Question

A sample of gas at 760 torr and 2.8 L is compressed at constant temperature to the pressure at 3.5 atm. What is the final volume of the gas?

My biggest problem with answering this question is the fact that I don't know what the "constant temperature" is..I know I'm using the combined gas law with formula: V2= p1v1/t1p2 * T2 and that p1=760 torr or 1 atm, v1=2.8L and p2=3.5 atm... Any help on this is very much appreciated.

Answer 1

Here Boyle's law is to be used instead of combined gas law. Boyle's law states that when temperature is kept constant then pressure and volume of a gas have an inverse relationship. Mathematically it can be expressed as

$P \propto (1/V)$                    (at constantt temperature for a fixed mass of a gas)

=>     PV= Constant             (at constantt temperature for a fixed mass of a gas)

=> P₁V₁= P₂V₂                  (at constantt temperature for a fixed mass of a gas)...........(1)

Here P₁= 760 torr (given) = 1atm, V₁= 2.8 L (given), P₂= 3.5atm (given), V₂= ? (To be calculated)

Substituting these given values in the above equation (1)

1 $\times$ 2.8 = 3.5 $\times$ V₂

=> V₂ = 2.8/3.5 = 0.8 L

So final volume of the gas will be 0.8 L