# Given the concentration and density of a sample, calculate moles of bleach?

Given the concentration of bleach ($6\%\,\mathrm{m/m}$), density of bleach ($1.07\,\mathrm{g\,mL^{-1}}$), and molar mass of bleach ($74.44\,\mathrm{g\,mol^{-1}}$) how many moles of bleach are in a $4.0\,\mathrm{mL}$ sample? I don't understand where the concentration factors in, but the problem says to use it.

The key issue to address this kind of problems is to determine the mass of the pure compound in the given volume of the solution. So, we'll use first the density to determine the mass of the solution. Then, the mass concentration to determine the mass of the pure compound. After that, we can readily compute the number of moles of the pure compound using the molar mass.

The mass of $1\,\mathrm{mL}$ of bleach solution is $1.07\,\mathrm{g}$. So, the mass of $4~\mathrm{mL}$ of bleach solution is $4 \cdot 1.07\,\mathrm{g}$

Or, each $100\,\mathrm{g}$ of bleach solution has $6\,\mathrm{g}$ of pure bleach. So, the mass of $4 \times 1.07\mathrm{g}$ of bleach solution has $\frac{4\cdot 6 \cdot 1.07}{100}\,\mathrm{g}$ of pure bleach.

The number of moles in $4\mathrm{mL}$ of bleach solution is: $$\frac{4\cdot 6 \cdot 1.07}{100\cdot 74.44}= 0.0034\,\mathrm{mol}$$

Dimensional analysis is a straightforward, easy, and beautiful way to solve this problem! Simply cancel the units!

$$4\,\mathrm{mL\,(solution)} \cdot \frac{1.07\,\mathrm{g\,(solution)}}{\mathrm{mL\,(solution)}} \cdot \frac{6\,\mathrm{g}\,\ce{NaClO}}{100\,\mathrm{g\,(solution)}} \cdot \frac{1\,\mathrm{mol}\,\ce{NaClO}}{74.44\,\mathrm{g}\,\ce{NaClO}}$$

$$=0.00345\,\mathrm{mol}\,\ce{NaClO}$$