Ideal gas laws , volume of gas

Question

If 470.4 liters of a gas at STP is held at a pressure of 78 atm and a temperature of 900 k what is the volume of the gas

Answer 1

Hi Isabel! In order to calculate the new volume of the gas, we can use a form of the ideal gas law: PV = nRT.

Because the moles of gas do not change, and we will be using the same R, we can set the new conditions equivalent to the old conditions by manipulating this equation: nR = PV/T.

Therefore, we can use the combined gas law and say that P₁V₁/T₁ = P₂V₂/T₂.

Plugging in our values for P₁, V₁, T_1, P₂ and T₂, we arrive at this equation with the substituted values (STP is T = 273 K and P = 1 atm):

(1atm)(470.4L)/273K = (78atm)(V₂)/(900K)

All we have to do now is solve for V₂! We would get:

V₂ = (1atm)(470.4L)(900K)/((273K)(78atm)) = 19.88 L

Therefore, the new volume would be 19.88 L at a pressure of 78 atm and 900 K, given that the original volume of the gas is 470.4 L at STP. Hope this helps!