To determine how many milliliters of 0.126 M \( \text{H}_2\text{O}_4 \) (which I assume is intended to refer to sulfuric acid \( \text{H}_2\text{SO}_4 \)) are needed to neutralize a given mass of sodium hydride \( \text{NaH} \), we can follow these steps:
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Calculate moles of NaH:
- The molar mass of NaH (sodium hydride) is approximately \( 22.99 , \text{g/mol (Na)} + 1.01 , \text{g/mol (H)} = 24.00 , \text{g/mol} \).
- The number of moles of \( \text{NaH} \) can be calculated using the formula: \[ \text{moles of NaH} = \frac{\text{mass of NaH}}{\text{molar mass of NaH}} = \frac{0.230 , \text{g}}{24.00 , \text{g/mol}} \approx 0.00958 , \text{mol} \]
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Determine moles of H2SO4 needed for neutralization:
- The reaction between sodium hydride and sulfuric acid can be represented as: \[ \text{NaH} + \text{H}_2\text{SO}_4 \rightarrow \text{Na}_2\text{SO}_4 + \text{H}_2 \]
- This indicates that one mole of \( \text{NaH} \) reacts with one mole of \( \text{H}_2\text{SO}_4 \). Therefore, the moles of \( \text{H}_2\text{SO}_4 \) required is equal to the moles of \( \text{NaH} \): \[ \text{moles of H}_2\text{SO}_4 = 0.00958 , \text{mol} \]
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Calculate the volume of H2SO4 solution needed:
- From the concentration formula \( M = \frac{\text{moles}}{\text{volume (L)}} \), we can rearrange it to find volume: \[ \text{Volume (L)} = \frac{\text{moles}}{M} \]
- Plugging in the values: \[ \text{Volume (L)} = \frac{0.00958 , \text{mol}}{0.126 , \text{mol/L}} \approx 0.0760 , \text{L} \]
- To convert to milliliters: \[ \text{Volume (mL)} = 0.0760 , \text{L} \times 1000 = 76.0 , \text{mL} \]
Thus, the volume of \( 0.126 , M , \text{H}_2\text{SO}_4 \) needed to neutralize \( 0.230 , \text{g} \) of \( \text{NaH} \) is 76.0 mL.
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