PROBLEM \(\PageIndex{1}\)
Explain what changes and what stays the same when 1.00 L of a solution of NaCl is diluted to 1.80 L.
 Answer

The number of moles always stays the same in a dilution.
The concentration and the volumes change in a dilution.
PROBLEM \(\PageIndex{2}\)
What does it mean when we say that a 200mL sample and a 400mL sample of a solution of salt have the same molarity? In what ways are the two samples identical? In what ways are these two samples different?
 Answer

The two samples contain the same proportion of moles of salt to liters of solution, but have different numbers of actual moles.
PROBLEM \(\PageIndex{3}\)
Determine the molarity for each of the following solutions:
 0.444 mol of CoCl_{2} in 0.654 L of solution
 98.0 g of phosphoric acid, H_{3}PO_{4}, in 1.00 L of solution
 0.2074 g of calcium hydroxide, Ca(OH)_{2}, in 40.00 mL of solution
 10.5 kg of Na_{2}SO_{4}·10H_{2}O in 18.60 L of solution
 7.0 × 10^{−3} mol of I_{2} in 100.0 mL of solution
 1.8 × 10^{4} mg of HCl in 0.075 L of solution
 Answer a

0.679 M
 Answer b

1.00 M
 Answer c

0.06998 M
 Answer d

1.75 M
 Answer e

0.070 M
 Answer f

6.6 M
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PROBLEM \(\PageIndex{4}\)
Determine the molarity of each of the following solutions:
 1.457 mol KCl in 1.500 L of solution
 0.515 g of H_{2}SO_{4} in 1.00 L of solution
 20.54 g of Al(NO_{3})_{3} in 1575 mL of solution
 2.76 kg of CuSO_{4}·5H_{2}O in 1.45 L of solution
 0.005653 mol of Br_{2} in 10.00 mL of solution
 0.000889 g of glycine, C_{2}H_{5}NO_{2}, in 1.05 mL of solution
 Answer a

0.9713 M
 Answer b

5.25 × 10^{3} M
 Answer c

6.122 × 10^{2} M
 Answer d

7.62 M
 Answer e

0.5653 M
 Answer f

1.13 × 10^{2} M
PROBLEM \(\PageIndex{5}\)
Calculate the number of moles and the mass of the solute in each of the following solutions:
(a) 2.00 L of 18.5 M H_{2}SO_{4}, concentrated sulfuric acid
(b) 100.0 mL of 3.8 × 10^{−5} M NaCN, the minimum lethal concentration of sodium cyanide in blood serum
(c) 5.50 L of 13.3 M H_{2}CO, the formaldehyde used to “fix” tissue samples
(d) 325 mL of 1.8 × 10^{−6} M FeSO_{4}, the minimum concentration of iron sulfate detectable by taste in drinking water
 Answer a

37.0 mol H_{2}SO_{4}
3.63 × 10^{3} g H_{2}SO_{4}
 Answer b

3.8 × 10^{−6} mol NaCN
1.9 × 10^{−4} g NaCN
 Answer c

73.2 mol H_{2}CO
2.20 kg H_{2}CO
 Answer d

5.9 × 10^{−7} mol FeSO_{4}
8.9 × 10^{−5} g FeSO_{4}
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PROBLEM \(\PageIndex{6}\)
Calculate the molarity of each of the following solutions:
(a) 0.195 g of cholesterol, C_{27}H_{46}O, in 0.100 L of serum, the average concentration of cholesterol in human serum
(b) 4.25 g of NH_{3} in 0.500 L of solution, the concentration of NH_{3} in household ammonia
(c) 1.49 kg of isopropyl alcohol, C_{3}H_{7}OH, in 2.50 L of solution, the concentration of isopropyl alcohol in rubbing alcohol
(d) 0.029 g of I_{2} in 0.100 L of solution, the solubility of I_{2} in water at 20 °C
 Answer a

5.04 × 10^{−3} M
 Answer b

0.499 M
 Answer c

9.92 M
 Answer d

1.1 × 10^{−3} M
PROBLEM \(\PageIndex{7}\)
There is about 1.0 g of calcium, as Ca^{2+}, in 1.0 L of milk. What is the molarity of Ca^{2+} in milk?
 Answer

0.025 M
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PROBLEM \(\PageIndex{8}\)
What volume of a 1.00M Fe(NO_{3})_{3} solution can be diluted to prepare 1.00 L of a solution with a concentration of 0.250 M?
 Answer

0.250 L

PROBLEM \(\PageIndex{9}\)
If 0.1718 L of a 0.3556M C_{3}H_{7}OH solution is diluted to a concentration of 0.1222 M, what is the volume of the resulting solution?
 Answer

0.5000 L
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PROBLEM \(\PageIndex{10}\)
What volume of a 0.33M C_{12}H_{22}O_{11} solution can be diluted to prepare 25 mL of a solution with a concentration of 0.025 M?
 Answer

1.9 mL
PROBLEM \(\PageIndex{11}\)
What is the concentration of the NaCl solution that results when 0.150 L of a 0.556M solution is allowed to evaporate until the volume is reduced to 0.105 L?
 Answer

0.794 M
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PROBLEM \(\PageIndex{12}\)
What is the molarity of the diluted solution when each of the following solutions is diluted to the given final volume?
 1.00 L of a 0.250M solution of Fe(NO_{3})_{3} is diluted to a final volume of 2.00 L
 0.5000 L of a 0.1222M solution of C_{3}H_{7}OH is diluted to a final volume of 1.250 L
 2.35 L of a 0.350M solution of H_{3}PO_{4} is diluted to a final volume of 4.00 L
 22.50 mL of a 0.025M solution of C_{12}H_{22}O_{11} is diluted to 100.0 mL
 Answer a

0.125 M
 Answer b

0.04888 M
 Answer c

0.206 M
 Answer d

0.0056 M
PROBLEM \(\PageIndex{13}\)
What is the final concentration of the solution produced when 225.5 mL of a 0.09988M solution of Na_{2}CO_{3} is allowed to evaporate until the solution volume is reduced to 45.00 mL?
 Answer

0.5005 M
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PROBLEM \(\PageIndex{14}\)
A 2.00L bottle of a solution of concentrated HCl was purchased for the general chemistry laboratory. The solution contained 868.8 g of HCl. What is the molarity of the solution?
 Answer

11.9 M
PROBLEM \(\PageIndex{15}\)
An experiment in a general chemistry laboratory calls for a 2.00M solution of HCl. How many mL of 11.9 M HCl would be required to make 250 mL of 2.00 M HCl?
 Answer

42.0 mL
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PROBLEM \(\PageIndex{16}\)
What volume of a 0.20M K_{2}SO_{4} solution contains 57 g of K_{2}SO_{4}?
 Answer

1.6 L
PROBLEM \(\PageIndex{17}\)
The US Environmental Protection Agency (EPA) places limits on the quantities of toxic substances that may be discharged into the sewer system. Limits have been established for a variety of substances, including hexavalent chromium, which is limited to 0.50 mg/L. If an industry is discharging hexavalent chromium as potassium dichromate (K_{2}Cr_{2}O_{7}), what is the maximum permissible molarity of that substance?
 Answer

4.8 × 10^{−6} M
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