Answer to Question #162194 in Chemistry for Zamaria Baugh

Question

A glass sphere is filled to full volume with a gas. The pressure of the gas inside the sphere is 30.0 atm, and the temperature is 30.0°C. The sphere is taken outside on a cold day. The temperature of the gas decreases to 10.0°C. What is the new pressure of the gas? Assume that the volume is constant.

Answer 1

P₁ = 30.0 atm

T₁ = 30.0°C + 273 = 303 K

V₁ = V₂ = const

P₂ = unknown

T₂ = 10.0°C + 273 = 283 K

Solution:

Since the volume doesn't change, Gay-Lussac's Law can be used.

Gay-Lussac's Law can be expressed as: P₁/T₁ = P₂/T₂

P₁T₂ = P₂T₁

To find the final pressure, solve the equation for P₂:

P₂ = P₁T₂/T₁

P₂ = (30.0 atm × 283 K) / (303 K) = 28.0198 atm = 28.0 atm

P₂ = 28.0 atm

Answer: 28.0 atm is the new pressure of the gas.