Question

Because zinc has nearly the same atomic radius as copper $(d=8.95g/c{m}^3)$zinc atom substitute for some copper atoms in many types of brass. Calculate the density of the brass with

1. 10.0 atom % Zn and
2. 38.0 atom % Zn.

Short answer

1. Density of the brass with 10% Zn is 8.96g/cm³
2. Density of brass with 38% Zn is 9.102g/cm³

Step-by-step solution

Density of the brass with 10% atom Zn

Given the density of copper atom is $d=8.95g/c{m}^3$. consider that in brass with 10%

Z_nhas 0.1mol of Z_nand 0.9mol of C_u.

Molecular mass of zinc =65.38g.

Molecular mass of copper = 63.54g.

Density of brass can be calculated as

$$\begin{gathered} d_{brass}=d_{cu}\left(\frac{W_{cu}\times M_{cu}+W_{Zn}\times M_{Zn}}{M_{cu}}\right) \\ =8.95g/c{m}^3\left(\frac{0.9mol\times 63.54g/mol+o.1mol\times 65.38g/mol}{63.54g}\right) \\ =8.96g/c{m}^3 \end{gathered}$$

Density of brass with 38% zinc

Consider that brass with 38% zinc has 0.38mol of Zn atom and 0.62mol of Cu atom.

Density of brass can be calculated as$$\begin{gathered} d_{brass}=d_{cu}\left(\frac{W_{cu}\times M_{cu}+W_{Zn}\times M_{Zn}}{M_{cu}}\right) \\ =8.95g/c{m}^3\left(\frac{0.38mol\times 63.54g/mol+0.62mol\times 65.38g/mol}{63.54g}\right) \\ =9.102g/c{m}^3 \end{gathered}$$