Final answer:
To find the mass of sodium that reacted, the volume of hydrogen collected is converted to moles using the ideal gas law, and then the moles of sodium are calculated based on the stoichiometry of the reaction. The resulting mass of sodium is approximately 0.173 grams.
Step-by-step explanation:
To determine the mass of sodium that reacted to produce 95.0 mL of hydrogen gas at 27 °C and 0.974 atm, we can use the ideal gas law: PV = nRT. Before we can use the ideal gas law, we need to convert the volume of hydrogen gas from mL to L (95.0 mL = 0.0950 L) and the temperature from Celsius to Kelvin (27 °C = 300.15 K).
Inserting the known values into the ideal gas law gives us P(0.0950 L) = n(0.0821 Latm/molK)(300.15 K). Solving for n (the number of moles of hydrogen gas), we get n ≈ 0.00376 mol.
From the balanced chemical equation, 2 Na (s) + 2 H2O (l) → 2 NaOH (aq) + H2 (g), we see that 2 moles of Na produce 1 mole of H2. This means that the 0.00376 mol of H2 comes from 0.00752 mol of Na. The molar mass of Na is approximately 22.99 g/mol, so the mass of sodium that reacted is 0.00752 mol × 22.99 g/mol = 0.173 g of Na.