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The number of molecules of ethane (molar mass = 30) present in 3 g of pure ethane is

  • A.\(6.023 \times 10^{23}\) molecules
  • B.\(6.023 \times 10^{22}\) molecules
  • C.\(6.023 \times 10^{21}\) molecules
  • D.\(6.023 \times 10^{20}\) molecules
  • E.\(6.023 \times 10^{19}\) molecules

Answer: B

3 g of ethane contains \(6.023 \times 10^{22}\) molecules.

Find the number of moles, then multiply by Avogadro's number.

\[ \begin{aligned} n &= \frac{3}{30} = 0.1 \text{ mol} \\ N &= 0.1 \times 6.023 \times 10^{23} \\ &= 6.023 \times 10^{22} \end{aligned} \]

\(6.023 \times 10^{23}\) would be one whole mole, 30 g. Each of the smaller options is a further factor of ten too small, the result of slipping a decimal place in the mole count.

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