A student adds 6.00 g of a solid to 30.0 ml of water. What is the concentration of this solution expressed as mass/volume percent?

(If necessary to the calculation, assume that 1.00 mL of water has a mass of 1.00gand that the total volume remains 30.0 ml.)

Mar 18, 2017

$\text{20.0% m/v}$

Explanation:

We use mass by volume percent concentration, $\text{m/v %}$, to show the number of grams of solute present for every $\text{100 mL}$ of solution.

In your case, the problem mentions that the volume of the solution is equal to the volume of water, which means that after you dissolve the solid, you will have $\text{30.0 mL}$ of solution that contains $\text{6.00 g}$ of solute.

As you know, solutions are homogeneous mixtures, which means that they have the same composition throughout.

This implies that you can use the known composition of the solution to scale up the sample to a total volume of $\text{100 m}$ of solution. In other words, you can use the known composition as a conversion factor.

100 color(red)(cancel(color(black)("mL solution"))) * "6.00 g solute"/(30.0color(red)(cancel(color(black)("mL solution")))) = "20.0 g solute"

So, you know that $\text{100 mL}$ of this solution would contain $\text{20.0 g}$ of solute, which means that the solution's mass by volume percent concentration is

color(darkgreen)(ul(color(black)("% m/v" = 20.0%)))

The answer is rounded to three sig figs.