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 of hydrogen gas in the 20.0 L headspace of a reactor vessel when 3.34 kg sodium is reacted with excess water at 50.0°C?

Answer 1

96.2 atm

Step-by-step explanation:

Step 1: Write the balanced equation

2 Na(s) + 2 H₂O(l) → 2 NaOH(aq) + H₂(g)

Step 2: Calculate the moles corresponding to 3.34 kg of sodium

The molar mass of Na is 22.99 g/mol.

`3.34 * 10^(3) g * (1mol)/(22.99g) =145mol`

Step 3: Calculate the moles of hydrogen formed from 145 moles of sodium

The molar ratio of Na to H₂ is 2:1. The moles of H₂ formed are 1/2 × 145 mol = 72.5 mol

Step 4: Convert the temperature to the Kelvin scale

K = °C + 273.15 = 50.0°C + 273.15 = 323.2 K

Step 5: Calculate the pressure exerted by the hydrogen gas

We will use the ideal gas equation.

`P * V = n * R * T\\P = (n * R * T)/(V) = (72.5mol * 0.0821atm.L/mol.K * 323.2K)/(20.0L) = 96.2 atm`