# fraction problems with answers

**Problem #1:** A solution of H_{2}SO_{4} with a molal concentration of 8.010 m has a density of 1.354 g/mL. What is the molar concentration of this solution?

**Solution:** 8.010 m means 8.010 mol / 1 kg of solvent

8.010 mol times 98.0768 g/mol = 785.6 g of solute

785.6 g + 1000 g = 1785.6 g total for solute and solvent in the 8.010 m solution.

1785.6 g divided by 1.354 g/mL = 1318.76 mL

8.01 moles / 1.31876 L = 6.0739 M

6.074 M (to four sig figs)

**Problem #2:** A sulfuric acid solution containing 571.4 g of H_{2}SO_{4} per liter of solution has a density of 1.329 g/cm 3 . Calculate the molality of H_{2}SO_{4} in this solution

**Solution:** 1 L of solution = 1000 mL = 1000 cm 3

1.329 g/cm 3 times 1000 cm 3 = 1329 g (the mass of the entire solution)

1329 g minus 571.4 g = 757.6 g = 0.7576 kg (the mass of water in the solution)

571.4 g / 98.0768 g/mol = 5.826 mol of H_{2}SO_{4}

5.826 mol / 0.7576 kg = 7.690 m

**Problem #3:** An aqueous solution is prepared by diluting 3.30 mL acetone (d = 0.789 g/mL) with water to a final volume of 75.0 mL. The density of the solution is 0.993 g/mL. What is the molarity, molality and mole fraction of acetone in this solution?

1) Preliminary calculations: mass of acetone: (3.30 mL) (0.789 g/mL) = 2.6037 g

moles of acetone: 2.6037 g / 58.0794 g/mol = 0.04483 mol

2) Molarity: 0.04483 mol / 0.0750 L = 0.598 M

3) Molality: 0.04483 mol / 0.0718713 kg = 0.624 m

4) Mole fraction: 0.04483 mol / (0.04483 mol + 3.9896 mol) = 0.0111

**Problem #4:** Calculate the molality of 15.00 M HCl with a density of 1.0745 g/cm 3

1) Let us assume 1000. mL of solution are on hand. In that liter of 15-molar solution, there are: 15.00 mol/L times 1.000 L = 15.00 mole of HCl

15.00 mol times 36.4609 g/mol = 546.9135 g of HCl

2) Use the density to get mass of solution 1000. mL times 1.0745 g/cm 3 = 1074.5 g of solution

1074.5 g minus 546.9135 g = 527.5865 g of water = 0.5275865 kg

3) Calculate molality: 15.00 mol / 0.5275865 kg = 28.43 m (to four sig figs)

Note: the mole fractions of water and HCl can also be calculated with the above data. There are 29.286 moles of water and 15.00 moles of HCl. You may work out the mole fractions on your own.

**Problem #5:** You are given 450.0 g of a 0.7500 molal solution of acetone dissolved in water. How many grams of acetone are in this amount of solution?

**Solution:** 0.7500 molal means 0.7500 mole of solute (the acetone) per 1000 g of water

mass of acetone —> 58.0794 g/mol times 0.7500 mol = 43.56 g

mass of solution —> 1000 g + 43.56 g = 1043.56 g

43.56 is to 1043.56 as x is to 450

**Problem #6:** A 0.391 m solution of the solute hexane dissolved in the solvent benzene is available. Calculate the mass (g) of the solution that must be taken to obtain 247 g of hexane (C_{6}H_{14}).

**Solution:** 0.391 mol times 86.1766 g/mol = 33.6950 g

33.6950 g + 1000 g = 1033.6950 g

In other words, every 1033.6950 g of 0.391 m solution delivers 33.6950 g of hexane

33.6950 is to 1033.6950 as 247 is to x

to three sig figs, 7.58 kg of solution

**Problem #7:** Calculate the mass of the solute C_{6}H_{6} and the mass of the solvent tetrahydrofuran that should be added to prepare 1.63 kg of a solution that is 1.42 m.

**Solution:** 1.42 m means 1.42 mole of C_{6}H_{6} in 1 kg of tetrahydrofuran

1.42 mol times 78.1134 g/mol = 110.921 g

110.921 g + 1000 g = 1110.921 g

110.921 is to 1110.921 as x is to 1630

To check, do this:

162.75 g / 78.1134 g/mol = 2.08351 mol

1630 g – 162.75 g = 1467.25 g

2.08351 mol / 1.46725 kg = 1.42 m

**Problem #8:** What is the molality of NaCl in an aqueous solution in which the mole fraction of NaCl is 0.100?

**Solution:** A mole fraction of 0.100 for NaCl means the mole fraction of water is 0.900.

Let us assume a solution is present made up of 0.100 mole of NaCl and 0.900 mole of water.

mass of water present —> 0.900 mol times 18.015 g/mol = 16.2135 g

molality of solution —> 0.100 mol / 0.0162135 kg = 6.1677 m

to three sig figs, 6.17 m

**Problem #9:** Calculate the molality (m) of a 7.55 kg sample of a solution of the solute CH_{2}Cl_{2} (molar mass = 84.93 g/mol) dissolved in the solvent acetone (CH_{3}COH_{3}C) if the sample contains 929 g of methylene chloride

**Solution:** mass solvent —> 7550 g – 929 g = 6621 g = 6.621 kg

moles solute —> 929 g/ 84.93 g/mol = 10.9384 mol

molality = 10.9384 mol / 6.621 kg = 1.65 m

**Problem #10:** What is the molality of a 3.75 M H_{2}SO_{4} solution with a density of 1.230 g/mL?

1) Determine mass of 1.00 L of solution: 1000 mL x 1.230 g/mL = 1230 g

2) Determine mass of 3.75 mol of H_{2}SO_{4}: 3.75 mol x 98.0768 g/mol = 367.788 g

3) Determine mass of solvent: 1230 – 367.788 = 862.212 g

4) Determine molality: 3.75 mol / 0.862212 kg = 4.35 molal (to three sig figs)