Find the formula mass of anhydrous CuSO₄. How many grams should be dissolved in 250.0 mL to make a 16.0 mM solution?

One of the metrics used to express the concentration of a solution is molarity.

Molarity$\mathbf{=}\mathbf{}\frac{\mathbf{number}\mathbf{}\mathbf{of}\mathbf{}\mathbf{moles}\mathbf{}\mathbf{of}\mathbf{}\mathbf{solute}}{\mathbf{}\mathbf{volume}\mathbf{}\mathbf{of}\mathbf{}\mathbf{solution}\mathbf{}\mathbf{in}\mathbf{}\mathbf{L}}$

The sum of the atomic masses of the elements in a compound's empirical formula is equal to the compound's formula mass.

The amount of anhydrous $CuS{O}_4$ to be dissolved in 250mL of 16.0mM solution has to be calculated.

Calculation of the formula mass of anhydrous ${\mathrm{CuSO}}_4$:

• Atomic mass of $\mathrm{Cu}=63.546\mathrm{amu}$.
• Atomic mass of $S=32.065\mathrm{amu}$.
• Atomic mass of $O=15.999\mathrm{amu}$.

Atomic mass of CU+ atomic mass of S+4 (atomic mass of O )

$$\begin{gathered} =63.546\mathrm{amu}+32.065\mathrm{amu}+4(15.999\mathrm{amu}) \\ =159.60\mathrm{amu} \\ =159.60\mathrm{g}/\mathrm{mol} \end{gathered}$$.

The formula mass of anhydrous copper sulfate $\left(CuS{O}_4\right)$is calculated by adding the atomic masses of copper, sulfur, and four oxygen atoms.

The formula mass of anhydrous copper sulfate $\left(CuS{O}_4\right)$is $159.60\mathrm{g}/\mathrm{moL}$.

The volume of the solution is $250.0\mathrm{mL}=\left(0.250\mathrm{L}\right)$.

Finding the amount of $\left(CuS{O}_4\right)$(in grams) to be dissolved to make 250.0mL of $16.0\mathrm{mM}{\mathrm{CuSO}}_4$solution:

$$\begin{gathered} \mathrm{Molarity}=\frac{\mathrm{number}\mathrm{of}\mathrm{moles}\mathrm{of}{\mathrm{CuSO}}_4}{0.250\mathrm{L}} \\ 16.0\mathrm{mM}=\frac{\mathrm{x}}{0.250\mathrm{L}} \\ \mathrm{x}=0.250\mathrm{L}\times 16.0\mathrm{mM} \\ \mathrm{x}=4\mathrm{mmol} \end{gathered}$$

Number of moles of$CuS{O}_4=\frac{mass}{molarmass}$.

$4\mathrm{mmol}=\frac{\mathrm{mass}}{159.60\mathrm{g}/\mathrm{mol}}$.

Mass of$$\begin{gathered} {\mathrm{CuSO}}_4=4\mathrm{mmol}\times 159.60\mathrm{g}/\mathrm{mol} \\ =4\times {10}^{-3}\mathrm{mol}\times 159.60\mathrm{g}/\mathrm{mol} \\ =0.638\mathrm{g} \end{gathered}$$

.

Thus, $0.638\mathrm{g}$is $CuS{O}_4$dissolved in 250mL of water to make 16.0Mm $CuS{O}_4$solution.