Can someone help me find the pressure? I would appreciate it, thank you!

Question

A sample of gas at 5.00 x 10​ to the 5th power mmHg inside a rigid tank is cooled from 500.0​ celcius to 0.0​ celcius.What is the final pressure of the gas inside the tank?

Answer 1

Use what you know - if you heat up a container the pressure builds and if you cool it the pressure drops - a direct action/proportional. The volume doesn’t change (rigid). The other rule is that the temperatures must be in Kelvin.

P₁/T₁ = P₂/T_2. Just putting in made up numbers a pressure of 5 at 5 K would be equal to a higher pressure if we heated it up to a higher temperature such as 100/100 K...so apply that to the equation. If it was cooled, the pressure would go down.

5.00 x 10⁵ mm Hg/(500+273) = x/(0+273). x = 1.76 x 10⁵ mm Hg

Answer 2

A "rigid tank" means the volume will remain constant.

The "constant volume" version of the Ideal Gas Law is Gay-Lussac's law which says:

P₁/T₁ = P₂/T₂

When using these laws, you MUST use temperature in Kelvin (absolute temperature). To get that, add 273.15 to temperature in °C so T₁ = 500° + 273.15° = 773.15 K and T₂ is 0° + 273.15° = 273.15 K.

We also have P1 = 5.00 x 10⁵ mm Hg

Since P₁/T₁ = P₂/T₂ we can say P₂ = (P₁•T₂)/T₁ and plugging in the numbers we get:

P₂ = (5.00 x 10⁵ mm Hg)(273.15)/773.15 or P2 = 1.77 x 10⁵ mm Hg