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Step 1:I'll solve this step-by-step, carefully following the LaTeX formatting guidelines:
Step 2:: Identify the chemical formula
The chemical formula for alum is $$\mathrm{KAl(SO_{4})_{2} \cdot 12\mathrm{H}_{2}\mathrm{O}
Step 3:: Calculate the atomic masses of each element
- Hydrogen (H): $$m_{\mathrm{H}} = 1.01 \mathrm{~g/mol}
- Aluminum (Al): m_{\mathrm{Al}} = 26.98 \mathrm{~g/mol}
Step 4:: Calculate the mass of each component
- $$12\mathrm{H}_{2}\mathrm{O}$$: $$(12 \times 2 \times 1.01) + (12 \times 16.00) = 24.24 + 192.00 = 216.24 \mathrm{~g/mol}
- Al: 1 \times 26.98 = 26.98 \mathrm{~g/mol}
Step 5:: Sum all components
39.10 + 26.98 + 192.56 + 216.24 = 474.88 \mathrm{~g/mol}
Final Answer
The molar mass of alum (\mathrm{KAl(SO_{4})_{2} \cdot 12\mathrm{H}_{2}\mathrm{O}) is 474.88 \mathrm{~g/mol}.
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