Q114CP - Chemistry: Molecular Nature Of Matter And Change

Question

Brass, an alloy of copper and zinc, can be produced by simultaneously electroplating the two metals from a solution containing their $\mathbf{2}\mathbf{+}$ ions. If $\mathbf{65}\mathbf{.}\mathbf{0}\mathbf{\%}$ of the total current is used to plate copper, while $\mathbf{35}\mathbf{.}\mathbf{0}\mathbf{\%}$ goes to plating zinc, what is the mass percent of copper in the brass?

Step-by-Step Solution

Answer

The mass percent of copper in the brass is $64.35\%$ .

Step 1: Concept Introduction

Electroplating (also known as electrodeposition) is a method of reducing cations of a desired metal in solution and forming a metallic coating using an electrical signal supplied by an external power source.

Step 2: Information Provided

• $65\%$ of the total current is used to plate Cu
• $35\%$ of the total current is used to plate Zn
• Calculate the mass% of Cu .
• The reactions are – $$\begin{gathered} C{u}^{2+}\left(aq\right)+2e^{-}\leftrightharpoons Cu\left(s\right) \\ Z{n}^{2+}\left(aq\right)+2e^{-}\leftrightharpoons Zn\left(s\right) \end{gathered}$$

Step 3: Mass Percentage of Copper

The equation for charge is –

Charge = Moles $e^{-}.F$

Here we can see that number of moles of electrons is directly proportional to charge.

We can also see, that in order to produce 1 moles of Cu , or 1 mole of Zn, we need equal number of electrons (2 moles of electron each).

Therefore, if we have 1 mole of brass, 65% of the moles will be Cu, and 35% of the moles will be Zn.

The mass of Cu, in 1 mole of brass is (molar mass of Cu is 63.546 g/mol) –

$$\begin{gathered} m_{cu}=65\% mol.63.546 g/mol \\ = 41.30g \end{gathered}$$

The mass of Zn, in 1 mol of brass is (molar mass of Zn is 65.38 g/mol) –

$$\begin{gathered} m_{zn}=35\%mol.65.38 g/mol \\ =22.88 g \end{gathered}$$

Total mass of  of brass is –

 m=$$\begin{gathered} m_{cu}+m_{zn} \\ =41.30 g+22.88 g \\ =64.18 g \end{gathered}$$

Hence, the mass percent of $Cu$ in brass is –

$$\begin{gathered} mass \%=\frac{m_{cu}}{m}.100\% \\ =\frac{41.30 g}{64.18 g}.100\% \\ =64.35\% \end{gathered}$$

 

Therefore, the value of mass percentage is obtained as 64.35% .