How many grams of hydrogen are needed to produce 1.80 g of water according to this equation? \[ \begin{array}{l}2 \mathrm{H}_{2}+\mathrm{O}_{2} \rightarrow 2 \mathrm{H}_{2} \mathrm{O} \\ 0.200 \mathrm{~g} \\ 2.00 \mathrm{~g} \\ 4.00 \mathrm{~g} \\ 0.180 \mathrm{~g} \\ 0.100 \mathrm{~g}\end{array} \]

To determine how many grams of hydrogen (\(\mathrm{H}_2\)) are needed to produce \(1.80\,\mathrm{g}\) of water (\(\mathrm{H}_2\mathrm{O}\)), follow these steps: ### 1. **Write the Balanced Chemical Equation:** \[ 2\,\mathrm{H}_2 + \mathrm{O}_2 \rightarrow 2\,\mathrm{H}_2\mathrm{O} \] ### 2. **Calculate Molar Masses:** - **Hydrogen (\(\mathrm{H}_2\)):** \[ \text{Molar mass of } \mathrm{H}_2 = 2 \times 1.008\,\mathrm{g/mol} = 2.016\,\mathrm{g/mol} \] - **Water (\(\mathrm{H}_2\mathrm{O}\)):** \[ \text{Molar mass of } \mathrm{H}_2\mathrm{O} = 2 \times 1.008 + 16.00\,\mathrm{g/mol} = 18.016\,\mathrm{g/mol} \] ### 3. **Determine Moles of Water Produced:** \[ \text{Moles of } \mathrm{H}_2\mathrm{O} = \frac{1.80\,\mathrm{g}}{18.016\,\mathrm{g/mol}} \approx 0.10\,\text{mol} \] ### 4. **Use Stoichiometry to Find Moles of Hydrogen Needed:** From the balanced equation, \(2\,\mathrm{H}_2\) produces \(2\,\mathrm{H}_2\mathrm{O}\). Therefore, the moles of \(\mathrm{H}_2\) needed are equal to the moles of \(\mathrm{H}_2\mathrm{O}\): \[ \text{Moles of } \mathrm{H}_2 = 0.10\,\text{mol} \] ### 5. **Convert Moles of Hydrogen to Grams:** \[ \text{Mass of } \mathrm{H}_2 = 0.10\,\text{mol} \times 2.016\,\mathrm{g/mol} = 0.2016\,\mathrm{g} \] Rounding to three significant figures: \[ \text{Mass of } \mathrm{H}_2 \approx 0.200\,\mathrm{g} \] ### **Answer:** **0.200 g** of hydrogen are needed to produce 1.80 g of water.