We know that at state 1, we can describe the gas at STP by P1V1=n1RT1
We change the volume, so now there is a second state, state 2 that can be described as
P2V2=n2RT2
We are told that temperatures are constant and since no gas is lost then moles don't change. Hence n1T1=n2T2. So rearrange the equations as follows
P1V1/R=n1T1
P2V2/R=n2T2
Set them equal per my explanation above:
P1V1/R=P2V2/R
Now multiply by R on both sides
P1V1=P2V2
We want to find the pressure at state 2
P1V1/V2=P2
(1 atm)(10L)/(3L) = 3.33 atm = P2
