Question

A quantity of ideal gas at 12°C and 54 kPa occupies a volume of 7.8 m³. (a) How many moles of the gas are present? (b) If the pressure is now raised to 270 kPa and the temperature is raised to 40.0°C, how much volume does the gas occupy? Assume no leaks.

Answer 1

(a) How many moles of the gas are present?

using an ideal gas law, we have

P V = n R T

where, V = volume of ideal gas = 7.8 m³

R = molar gas constant = 8.314 J/mol.K

P = pressure of ideal gas = 54 x 10³ Pa

T = temperature of ideal gas = 12 ⁰C = 285.15 K

then, we get

n = [(54 x 10³ Pa) (7.8 m³)] / [(8.314 J/mol.K) (285.15 K)]

n = [(421200 J) / (2370.7 J/mol)]

n = 177.6 moles

(b) If the pressure is now raised to 270 kPa and the temperature is raised to 40 ⁰C, how much volume does the gas occupy?

using combined gas law & we get

P₁ V₁ T₁ = P₂ V₂ T₂

[(54 x 10³ Pa) (7.8 m³) (285.15 K)] = [(270 x 10³ Pa) V₂ (313.15 K)]

V₂ = (120105180 J.K) / (84550500 Pa.K)

V₂ = 1.42 m³