Ideal gas law relations

Question

Hi there!

I have solved a question about the ideal gas law, and I wonder if anyone would please check if I answered it correctly.Thanks in advance.

Question: A certain gas is in a pressure vessel with the temperature 25 degrees Celsius. We would like to double the pressure by increasing the temperature. The gas volume and amount of moles is constant. What is the new temperature?

Answer= According to pV= nRT, T has a direct ratio to p, so we just need to double T to double p. The new temp is 50 degrees Celsius

Answer 1

Maya - your logic is good, you do need to double the temperature! However, the gas laws are all based around the concept of kinetic molecular theory, and the concept of temperature as a measure of the average kinetic energy of the molecules in the sample... With this in mind, we need to realize that in these situations, Temperature must be measured/calculated using the Kelvin scale! The Kelvin scale says that at 0 Kelvins molecular motion ceases (and therefore Pressure would be theoretically zero also).

Think about what happens in this problem if your starting temperature is - 20 °C. You want to double your pressure, so you double your temperature, right? So would that be - 40 °C? That's colder! Making the sample colder slows the molecules down and decreases pressure. That's obviously wrong!

And what would you do if your starting temperature was 0 °C? And you double it? It would still be 0 °C...

Long story short - when dealing with the gas laws, you MUST use temperature in Kelvins, which is called the "absolute" temperature scale.

Therefore, your starting temperature was 25 degrees Celsius, which is 298 Kelvins. So to double the temperature, we need to go to 2 x 298 K, which is 596 K. You can then translate this back to Celsius if you want, 596-273 = 323 °C. Hope that helps!

Answer 2

Maya

Correct, good justification. V, n and R being constant.

Mike