Gas Laws Math

Question

6. A container holding a gas at 500atm is held at 298K (room temperature). What is the pressure of the gas in the container when it is heated to 1000K? 7. Why is the situation in #6 dangerous?

Answer 1

Hello Alyssa

 

This question deals with Gay-Lusaac's Law, which states that the pressure (P) of a gas varies directly with the Kelvin temperature (T).

 

P ∝ T

 

In your question, you can see that the temperature is increasing from 298 K to 1000 K.  The effect will be a significant increase in the pressure, which can be dangerous depending on the equipment being used.

 

In your question, you have an initial state where the initial pressure (P_i) = 500 atm and the initial temperature (T_i) = 298 K.  We need to determine the pressure (P_f) of the final state when the temperature (T_f) is increased to 1000 K.

 

The Gay-Lusaac's equation is:

 

P_i / T_i = P_f / T_f

 

Rearrange to solve for P_f, you get

P_f = P_i x Tf / T_i  = 500 atm x 1000 K / 298 K = 1678 atm

 

The situation is dangerous because the pressure has increased to 1678 atm, which is more than 3 times the initial pressure.

 

Hope that above is helpful.