A chemical reaction occurring in a cylinder equipped with a moveable piston produces 0.661 mol of a gaseous product. If the cylinder contained 0.120 mol of gas before the reaction and had an initial volume of 2.04 L, what was its volume after the reaction? (Assume that pressure and temperature are constant and that the initial amount of gas completely reacts.)
Express the volume to thee significant figures and include the appropriate units.
First, we need to find the total amount of gas after the reaction:
Total amount of gas = initial amount of gas + amount of gas produced
Total amount of gas = 0.120 mol + 0.661 mol
Total amount of gas = 0.781 mol
Since pressure and temperature are constant, we can use the ideal gas equation to find the final volume:
PV = nRT
Initially:
P1V1 = n1RT
(assuming the volume is V1 and the initial gas amount is n1)
0.120 mol * V1 = 0.120 mol * R * T
Finally:
P2V2 = n2RT
(assuming the volume after the reaction is V2 and the total gas amount is n2)
0.781 mol * V2 = 0.781 mol * R * T
Therefore:
V2 = (n1V1) / n2
Plugging in the values:
V2 = (0.120 mol * 2.04 L) / 0.781 mol
V2 = 0.314 L
Therefore, the volume after the reaction is 0.314 L.