H_3PO_4 in this solution and what is the molality?

Solution: We can choose a sample volume of this solution and get the mass of it by multiplying the volume times the density. Suppose we choose a 1.00 \ L sample.

\text{mass of solution} &= (1000. \ mL)(1.20 \ g/mL) = 1200. \ grams\\\text {mass of} \ H_3PO_4 \ \text{in the solution} &= (0.354)(1200. \ grams) = 425 \ grams\\\text{mass of} \ H_2O &= 1200. \ grams - 425 \ grams = 775 \ grams\\moles \ H_3PO_4 &=  \frac {425 \ g} {98.0 \ g/mol} = 4.34 \ moles\\moles \ H_2O  &=  \frac {775 \ g} {18.0 \ g/mol} = 43.1 \ moles\\mole \ \text{fraction of} \ H_3PO_4 &= \frac {4.34 \ mol} {47.4 \ mol} = 0.0916 \\molality & =  \frac {4.34 \ mol} {0.775 \ kg} = 5.60 \ m

Exercises

  1. What is the mole fraction of MgF_2 in a solution that has 20.0 \ g of MgF_2 dissolved in 80.0 \ grams of water?
  2. What is the molality of the solution in question 1?
  3. The density of a 30.0\% by mass solution of NaOH in water is 1.33 \ g/mL. What is the mole fraction of NaOH in this solution?
  4. What is the molality of the solution in problem 3?
  5. What is the molality of a solution prepared by dissolving 4.00 \ g of NaCl in 100. \ g of water?
  6. How many grams of beryllium chloride would you need to add to 125 \ g of water to make a 0.500 \ m solution?
  7. What would be the mole fraction of BeCl_2 in the solution in problem 6?
  8. A solution is prepared by dissolving 66.0 \ g of acetone, C_3H_6O, in 146.0 \ g of water. The density of the solution is 0.926 \ g/mL. What is the molality of this solution?
  9. What is the mole fraction of acetone in the solution in problem 8?

Molarity Worksheet

CK-12 Foundation Chemistry

Name______________________ Date_________

The definition of molarity is the ratio of the mols of solute divided by the volume of the solution.

 molarity =  \frac {moles \ of \ solute}{liters \ of \ solution}

Example: What is the molarity of a solution prepared by dissolving 60.0 \ grams of NaOH in sufficient water to produce 2.00 \ liters of solution?

Solution:

moles \ NaOH & = \frac {60.0 \ g} {40.0 \ g/mol} = 1.50 \ moles\\molarity & =  \frac {1.50 \ mol} {2.00 \ L} = 0.750 \ M

Example: What volume of 0.750 \ M \ NaOH solution will contain 10.0 \ gram of NaOH?

moles \ NaOH & = \frac {10.0 \ g} {40.0 \ g/mol} = 0.250 \ moles\\volume = \frac {mol}{M} & =  \frac {0.250 \ mol} {0.750 \ mol/L} = 0.333 \ L

Exercises

  1. What is the molarity of a solution in which 4.50 \ g of NaNO_3 is dissolved in 265 \ mL of solution?
  2. How many grams of ammonia, NH_3 are present in 5.0 \ L of 0.100 \ M solution?
  3. How many milliliters of 0.200 \ M \ NaOH solution is necessary to contain 6.00 \ grams of NaOH?
  4. How many liters of 0.500 \ M \ CaF_2 solution is required to contain 78.0 \ g of CaF_2?
  5. What mass of ammonium phosphate is needed to make 100. \ mL of 0.500 \ M \ (NH_4)_3PO_4 solution?
  6. What is the molarity of a solution prepared by dissolving 198 \ g of BaBr_2 in 2.00 \ liters of solution?
  7. How many grams of glycerine, C_3H_8O_3, are needed to make 100. \ mL of 2.60 \ M solution?
  8. A test tube contains 10.0 \ mL of 3.00 \ M \ CaCO_3 solution. How many grams of calcium carbonate are in the tube?

Dilution Worksheet

CK-12 Foundation Chemistry

Name______________________ Date_________

The process of dilution involves increasing the amount of solvent in a solution without changing the amount of solute. For example, you could dilute 50. \ mL of 0.250 \ M HCl solution by placing the solution in a 100. \ mL graduated cylinder and adding water until the solution reached the 100. \ mL line in the graduate. The original solution contained 0.0125 \ moles of HCl before it was diluted and therefore, it also contains 0.0125 \ moles of HCl after the dilution. In the process of dilution, the amount of solute never changes. The amount of solvent, the total volume of the solution, and the concentration change but the amount of solute remains the same.

