Question

I am trying to solve the following elementary problem of volume percent, however, I am not quite sure where my mistake is:

Ethanol has a volume-by-volume concentration of 93.3%. Calculate the volume of water in 10 L
of this alcohol.

My Attempts:

By definition,

volume concentration=volume of solutevolume of solution×100%

From the exercise, we know that volume concentration=93.3%
and volume of solute=10 L
. By substituting those values in the equation above, we then have

93.3%=10 Lvolume of solution×100%

Working forward from the last equation and solving it for the volume of the solution, we find

volume of solution=10.71 L
. Therefore, the volume of water or the volume of solvent becomes

volume of solution=volume of solute+volume of solvent

10.71 L=10 L+volume of solvent

Therefore, volume of solvent=0.71 L
.

However, the actual answer to this problem is 667 g
. Based on the above, what is my mistake here?

Answer 1

The mistake lies in assuming the volume of solute is equal to the volume of solution. The actual volume of water in 10 L of ethanol is 0.67 L. The corresponding mass is 0.67 g.

Step-by-step explanation:

The mistake in your calculation lies in your assumption that the volume of the solute is equal to the volume of the solution. In this case, the solute is ethanol and the solvent is water. The volume-by-volume concentration of ethanol is given as 93.3%, which means that 93.3% of the total volume is ethanol. To calculate the volume of water, you subtract the volume of ethanol from the total volume of the solution. In this case, the volume of water would be 10 L - (10 L * 0.933) = 10 L - 9.33 L = 0.67 L.

However, the actual answer to this problem is given as 667 g, which is a mass rather than a volume. To convert the volume of water to mass, you need to consider the density of water. The density of water at room temperature is approximately 1 g/mL. Therefore, the mass of water would be 0.67 L * 1 g/mL = 0.67 g.

In conclusion, the volume of water in 10 L of ethanol with a volume-by-volume concentration of 93.3% is 0.67 L and the corresponding mass is 0.67 g.