Question

calculate the percent composition by mass of zinc in the fictional compound shown below. include the units, but do not write the chemical formula. round the answer to 3 significant figures. rb₇(zn₃si₄)₇ zinc =

Explanation:

Step1: Determine moles of each atom

First, we analyze the formula \( \text{Rb}_7(\text{Zn}_3\text{Si}_4)_7 \). For Rb: 7 atoms. For Zn: \( 3\times7 = 21 \) atoms. For Si: \( 4\times7 = 28 \) atoms.

Step2: Calculate molar mass of each element

• Molar mass of Rb (\( M_{\text{Rb}} \)): \( 85.47 \, \text{g/mol} \)
• Molar mass of Zn (\( M_{\text{Zn}} \)): \( 65.38 \, \text{g/mol} \)
• Molar mass of Si (\( M_{\text{Si}} \)): \( 28.09 \, \text{g/mol} \)

Step3: Calculate total mass of each element in the compound

• Mass of Rb: \( 7\times85.47 = 598.29 \, \text{g/mol} \)
• Mass of Zn: \( 21\times65.38 = 1372.98 \, \text{g/mol} \)
• Mass of Si: \( 28\times28.09 = 786.52 \, \text{g/mol} \)

Step4: Calculate molar mass of the compound

Total molar mass (\( M_{\text{total}} \)): \( 598.29 + 1372.98 + 786.52 = 2757.79 \, \text{g/mol} \)

Step5: Calculate percent composition of Zn

Percent composition of Zn (\( \% \text{Zn} \)): \( \frac{\text{Mass of Zn}}{\text{Total molar mass}} \times 100 = \frac{1372.98}{2757.79} \times 100 \)

Step6: Compute the value and round

\( \frac{1372.98}{2757.79} \times 100 \approx 49.78\% \), rounded to 3 significant figures is \( 49.8\% \)

Answer:

\( 49.8\% \)