Answer:
5.54 m³.
Explanation:
- We should use the ideal gas law: <em>PV = nRT,</em>
where, P is the pressure of the gas in atm,
V is the volume of the gas in L,
n is the number of moles in mole,
R is the general gas constant (R = 0.082 L.atm/mol),
T is the temperature of the gas in K.
<em>We have two different cases at different (P, V and T) while the number of moles of He and R is constants.</em>
<em>∴ (P₁V₁) / (T₁) = (P₂V₂) / (T₂).</em>
We can use P in KPa and V in m³ that the conversion factor can be canceled by division, but we should use T in K because its conversion factor is additive value.
P₁ = 101.0 kPa, V₁ = <em>??? m³</em>, and T₁ = (20 °C + 273) = 293.0 K.
P₂ = 11.7 kPa, V₂ = 35.4 m³, and T₂ = (-56 °C + 273) = 217 K.
∴ The initial volume (V₁) = (P₂V₂T₁) / (P₁T₂) = (11.7 kPa)(35.4 m³)(293.0 K) / (101.0 kPa)(217.0 K) = (121354.74) / (21917) = 5.537 m³ ≅ 5.54 m³.
