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Answer Key for Problem Set Dealing with Concentration Units

1 a. The formula for sodium sulfate is Na2SO4. w/w% Na2SO4 = grams Na2SO4grams solution x 100

The mass of solute is 15.0 g Na2SO4. The mass of solvent (water) is 400.0 g, so the mass of solution is:

15.0 g Na2SO4 + 400.0 g H2O = 415.0 g solution w/w% Na2SO4 = 15. 0 g Na2SO4 415.0 g solution x 100 = 3.61% Na2SO4

1 b. The molar mass of Na2SO4. must be calculated to find the moles of Na2SO4.

Molar mass of Na2SO4. = 2 AW of Na + AW of S + 4 AW of O (where AW = atomic weight)

= 2(22.99 g/mol) + 32.07 g/mol + 4(16.00 g/mol) = 142.05 g Na2SO4./mol Na2SO4.

Find the moles of Na2SO4.: 15.0 g Na2SO4 x 1 mole Na2SO4142.05 g Na2SO4 = 0.106 mol Na2SO4 Find the volume of solution in liters. Recall from part a, the mass of solution is 415.0g.

415.0 g solution x 1 mL solution1.056 g solution x 1 L solution1000 mL solution = 0.3930 L solution

Calculate the molarity:

Molarity of Na2SO4 = 0.106 mol Na2SO40.3930 L solution = 0.270 M Na2SO4 1 c. The moles of Na2SO4 is already known from part b. Find the kilograms of solvent (water):

400.0 g H2O x 1 kg H2O1000 g H2O = 0.4000 kg H2O

Calculate the molality of Na2SO4 : molality of Na2SO4 = 0.106 mol Na2SO40.4000 kg water = 0.265 m Na2SO4

1 d. Calculate the parts per thousand of Na2SO4 from the mass of solute and mass of solution:

ppt Na2SO4 = 15.0 g Na2SO4415 g solution x 1000 = 36.1 ppt Na2SO4 1 e. Parts per million may also be expressed as mg solute/L solution. In this case, converting the molarity to ppm will be the simplest route:

0.270 mol Na2SO4L solution x 2 mol Na+1 mol Na2SO4 x 22.99 g Na+1 mol Na+ x 1000 mg Na+1 g Na+ = 1.24 x 104 ppm Na+

1 e. For the mole fraction of sulfate, we need to have: mole fraction SO42- = mol SO42-mol SO42- + mol Na+ + mol H2O

Find the moles of Na+ :
0.106mol Na2SO4 x 2 mol Na+1 mol Na2SO4 = 0.212 mol Na+

Find the moles of SO42- :
0.106 mol Na2SO4 x 1 mol SO42-1 mol Na2SO4 = 0.106 mol SO42- Find the moles of H2O: 400.0 g H2O x 1 mol H2O18.02 g H2O = 22.20 mol H2O

Calculate the mole fraction of sulfate: X of SO42- = 0.106 mol SO42-0.212 mol Na+ + 0.106 mol SO42- + 22.20 mol H2O = 0.00471

2 a. Assume exactly 1 liter (1000 mL) of solution, which is the quantity present in the denominator of the known concentration unit (molarity). This also means you have 12.0 mol HCl present. Convert the moles of HCl to a mass of HCl:
12.0 mol HCl x 36.46 g HCl1 mol HCl = 437.5 g HCl

Find the mass of solution using the density of the solution: 1000 mL solution x 1.107 g solution1 mL solution = 1107 g solution Calculate the mass percent of HCl: 437.5 g HCl1107 g solution x 100 = 39.5 %HCl
2 b. Find the mass of solvent:

1107 g solution – 437.5 g HCl = 670 g H2O

Convert the mass of solvent to kilograms:

670g H2O x 1 kg H2O1000 g H2O = 0.670 kg H2O Calculate the molality: 12.0 mol HCl0.670 kg H2O = 17.9 m HCl
2 c. Find the moles of H2O:

670 g H2O x 1 mol H2O18.02 g H2O = 37.2 mol H2O

Calculate the mole fraction of HCl: X of HCl = 12.0 mol HCl12.0 mol HCl + 37.2 mol H2O = 0.244

3 a. Assume exactly 1 kg (1000 g) of water (solvent), which is the quantity present in the denominator of the known concentration unit (molality). This also means you have 0.300 mol Ca(NO3)2.

