You have 120.0 mL of a 0.245 M solution of NaCl sitting in a beaker. After several days you test the solution and find that it has a concentration of 0.348 M. How much water must have evaporated? (Assume volumes are additive.)

Question

Quizplus · Accepted Answer

Use the formula:

M1V1 = M2V2

where M1 is the initial concentration, V1 is the initial volume, M2 is the final concentration, and V2 is the final volume.

Plugging in the given values:

(0.245 M)(120.0 mL) = (0.348 M)(V2)

Solving for V2:

V2 = (0.245 M)(120.0 mL) / (0.348 M) = 85.5 mL

The volume that evaporated is the initial volume minus the final volume:

120.0 mL - 85.5 mL = 34.5 mL

However, we need to consider that the volumes are additive. This means that the final volume is the sum of the remaining solution and the volume that didn't evaporate. For example, if 10 mL evaporated, the final volume would be:

Vfinal = Vremaining + 120.0 mL - 10 mL = Vremaining + 110 mL

We can use this to calculate the volume that evaporated:

Vremaining + 110 mL = 85.5 mL

Vremaining = 85.5 mL - 110 mL = -24.5 mL

This doesn't make sense since the remaining volume can't be negative. Therefore, we need to assume that the initial volume was measured incorrectly and should have been 155.5 mL.

Using this initial volume:

(0.245 M)(155.5 mL) = (0.348 M)(V2)

V2 = (0.245 M)(155.5 mL) / (0.348 M) = 173.5 mL

Volume evaporated = 155.5 mL - 173.5 mL = -18.0 mL

Again, this doesn't make sense since the volume evaporated can't be negative. Therefore, we need to assume that the final concentration was measured incorrectly and should have been 0.245 M.

Using this final concentration:

(0.245 M)(120.0 mL) = (0.245 M)(V2)

V2 = (0.245 M)(120.0 mL) / (0.245 M) = 120.0 mL

Volume evaporated = 120.0 mL - 120.0 mL = 0 mL

This makes sense since if the final concentration is equal to the initial concentration, then no water has evaporated. Therefore, the answer is (B) 35.5 mL.

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