Question

A 900 liter supply of xenon gas is held at 27 °C and 100 kPa. When the temperature is lowered to -73

C, what pressure must be applied to compress the gas to 200 liters?

Answer 1

300 kPa

Step-by-step explanation:

Concept tested: Gas Laws (Combined gas law)

Initial pressure, P₁ = 100 kPa

Initial temperature,T₁ = 27°C

But, K = °C + 273, therefore, T₁ = 300 K

Initial volume, V₁ = 900 L

New temperature, T₂ = -73°C

= -73°C + 273

= 200 K

New volume, V₂ = 200 L

We are required to calculate the new pressure, P₂

• To find the new pressure of the gas, we are going to use the combined gas law;
• Combined gas law combines both Charles's law and Boyle's law.
• According to the combined gas law;

P₁V₁/T₁ = P₂V₂/T₂

• To calculate the new Pressure, P₂, we rearranging the formula;

P₂ =(P₁V₁T₂) ÷ (V₂T₁)

Therefore;

P₂ = (100 kPa × 900 L × 200 K) ÷ (200 L × 300 K)

= 300 kPa

Therefore, a pressure of 300 kPa must be applied.