Question

determine the number of molecules in 38.7 grams of ch₄.

Explanation:

Step1: Calculate molar mass of \( \text{CH}_4 \)

Molar mass of \( \text{C} = 12.01 \, \text{g/mol} \), molar mass of \( \text{H} = 1.008 \, \text{g/mol} \). For \( \text{CH}_4 \), molar mass \( M = 12.01 + 4\times1.008 = 16.042 \, \text{g/mol} \).

Step2: Find moles of \( \text{CH}_4 \)

Moles \( n = \frac{\text{mass}}{\text{molar mass}} = \frac{38.7 \, \text{g}}{16.042 \, \text{g/mol}} \approx 2.412 \, \text{mol} \).

Step3: Calculate number of molecules

Using Avogadro's number \( N_A = 6.022\times10^{23} \, \text{molecules/mol} \), number of molecules \( N = n\times N_A = 2.412 \, \text{mol} \times 6.022\times10^{23} \, \text{molecules/mol} \approx 1.452\times10^{24} \).

Answer:

\( \approx 1.45\times10^{24} \) molecules (or more precisely \( \approx 1.452\times10^{24} \) molecules)