Chapter 2.9, Problem 33AAP

To determine

The atomic percentages of copper and nickel in the alloy.

Answer to Problem 33AAP

The atomic percentages of copper and nickel in the alloy are $28.4\%$ and $71.6\%$ respectively.

Explanation of Solution

Write the expression to calculate number of gram-moles of copper $\left(n_{\text{Cu}}\right)$.

 $n_{\text{Cu}}=\frac{m_{\text{Cu}}}{M_{\text{Cu}}}$                                                                                                              (I)

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

Write the expression to calculate number of gram-moles of nickel $\left(n_{\text{Ni}}\right)$.

 $n_{\text{Ni}}=\frac{m_{\text{Ni}}}{M_{\text{Ni}}}$                                                                                                            (II)

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

Write the expression to calculate total number of gram-moles of alloy $\left(n\right)$.

 $n=n_{\text{Cu}}+n_{\text{Ag}}$                                                                                                        (III)

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

 ${\text{at\%}}_{\text{Cu}}=\frac{n_{\text{Cu}}}{n}\times 100$                                                                                               (IV)

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

 ${\text{at\%}}_{\text{Ni}}=\frac{n_{\text{Ni}}}{n}\times 100$                                                                                                  (V)

Conclusion:

It is given that the Monel alloy has $\text{70wt\%}$ nickel and $\text{30wt\%}$ copper. Then, the masses of nickel and copper are $\text{70}\text{g}$ and $\text{30}\text{g}$ respectively.

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

Substitute $63.55\text{g}/\text{mol}$ for $M_{\text{Cu}}$ and $30\text{g}$ for $m_{\text{Cu}}$ in Equation (I).

 $\begin{array}{c}{n}_{\text{Cu}}=\frac{\text{30}\text{g}}{63.55\text{g}/\text{mol}}\\ =0.472\text{mol}\end{array}$

Substitute $58.69\text{g}/\text{mol}$ for $M_{\text{Ni}}$ and $70\text{g}$ for $m_{\text{Ni}}$ in Equation (II).

 $\begin{array}{c}{n}_{\text{Ni}}=\frac{\text{70}\text{g}}{58.69\text{g}/\text{mol}}\\ =1.192\text{mol}\end{array}$

Substitute $0.472\text{mol}$ for $n_{\text{Cu}}$ and $1.192\text{mol}$ for $n_{\text{Ni}}$ in Equation (III).

 $\begin{array}{c}n=0.472\text{mol}+1.192\text{mol}\\ =1.664\text{mol}\end{array}$

Substitute $0.472\text{mol}$ for $n_{\text{Cu}}$ and $1.664\text{mol}$ for $n$ in Equation (IV).

 $\begin{array}{c}{\text{at\%}}_{\text{Cu}}=\frac{0.472\text{mol}}{1.664\text{mol}}\times 100\\ =28.4\%\end{array}$

Substitute $1.192\text{mol}$ for $n_{\text{Ni}}$ and $1.664\text{mol}$ for $n$ in Equation (V).

 $\begin{array}{c}{\text{at\%}}_{\text{Ni}}=\frac{1.192\text{mol}}{1.664\text{mol}}\times 100\\ =71.6\%\end{array}$

Thus, the atomic percentages of nickel and copper in the alloy are $28.4\%$ and $71.6\%$ respectively.