Question

1. how many moles are in 3.90 × 10²⁸ molecules of methane (ch₄)?

Explanation:

Step1: Recall Avogadro's number

Avogadro's number is \( 6.022\times 10^{23} \) molecules per mole. The formula to find moles from number of molecules is \( n=\frac{N}{N_A} \), where \( n \) is moles, \( N \) is number of molecules, and \( N_A \) is Avogadro's number.

Step2: Substitute values into the formula

Given \( N = 3.90\times 10^{28} \) molecules and \( N_A=6.022\times 10^{23} \) molecules/mol. So \( n=\frac{3.90\times 10^{28}}{6.022\times 10^{23}} \).

Step3: Perform the calculation

First, divide the coefficients: \( \frac{3.90}{6.022}\approx0.6476 \). Then, for the exponents, use the rule \( \frac{10^a}{10^b}=10^{a - b} \), so \( 10^{28-23}=10^5 \). Multiply these results: \( 0.6476\times 10^5 = 6.476\times 10^4\approx6.48\times 10^4 \) moles (or 64800 moles when rounded appropriately).

Answer:

Approximately \( \boldsymbol{6.48\times 10^{4}} \) moles (or 64800 moles)