how to find gas pressure when gas varies jointly to amount gas & temp & inversely to volume

Question

The pressure of a gas varies jointly with the amount of gas (measured in moles) and the temperature with the volume of the gas If the pressure is 1218 kPq (killo Pascals) when the number of moles is 8, the temperature is 290 degrees ◦ kelvin, and the volume is 960cc find the pressure when the number of moles is 6, the temperature is 250◦ kelvin, and the volume is 360cc.

I would like to see the formula and the steps. Because every know am writing this formula out right but I am not getting an correct answer.

Answer 1

The first thing we need to do is to make sure we are comparing similar molarities. If we divide the volume of the first gas by 8 we get 120 cc and if we divide the volume of the second gas by 6 we get 60 cc. Now we know that the molarity is 1 in both cases so we can apply the gas law PV/T=k, a constant.

First gas: 1218×120/290=60P/250 where P is the gas pressure for the second gas.

Therefore P=1218×120×250/(290×60)=2100kP.