The balanced chemical equation for the reaction of sodium with water is:
2Na + 2H2O → 2NaOH + H2
From the equation, we can see that 2 moles of sodium react to produce 1 mole of hydrogen gas.
To calculate the volume of hydrogen gas produced, we need to use the ideal gas law:
PV = nRT
where P is the pressure, V is the volume, n is the number of moles, R is the gas constant, and T is the temperature in Kelvin.
First, we need to calculate the number of moles of hydrogen gas produced. We know that 2 moles of sodium produce 1 mole of hydrogen gas, so:
1 mole H2 = 2 moles Na
4.78 g Na x (1 mol Na / 23 g Na) x (1 mol H2 / 2 mol Na) = 0.104 mol H2
Next, we need to convert the temperature from Celsius to Kelvin:
T = 34°C + 273.15 = 307.15 K
Finally, we can use the ideal gas law to calculate the volume of hydrogen gas produced:
V = nRT/P
V = (0.104 mol)(0.08206 L·atm/mol·K)(307.15 K) / (88.9 kPa)
V = 0.00358 L or 3.58 mL (rounded to two significant figures)
Therefore, when 4.78g of sodium reacts with water at 88.9 kPa and 34 degrees Celsius, 3.58 mL of hydrogen gas is produced.