How do I solve this?

Question

Solid sodium reacts with liquid water to form hydrogen gas according to the equation 2 Na(s) + 2 H₂O(l) → 2 NaOH(aq) + H₂(g) What is the pressure (in atm) of hydrogen gas in the 20.0 L headspace of a reactor vessel when 1.00 kg sodium is reacted with excess water at 50.0 °C?

Answer 1

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

First, find the moles of H₂ gas generated:

1.00 kg Na x 1000 g / kg x 1 mol Na / 23 g = 43.48 moles Na(s)

moles H₂ generated = 43.48 mols Na x 1 mol H₂ / 2 mol Na = 21.74 moles H₂

Use the ideal gas law for find the pressure:

PV = nRT

P = pressure = ?

V = volume in liters = 20.0 L

n = moles of H₂ = 21.74

R = gas constant = 0.0821 Latm/Kmol

T = temperature in Kelvin = 50º + 273 = 323K

Solving for P we have ..

P = nRT / V = (21.74)(0.0821)(323) / 20.0

P = 28.83 atm = 28.8 atm (3 sig. figs.)