For a solution whose concentration is expressed in molarity, the moles of solute can be calculated by multiplying the volume in liters times the molarity.

moles \ solute = (molarity)(liters)

For the moles of solute in the original solution, moles_{initial} = molarity_{initial}  \times liters_{initial} or mols_i = M_i \times V_i. After the solution has been diluted, the moles in the final solution can be calculated with mols_f = M_f \times V_f. Since the mols do not change during dilution,

mols_i = mols_f \quad \text{and} \quad M_i \times V_i = M_f \times V_f.

In the dilution problems you will be given, for the most part, three of the four variables or ways to find three of the four variables and you will asked to calculate the fourth variable.

Example: How many milliliters of 6.00 \ M \ NaOH solution are necessary to prepare 300. \ mL of 1.20 \ M \ NaOH solution?

Solution:

(M_i)(V_i) &= (M_f)(V_f)\\V_i &= \frac {(M_f)(V_f)} {(M_i)} = \frac {(1.20 \ M)(0.300 \ L)} {(6.00 \ M)} =  0.0600 \ L = 60.0 \  mL

Exercises

  1. 200. \ mL of 3.00 \ M \ NaCl solution is diluted to a final volume of 500. \ mL. What is the concentration of the final solution?
  2. 100. \ mL of concentrated hydrochloric acid was diluted to 1.20 \ liters of 1.00 \ M solution. What was the concentration of the original concentrated solution?
  3. What volume of 6.00 \ M \ NaOH is needed to prepare 250. \ mL of 0.600 \ M \ NaOH?
  4. If 25.0 \ mL of 16.0 \ M \ HNO_3 is diluted to 500. \ mL, what is the final concentration?
  5. To what volume must you dilute 10.0 \ mL of 6.00 \ M \ H_2SO_4 to produce a solution that is 1.00 \ M \ H_2SO_4?
  6. Solution A is 5.00 \ mL of 12.0 \ M \ HCl. Solution B is prepared by diluting solution A to a new volume of 100. \ mL. Solution C is produced by taking 5.00 \ mL of solution B and diluting it to 100. \ mL. What is the molarity of solution C?

Colligative Properties: Solution Vapor Pressure Worksheet

Colligative properties are those properties of a solution that depend on the number of particles of solute present in the solution, and not on the chemistry nor the mass of the particles. That is, the chemical behavior and the molar masses of urea, (NH_2)_2CO, and glucose, C_6H_{12}O_6, are very different, but the colligative properties of a 1.0 \ M solution of urea will be exactly the same as the colligative properties of a 1.0 \ M solution of glucose.

The colligative properties of solutions include vapor pressure lowering, boiling point elevation, freezing point depression, and changes in osmotic pressure. The changes in these properties are dependent entirely on the concentration of particles of solute in the solution. It must be noted that ionic solutes dissociate when dissolved in water and therefore, add more particles to the solution than a substance that does not dissociate in water.

Vapor Pressure Lowering

The vapor pressure of a solution can be calculated from the individual vapor pressures of the components (solute and solvent) and the mole fractions of each component. Raoult's Law is an expression of the relationship.

& \text{Vapor Pressure}_{\text{solution}} = (X_{\text{mol fraction solvent}})(\text{Vapor Pressure}_{\text{solvent}})\\& \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad +\\& \qquad \qquad \qquad \qquad \qquad \ \ (X_{\text{mol fraction solute}})(\text{Vapor Pressure}_{\text{solute}})

Example: What is the vapor pressure, at 25^ \circ C, of a solution produced by dissolving 50.0 of acetone, C_3H_6O, in 50.0 \ grams of water? The vapor pressure of pure acetone at 25^ \circ C is 230. \ mm of Hg and the vapor pressure of pure water at 25^ \circ C is 23.7 \ mm of Hg.

Solution: 50.0 \ g of acetone is 0.86 \ moles and 50.0 \ g of water is 2.78 \ moles.

Therefore, the mole fractions in this solution are 0.236 acetone and 0.764 water.

 VP_{\text{SOLUTION}} & = (0.764)(23.7 \ mm \ of \ Hg) + (0.236)(230. \ mm \ of \ Hg)\\& = 18.1 \ mm \ of \ Hg + 54.3 \ mm \ of \ Hg \\& = 72.4 \ mm \ of \ Hg

In this case, the vapor pressure of the solution is higher than the vapor pressure of the solvent. That is due to the fact that acetone is a volatile (weak intermolecular forces of attraction) and therefore, evaporates readily. When we refer to vapor pressure lowering, we are referring to solutions in which the solute is non-volatile. When the solute is a solid, it can be generally be assumed that the solute is non-volatile.

Suppose we are making a solution of glucose in water. Glucose is a non-volatile, solid solute whose vapor pressure at room conditions is so small that it is negligible compared to the vapor pressure of water. When we substitute the values for a glucose solution into Raoult's Law, the second term (the one for the solute) is essentially zero because the vapor pressure of the pure solute is essentially zero.

