Question

A perchloric acid solution is 60.0%by mass. It is simultaneously 9.20Mat${25}^{0}C$.

(a) Compute the density of this solution.

(b) What volume of this solution should be used in mixing1.00Lof a 1.00Mperchloric acid solution?

Short answer

Step-by-step solution

Explain the density of a solution and the formulas used to determine the number of moles of solute and the molarity of a solution

Find the number of moles of perchloric acid 

Find the mass of perchloric acid

Calculate the mass of water and the total mass of solution

Determine the density of the perchloric acid solution

Substitute the values of mass and volume of the solution in the above density formula:

$\begin{array}{l}D\left(Solution\right)=\frac{1540\mathrm{g}}{1000\mathrm{mL}}\\ D\left(Solution\right)=1.54{\mathrm{gmL}}^{-1}\end{array}$

Thus, the density of perchloric acid solution at ${25}^{0}C$$1.54{\mathrm{gmL}}^{-1}$

Calculate the number of moles of the solution

(b)

Substitute the values of molarity and volume of solution in the above molarity formula:

$1.00 \mathrm{mol}{\mathrm{L}}^{-1}=\frac{\mathrm{Molessolution}}{1.00\mathrm{L}}$

Rearrange this equation to find the number of moles of the solution as follows:

$\begin{array}{l}\mathrm{n}(\mathrm{solution})=1.00\mathrm{mol}{\mathrm{L}}^{-1}\times 1.00\mathrm{L}\\ \mathrm{n}(\mathrm{solution})=1.00\mathrm{mol}\end{array}$

Calculate the mass of the solution

Substitute the values of number of moles of solution and its molar mass as follows:

$\begin{array}{l}n(\mathrm{solution})=\frac{\mathrm{m}(\mathrm{solution})}{\mathrm{Molarmass}}\\ \mathrm{m}(\mathrm{solution})=1.00\mathrm{mol}\times 100.46{\mathrm{gmol}}^{-1}\\ \mathrm{m}(\mathrm{solution})=100.46\mathrm{g}\end{array}$

Determine the volume of the solution

Substitute the values of mass and density of the solution in the above formula as:

$\begin{array}{l}\mathrm{V}=\frac{Massofsolution}{Densityofsolution}\\ \mathrm{V}=\frac{100.46\mathrm{g}}{0.924\mathrm{gm}/\mathrm{L}}\\ \mathrm{V}=109\mathrm{mL}\end{array}$

Thus, the volume of this solution used in mixing 1.00L of a 1.00M perchloric acid solution is 109mL.