Combined Gas Law: Calculating New Temperature of an Ideal Gas

What will the temperature be if the pressure is changed to 4.00 atm, and the volume is changed to 1.50 L?

As the volume was decreased and pressure increased to the given values, the new temperature of the ideal gas is 226.9°C.

Combined gas law put together both Boyle's Law, Charles's Law, and Gay-Lussac's Law. It states that "the ratio of the product of volume and pressure and the absolute temperature of a gas is equal to a constant.

Given the data in the question:

  • Initial volume V₁ = 3.50L
  • Initial pressure P₁ = 795torr = 1.04605atm
  • Initial temperature T₁ = 32.0°C = 305.15K
  • Final volume V₂ = 1.50L
  • Final pressure P₂ = 4.00atm
  • Final temperature T₂ = ?

To calculate the new temperature of the gas, we substitute our given values into the expression above.

P₁V₁/T₁ = P₂V₂/T₂

P₁V₁T₂ = P₂V₂T₁

T₂ = P₂V₂T₁/P₁V₁

T₂ = (4.00atm × 1.50L × 305.15K) / (1.04605atm × 3.50L)

T₂ = 1830.9LatmK / 3.661175Latm

T₂ = 500.085K

T₂ = 226.9°C

Therefore, as the volume was decreased and pressure increased to the given values, the new temperature of the ideal gas is 226.9°C.

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