Final answer:
0.52 g of Na reacts to produce 5.2 mL of hydrogen gas at 20°C and 745 mmHg.
Step-by-step explanation:
To determine the volume of hydrogen gas evolved from the reaction between Na and water, we need to use the stoichiometry of the reaction. The balanced equation for this reaction is:
2Na + 2H2O → 2NaOH + H2
From the equation, we can see that for every 2 moles of Na, 1 mole of H2 is produced. We can use the molar mass of Na and the balanced equation to calculate the number of moles of Na in 0.52 g:
Molar mass of Na = 22.99 g/mol
moles of Na = mass of Na / molar mass of Na = 0.52 g / 22.99 g/mol = 0.0226 mol
Since the molar ratio between Na and H2 is 2:1, the moles of H2 produced would be half the moles of Na:
moles of H2 = 0.0226 mol / 2 = 0.0113 mol
To find the volume of H2 gas, we can use the ideal gas law equation:
PV = nRT
Where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature.
Given the conditions, we have:
Pressure (P): 745 mmHg
Temperature (T): 20°C = 293 K
Volume (V): ?
Number of moles (n): 0.0113 mol
Ideal gas constant (R): 0.0821 L·atm/(mol·K)
Plugging these values into the ideal gas law equation:
V = (nRT) / P
V = (0.0113 mol) * (0.0821 L·atm/(mol·K)) * (293 K) / (745 mmHg)
Simplifying the units and calculating:
V ≈ 0.0052 L ≈ 5.2 mL