Question

What is the new pressure of 150 mL of a gas that is compressed to 50 mL when the original pressure was 2.0 atm and the temperature is held constant?
2. A sample of a gas in a rigid container at 30.0°C and 2.00 atm has its temperature increased to 40.0°C. What will be the new pressure?

Answer 1

Answer:

1) 6.0 atm.

2) 2.066 atm.

Explanation:

• From the general law of ideal gases:

PV = nRT.

where, P is the pressure of the gas.

V is the volume of the container.

n is the no. of moles of the gas.

R is the general gas constant.

T is the temperature of the gas (K).

1) What is the new pressure of 150 mL of a gas that is compressed to 50 mL when the original pressure was 2.0 atm and the temperature is held constant?

• At constant T and at two different (P, and V):

P₁V₁ = P₂V₂.

P₁ = 2.0 atm, V₁ = 150.0 mL.

P₂ = ??? atm, V₂ = 50.0 mL.

∴ P₂ = P₁V₁/V₂ = (2.0 atm)(150.0 mL)/(50.0 mL) = 6.0 atm.

2. A sample of a gas in a rigid container at 30.0°C and 2.00 atm has its temperature increased to 40.0°C. What will be the new pressure?

• Since the container is rigid, so it has constant V.

• At constant V and at two different (P, and T):

P₁/T₁ = P₂/T₂.

P₁ = 2.0 atm, T₁ = 30.0°C + 273 = 303 K.

P₂ = ??? atm, T₂ = 40.0°C + 273 = 313 K.

∴ P₂ = P₁T₂/T₁ = (2.0 atm)(313.0 K)/(303.0 K) = 2.066 atm.