Chapter 2.9, Problem 30AAP

Each quarter produced by the U.S. mint is made up of a copper and nickel alloy. In each coin, there is 0.00740 mole of Ni and 0.0886 mole of copper. (a) What is the total mass of a quarter? (b) What percentage of the mass of a quarter is nickel and what percentage is copper?

To determine

The total mass of the quarter.

Answer to Problem 30AAP

The total mass of the quarter is $\text{6}\text{.06}\text{g}$.

Explanation of Solution

Write the expression to calculate mass of nickel $\left(m_{\text{Ni}}\right)$.

 $m_{\text{Ni}}=n_{\text{Ni}}\times M_{\text{Ni}}$                                                                                                      (I)

Here, number of moles of nickel is $n_{\text{Ni}}$ and molar mass of nickel is $M_{\text{Ni}}$.

Write the expression to calculate mass of copper $\left(m_{\text{Cu}}\right)$.

 $m_{\text{Cu}}=n_{\text{Cu}}\times M_{\text{Cu}}$                                                                                                    (II)

Here, number of moles of copper is $n_{\text{Cu}}$ and molar mass of copper is $M_{\text{Cu}}$.

Write the expression to calculate total mass of the quarter $\left(m\right)$.

 $m=m_{\text{Ni}}+m_{\text{Cu}}$                                                                                                      (III)

Conclusion:

The molar masses of copper and nickel are $63.55\text{g}/\text{mol}$ and $58.69\text{g}/\text{mol}$ respectively.

Substitute $0.00740\text{moles}$ for $n_{\text{Ni}}$ and $58.69\text{g}/\text{mol}$ for $M_{\text{Ni}}$ in Equation (I).

 $\begin{array}{c}{m}_{\text{Ni}}=0.00740\text{moles}\times 58.69\text{g}/\text{mol}\\ =0.434\text{g}\end{array}$

Substitute $0.0886\text{moles}$ for $n_{\text{Cu}}$ and $63.55\text{g}/\text{mol}$ for $M_{\text{Cu}}$ in Equation (II).

 $\begin{array}{c}{m}_{\text{Cu}}=0.0886\text{moles}\times 63.55\text{g}/\text{mol}\\ =5.63\text{g}\end{array}$

Substitute $0.434\text{g}$ for $m_{\text{Ni}}$ and $5.63\text{g}$ for $m_{\text{Cu}}$ in Equation (III).

 $\begin{array}{c}m=0.434\text{g}+5.63\text{g}\\ =6.06\text{g}\end{array}$

Thus, the total mass of the quarter is $\text{6}\text{.06}\text{g}$.

To determine

The percentages of mass of nickel and mass of copper in the quarter.

Answer to Problem 30AAP

The percentages of mass of nickel and mass of copper in the quarter are $\text{7}\text{.16\%}$ and $\text{92}\text{.9\%}$ respectively.

Explanation of Solution

Write the expression to calculate percentage of mass of nickel $\left(\%\text{Ni}\right)$.

 $\%\text{Ni}=\frac{m_{\text{Ni}}}{m}\times 100$                                                                                                 (IV)

Write the expression to calculate percentage of mass of copper $\left(\%\text{Cu}\right)$.

 $\%\text{Cu}=\frac{m_{\text{Cu}}}{m}\times 100$                                                                                                 (V)

Conclusion:

Substitute $0.434\text{g}$ for $m_{\text{Ni}}$ and $6.06\text{g}$ for $m$ in Equation (IV).

 $\begin{array}{c}\%\text{Ni}=\frac{0.434\text{g}}{6.06\text{g}}\times 100\\ =7.19\%\end{array}$

Substitute $5.63\text{g}$ for $m_{\text{Cu}}$ and $6.06\text{g}$ for $m$ in Equation (V).

 $\begin{array}{c}\%\text{Cu}=\frac{5.63\text{g}}{6.06\text{g}}\times 100\\ =92.9\%\end{array}$

Thus, the percentages of mass of nickel and mass of copper in the quarter are $\text{7}\text{.16\%}$ and $\text{92}\text{.9\%}$ respectively.