To find the mass of calcium nitrate, you need the molar mass of Ca(NO3)2:

Molar mass of Ca(NO3)2 = AW of Ca + 2 AW of N + 6 AW of O (where AW = atomic weight)

= 40.08 g/mol + 2(14.01 g/mol) + 6(16.00 g/mol) = 164.10 g Ca(NO3)2/mol Ca(NO3)2

Calculate the mass of Ca(NO3)2 : 0.300 mol Ca(NO3)2 x 164.10 g Ca(NO3)21 mol Ca(NO3)2 = 49.2 g Ca(NO3)2

Find the mass of solution:

mass of solution = 49.2 g Ca(NO3)2 + 1000.0 g H2O = 1049.2 g solution

Calculate the mass percent of Ca(NO3)2 : 49.2 g Ca(NO3)21049.2 g solution x 100 = 4.69 %Ca(NO3)2

3 b. To find the mass of nitrate ion, you need the molar mass of nitrate ion (NO3¯ ):

Molar mass of NO3¯ = AW of N + 3 AW of O (where AW = atomic weight)

= 14.01 g/mol + 3(16.00 g/mol) = 62.01 g NO3¯/mol NO3¯ Calculate the mass of nitrate ion: 0.300 mol Ca(NO3)2 x 2 mol NO3-1 mol Ca(NO3)2 x 62.01 g NO3-1 mol NO3- = 37.2 g NO3-

Calculate the mass percent of nitrate ion: 37.2 g NO3-1049.2 g Ca(NO3)2 x 100 = 3.55 %NO3-

3 c. Find the mass of calcium ion: 0.300 mol Ca(NO3)2 x 1 mol Ca2+1 mol Ca(NO3)2 x 40.08 g Ca2+1 mol Ca2+ = 12.0 g Ca2+ Calculate the mass percent of calcium ion: 12. 0 g Ca2+1049.2 g Ca(NO3)2 x 100 = 1.14 %Ca2+

Notice how the sum of %Ca2+ and %NO3¯ sum to the %Ca(NO3)2.

3 d. Convert the mass of solution to volume of solution in liters: 1049.2 g solution x 1 mL solution1.009 g solution x 1 L solution1000 mL solution = 1.040 L solution Calculate the molarity: 0.300 mol Ca(NO3)21.040 L solution = 0.288 M Ca(NO3)2

3 e. Calculate the molarity of nitrate ions: 0.288 mol Ca(NO3)21 L solution x 2 mol NO3-1 mol Ca(NO3)2 = 0.576 M NO3-

3 f. Find the moles of calcium ion:
0.300 mol Ca(NO3)2 x 1 mol Ca2+1 mol Ca(NO3)2 = 0.300 mol Ca2+

Find the moles of nitrate ion: 0.300 mol Ca(NO3)2 x 2 mol NO3-1 mol Ca(NO3)2 = 0.600 mol NO3- Find the moles of water: 1000 g H2O x 1 mol H2O18.02 g H2O = 55.49 mol H2O Calculate the mole fraction of calcium ion: 0.300 mol Ca2+0.300 mol Ca2+ + 0.600 mol NO3- + 55.49 mol H2O = 0.00532

3 g. Calculate the mole fraction of nitrate ion: 0.600 mol NO3-0.300 mol Ca2+ + 0.600 mol NO3- + 55.49 mol H2O = 0.0106

4. Recall that parts per million may also be expressed as mg solute/liter of solution or mg solute per kilograms solution. Either case will work here because the density of the solution is given as 1.00 g/mL. Assume exactly 1 liter of solution (1000 g solution) so that the mass of solute (25.0 mg of magnesium ion) is known.

4 a. Convert milligrams of magnesium ion to grams magnesium ion: 25.0 mg Mg2+ x 1 x 10-3g Mg2+1 mg Mg2+ = 0.0250 g Mg2+

Calculate the w/w% magnesium ion: 0.0250 g Mg2+1000 g solution x 100 = 0.00250 %Mg2+

4 b. Find the number of grams of chloride ion keeping in mind the chemical formula of magnesium chloride is MgCl2: 0.0250 g Mg2+ x 1 mol Mg2+24.30 g Mg2+ x 2 mol Cl-1 mol Mg2+ x 35.45 g Cl-1 mol Cl- = 0.0729 g Cl- Calculate the w/w% of Cl¯: 0.0729 g Cl-1000 g solution x 100 = 0.00729 %Cl-

4 c. Find the number of grams of magnesium chloride:

0.0250 g Mg2+ x 1 mol Mg2+24.30 g Mg2+ x1 mol MgCl21 mol Mg2+ x 95.20 g MgCl21 mol MgCl2 = 0.0979 g MgCl2

Calculate the w/w % MgCl2: 0.0929 g MgCl21000 g solution x 100 = 0.00929 %MgCl2

4 d. Find the moles of magnesium chloride:

0.0979 g MgCl2 x 1 mol MgCl295.20 g MgCl2 = 0.00103 mol MgCl2

Calculate the molarity of MgCl2: 0.00103 mol MgCl21 L solution = 0.00103 M MgCl2

4 e. Calculate the molarity of magnesium ions: 0.00103 mol MgCl21 L solution x 1 mol Mg2+1 mol MgCl2 = 0.00103 M Mg2+

4 f. Calculate the molarity of chloride ions: 0.00103mol MgCl21 L solution x 2mol Cl-1 mol MgCl2 = 0.00206 mol Cl-

4 g. Find the mass of water:

1000 g solution – 0.0979 g MgCl2 = 999.9021 g H2O

Convert this mass to kilograms:

999.9021 g H2O x 1 kg H2O1000 g H2O = 0.9999021 kg H2O

Calculate the molality of MgCl2: 0.00103 mol MgCl20.9999021 kg H2O = 0.00103 m MgCl2…...

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