& \text{Vapor Pressure}_{\text{Solution}} = (X_{\text{Mol fraction solvent}})(\text{Vapor Pressure}_{\text{Solvent}})\\& \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad +\\& \qquad \qquad \qquad \qquad \qquad \ \ (X_{\text{Mol fraction solute}})(\text{Vapor Pressure}_{\text{Solute}})

If the second term in this equation, (X_{\text{Mol fraction solute}})(\text{Vapor Pressure}_{\text{Solute}}), becomes zero, then for a solution with a non-volatile solute, Raoult's Law becomes:

\text{Vapor Pressure}_{\text{Solution}} = (X_\text{Mol fraction solvent})(\text{Vapor Pressure}_{\text{Solvent}})

This is Raoult's Law for solutions whose solute is a non-volatile.

\text{VP}_{\text{Solution}} = (X_{\text{Solvent}})(\text{VP}_{\text{Solvent}})

Example: What is the vapor pressure, at 25^oC, of a solution produced by dissolving 50.0 of glucose, 25^ \circ C, in 50.0 \ grams of water? Glucose is non-volatile and the vapor pressure of pure water at 25^ \circ C is 23.7 \ mm of Hg.

Solution: 50.0 \ g of water is 2.78 \ moles and 50.0 \ g of glucose is 0.278 \ moles.

Therefore, the mole fraction of water in this solution is 0.909. We do not need to calculate the mole fraction of glucose because it isn't needed in Raoult's Law for non-volatile solutes.

\text{VP}_{\text{Solution}} = (X_{\text{Solvent}})(\text{VP}_{\text{Solvent}} = (0.909)(23.7 \ mm \ of \ Hg) = 21.5 \ mm \ of \ Hg

In this case, and in all cases of non-volatile solutes, the vapor pressure of the solution is less than the vapor pressure of the pure solvent.

Exercises

  1. If 25.0 \ grams of sodium chloride is added to 500. \ grams of water at 25^ \circ C, what will be the vapor pressure of the resulting solution in kPa? The vapor pressure of pure water at 25^ \circ C is 3.17 \ kPa.
  2. 125 \ g of the non-volatile solute glucose, C_6H_{12}O_6, is dissolved in 125 \ g of water at 25^ \circ C. IF the vapor pressure of water at 25^ \circ C is 23.7 \ Torr, what is the vapor pressure of the solution?
  3. Glycerin, C_3H_8O_3, is a non-volatile, non-electrolyte solute. If 53.6 \ g of glycerin is dissolved in 133.7 \ g of ethanol at 40.^ \circ C, C_2H_5OH, what is the vapor pressure of the solution? The vapor pressure of pure ethanol is 113 \ Torr at 40.^ \circ C.
  4. The vapor pressure of hexane, C_6H_{14}, at 60.0^ \circ C is 573 \ Torr. The vapor pressure of benzene at the same temperature is 391 \ Torr. What will be the vapor pressure of a solution of 58.9 \ g of hexane with 44.0 \ g of benzene?

Colligative Properties: B.P. Elevation and M.P. Depression Worksheet

When a non-volatile, solid solute is added to a solvent, the boiling point of the solution will be higher than the boiling point of the solvent, and the melting point of the solution will be lower than the melting point of the solvent. The size of the boiling point elevation and the melting point depression are colligative properties, that is, they are dependent not on the chemistry of the solute but only on the number of solute particles present in the solution.

The formula used to calculate boiling point elevation is  \Delta T_b =  imK_b, where  \Delta T_b is the increase in the boiling point, m is the molality of the solute, K_b is the boiling point elevation constant, and i is the van't Hoff factor.

The boiling point elevation constant, K_b, is an experimentally determined constant for the solvent. Each solvent will have its own K_b and these values are determined in the laboratory and listed in reference tables. For example, the boiling point elevation constant for water is 0.512^ \circ C/m. As the molality of the solution increases, the boiling point of the solution increases by 0.512^ \circ C for each increase of 1.00 in the molality.

The van't Hoff factor is the ratio between the actual concentration of particles produced when the substance is dissolved, and the concentration of the molecules dissolved. For most non-electrolytes dissolved in water, the van't Hoff factor is essentially 1. For most ionic compounds dissolved in water, the van't Hoff factor is equal to the number of discrete ions in a formula unit of the substance. For example, a glucose solution that is 1.00 \ molal will have a particle concentration that is also 1.00 \ molal because glucose molecules do not dissociate. A 1.00 \ molal sodium chloride solution, on the other hand, since it dissociates into two ions will have a particle molality of 2.00 \ m. The van't Hoff factor, i, is the number of ions that the molecule will dissociate into when dissolved. Sometimes, in concentrated solutions, an ionic substance does not dissociate 100\% and therefore, the value of i will not be exactly equal to the apparent number of ions produced. In such cases, the value of i must also be determined experimentally. If you are not given an actual value for i in the problem, assume that i is the number of ions apparently produced per molecule. This is true in most dilute solutions.

