Determining the Mass of a Product of a Gas Phase Reaction

Question

How many grams of sodium are needed to produce 10.5 L of hydrogen gas according to the following reaction at 25 °C and 1 atm? Answer in grams of sodium

sodium (s) + water(ℓ) ----> sodium hydroxide (aq) + hydrogen (g)

Answer 1

2Na(s) + 2H₂O(l) ==> 2NaOH(aq) + H₂(g) ... balanced equation

Assuming H2(g) behaves as an ideal gas, we can use the ideal gas law equation to find moles (n) of H₂(g)

PV = nRT

n = PV/RT = (1 atm)(10.5 L)/(0.0821 Latm/Kmol)(298K)

n = 0.429 moles H₂

Now, from the balanced equation, we can find the moles and mass of Na needed to produce 0.429 moles H₂:

0.429 mol H₂ x 2 mol Na/mol H₂ x 22.99 g/mol = 19.7 g of Na needed