QuestionMay 9, 2025

8. How many molecules are there in a 42.3 g sample of water, H_(2)O

8. How many molecules are there in a 42.3 g sample of water, H_(2)O
8. How many molecules are there in a 42.3 g sample of water, H_(2)O

Solution
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Answer

1.413 \times 10^{24} \, \text{molecules} Explanation 1. Calculate moles of water Use n = \frac{m}{M}, where m is mass and M is molar mass. For water, M = 18.015 \, \text{g/mol}. n = \frac{42.3}{18.015} = 2.348 \, \text{mol}. 2. Calculate number of molecules Use N = n \cdot N_A, where N_A = 6.022 \times 10^{23} \, \text{mol}^{-1} (Avogadro's number). N = 2.348 \cdot 6.022 \times 10^{23} = 1.413 \times 10^{24} \, \text{molecules}.

Explanation

1. Calculate moles of water<br /> Use $n = \frac{m}{M}$, where $m$ is mass and $M$ is molar mass. For water, $M = 18.015 \, \text{g/mol}$. $n = \frac{42.3}{18.015} = 2.348 \, \text{mol}$.<br /><br />2. Calculate number of molecules<br /> Use $N = n \cdot N_A$, where $N_A = 6.022 \times 10^{23} \, \text{mol}^{-1}$ (Avogadro's number). $N = 2.348 \cdot 6.022 \times 10^{23} = 1.413 \times 10^{24} \, \text{molecules}$.
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