SOLUTION:
Step 1: Calculate the molar mass of Cu₁₂As₄S₁₃.
Note that the molar masses of Cu, As, and S are 63.546 g, 74.922 g, and 32.06 g, respectively.
[tex]\begin{aligned} \text{molar mass of} \: \text{Cu}_{12}\text{As}_4\text{S}_{13} & = \text{12(63.546 g) + 4(74.922 g) + 13(32.06 g)} \\ & = \text{1479.02 g} \end{aligned}[/tex]
Step 2: Solve for the percentage composition of Cu₁₂As₄S₁₃.
• For Cu
[tex]\begin{aligned} \%\text{Cu} & = \frac{n \times \text{molar mass of Cu}}{\text{molar mass of} \: \text{Cu}_{12}\text{As}_4\text{S}_{13}} \times 100\% \\ & = \frac{12 \times \text{63.546 g}}{\text{1479.02 g}} \times 100\% \\ & = \boxed{51.56\%} \end{aligned}[/tex]
• For As
[tex]\begin{aligned} \%\text{As} & = \frac{n \times \text{molar mass of As}}{\text{molar mass of} \: \text{Cu}_{12}\text{As}_4\text{S}_{13}} \times 100\% \\ & = \frac{4 \times \text{74.922 g}}{\text{1479.02 g}} \times 100\% \\ & = \boxed{20.26\%} \end{aligned}[/tex]
• For S
[tex]\begin{aligned} \%\text{S} & = \frac{n \times \text{molar mass of S}}{\text{molar mass of} \: \text{Cu}_{12}\text{As}_4\text{S}_{13}} \times 100\% \\ & = \frac{13 \times \text{32.06 g}}{\text{1479.02 g}} \times 100\% \\ & = \boxed{28.18\%} \end{aligned}[/tex]
Hence, Cu₁₂As₄S₁₃ is composed of 51.56% Cu, 20.26% As, and 28.18% S by mass.
---------------------------------------------------------
Note: The value of n in the formula of percent composition is the subscript of each element in the compound. If there is no subscript, it means that the value of n is 1.
[tex]\\[/tex]
#CarryOnLearning