The formula used to calculate melting point depression is  \Delta T_f  =  imK_f, where  \Delta T_f is the decrease in the melting point, m is the molality of the solute, K_f is the melting point depression constant, and i is the van't Hoff factor.

The melting point depression constant, K_f, is an experimentally determined constant for the solvent. Each solvent will have its own K_f and these values are determined in the laboratory and listed in reference tables. For example, the freezing point depression constant for water is 1.86^ \circ C/m. As the molality of the solution increases, the melting point of the solution decreases by 1.86^ \circ C for each increase of 1.00 in the molality.

Example: What is the boiling point of a 5.00 \ m glucose solution in water? Glucose is a non-volatile, non-electrolyte solute. K_b for water = 0.512^  \circ C/m.

Solution:  \Delta T_b = imK_b = (1)(5.00 \ m)(0.512^ \circ C/m) =  2.56^ \circ C

Since the boiling point of the pure solvent was 100.00^ \circ C, the b.p. of the solution is 100.00^ \circ C +  2.56^ \circ C  =  102.56^ \circ C

Example: What is the melting point of a 5.00 \ m \ NaCl solution in water? Sodium chloride is a non-volatile solute that dissociates 100\% in water. K_f for water = 1.86^ \circ C/m.

Solution:  \Delta T_f =  imK_f  = (2)(5.00 \  m)(1.86^ \circ C/m)  =  18.6^ \circ C (Since NaCl produces two ions in solution, i = 2.)

Since the melting point of the pure solvent was 0.00^ \circ C, the m.p. of the solution is 0.00^ \circ C -  18.6^ \circ C  =   - 18.6^ \circ C

Exercises

  1. What is the melting point of a solution produced by dissolving 45.0 \ g of NaCl in 500. \ g of water. K_f for water = 1.86^ \circ C/m.
  2. What is the boiling point of a solution produced by dissolving 45.0 \ g of NaCl in 500. \ g of water. K_b for water = 0.512^ \circ C/m.
  3. Which solution will have higher boiling point: a solution containing 105 \ g of C_{12}H_{22}O_{11} in 500. \ g of water or a solution containing 35.0 \ g of NaCl in 500. \ g of water?
  4. When 25.0 \ g of an unknown, non-volatile, non-electrolyte is dissolved in 130. \ g of water, the boiling point of the solution is 102.5^ \circ C. What is the molar mass of the unknown?
  5. How many grams of C_2H_6O_2 (anti-freeze, a non-electrolyte) must be added to 4,000. \ grams of water to reduce the melting point to -40.^ \circ C?
  6. The melting point constant for benzene is 4.90^ \circ C/m. The normal melting point of benzene is 5.50^ \circ C. What is the melting point of a solution of 9.30 \ g of C_{12}H_{25}OH (a non-electrolyte) in 250. \ g of benzene?
  7. Assuming 100\% dissociation, what is the boiling point of a solution of 200. \ g of AlF_3 in 500. \ g of water?

Reactions Between Ions in Solution Worksheet

CK-12 Foundation Chemistry

Name______________________ Date_________

For the following five reactions (all reactants are in water solution):

  • Write and balance the molecular equation indicating the state of each reactant and product.
  • Write the total ionic equation.
  • Identify the precipitate.
  • Identify the spectator ions.
  • Write the net ionic equation.

1. iron (III) chloride + sodium hydroxide

Balanced molecular equation _____________

Total ionic equation _____________

Precipitate = _____________ Spectator ions = _____________

Net ionic equation _____________

2. barium chloride + silver nitrate

Balanced molecular equation _____________

Total ionic equation _____________

Precipitate = _____________ Spectator ions = _____________

Net ionic equation _____________

3. magnesium sulfate + potassium phosphate

Balanced molecular equation _____________

Total ionic equation _____________

Precipitate = _____________ Spectator ions = _____________

Net ionic equation _____________

4. copper (II) nitrate + calcium hydroxide

Balanced molecular equation _____________

Total ionic equation _____________

Precipitate = _____________ Spectator ions = _____________

Net ionic equation _____________

5. sodium chromate + strontium nitrate

Balanced molecular equation _____________

Total ionic equation _____________

Precipitate = _____________ Spectator ions = _____________

Answers to Worksheets

  • The worksheet answer keys are available upon request. Please send an email to teachers-requests@ck12.org to request the worksheet answer keys.

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Aug 18, 2012

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CK.SCI.ENG.TE.2.Chemistry.17.11

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