1. **Problem statement:** Calculate the mass of one molecule of methane and the number of molecules in 1 gram of methane. 2. **Given data:** - Mass of hydrogen atom = $1.67 \times 10^{-24}$ grams - Mass of carbon atom = $1.99 \times 10^{-23}$ grams - Methane molecule contains 4 hydrogen atoms and 1 carbon atom 3. **Formula for mass of methane molecule:** $$\text{Mass of methane} = 4 \times \text{mass of H} + 1 \times \text{mass of C}$$ 4. **Calculate mass of methane molecule:** $$4 \times 1.67 \times 10^{-24} + 1.99 \times 10^{-23} = 6.68 \times 10^{-24} + 1.99 \times 10^{-23}$$ 5. **Add the terms (express both with same power of 10):** $$6.68 \times 10^{-24} = 0.668 \times 10^{-23}$$ $$0.668 \times 10^{-23} + 1.99 \times 10^{-23} = (0.668 + 1.99) \times 10^{-23} = 2.658 \times 10^{-23}$$ 6. **Answer for (a):** Mass of one methane molecule = $2.658 \times 10^{-23}$ grams 7. **For (b), calculate number of molecules in 1 gram:** Number of molecules = $\frac{\text{mass given}}{\text{mass of one molecule}} = \frac{1}{2.658 \times 10^{-23}}$ 8. **Calculate:** $$\frac{1}{2.658 \times 10^{-23}} = \frac{1}{2.658} \times 10^{23} \approx 0.376 \times 10^{23} = 3.76 \times 10^{22}$$ 9. **Answer for (b):** Number of molecules in 1 gram of methane = $3.76 \times 10^{22}$ molecules (3 significant figures)