Suppose you have \(100.0 \mathrm{~g}\) of \(\mathrm{H}_{2} \mathrm{O}\). (a) How many moles of \(\mathrm{H}_{2} \mathrm{O}\) molecules do you have? (b) How many \(\mathrm{H}_{2} \mathrm{O}\) molecules do you have? Answer: (a) \(100.0 \mathrm{~g} \mathrm{H}_{2} \mathrm{O} \times \frac{1 \mathrm{~mol} \mathrm{H}_{2} \mathrm{O}}{18.015 \mathrm{~g} \mathrm{H}_{2} \mathrm{O}}=5.551 \mathrm{~mol} \mathrm{H}_{2} \mathrm{O}\) or \(\frac{100.0 \mathrm{~g} \mathrm{H}_{2} \mathrm{O}}{18.015 \mathrm{~g} \mathrm{H}_{2} \mathrm{O} / \mathrm{mol}}=5.551 \mathrm{~mol} \mathrm{H}_{2} \mathrm{O}\) (b) \(5.551 \mathrm{~mol} \mathrm{H}_{2} \mathrm{O} \times \frac{6.022 \times 10^{23} \mathrm{molecules} \mathrm{H}_{2} \mathrm{O}}{1 \mathrm{~mol} \mathrm{H}_{2} \mathrm{O}}=3.343 \times 10^{24} \mathrm{molecules} \mathrm{H}_{2} \mathrm{O}\)

Step by step solution

01

Calculate moles of water

Using the given mass of water (100.0 g), we can find the number of moles by dividing the mass by the molar mass of water (18.015 g/mol). \(\text{moles of water } = \frac{\text{mass of water}}{\text{molar mass of water}}\) moles of water \(= \frac{100.0 \, \text{g}}{18.015 \, \text{g/mol}}\) moles of water \(= 5.551 \, \text{mol H}_2\text{O}\)

02

Calculate the number of water molecules

Next, we will use Avogadro's number (6.022 x 10^23 molecules/mol) to find the number of water molecules from the number of moles calculated in Step 1. \(\text{number of water molecules } = \text{moles of water } \times \text{Avogadro's number}\) number of water molecules \(= 5.551 \, \text{mol H}_2\text{O} \times 6.022 \times 10^{23} \, \text{molecules/mol}\) number of water molecules \(= 3.343 \times 10^{24} \, \text{molecules H}_2\text{O}\) Hence, we have: (a) 5.551 moles of H₂O (b) 3.343 x 10²⁴ molecules of H₂O

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