Answer:
44.1 liters
Step-by-step explanation:
We can use the combined gas law:
P1V1/T1 = P2V2/T2,
where P, V, and T are the pressures(P), volumes(V), and temperatures(T), for the initial (P1,V1,T1) and final states (P2,V2,T2). Note that the temperatures must be in Kelvin (add 273.15 to C to make it K).
We are given all the conditions except V2, the final volume. Let's rearrange the gas law to solve for V2:
V2 = V1(T2/T1)(P1/P2)
Note the way I organized the temperature and pressures into ratios of their starting and final conditions. This makes it easier to visualize how changes will impact the final volume. If the temperatue goes up, (T2/T1) will increase and V2 will increse. But it we increase pressure, (P1/P2) will drop, casuing a reduction in volume.
Enter the data.
V1 =36.4L
T1 = 298.2K
T2 = 361.2K
Pressures are not given, but are said to remain the same: "at constant pressure." We need a pressure, so we can assume for the sake of simplicity, that the pressure is 1 atm (both P1 and P2). We can see from the ratio of the two, that the absolute value of the pressure makes no difference (P1/P2) since P1=P2 and the ratio is simply 1.
V2 = V1(T2/T1)(P1/P2)
V2 = (36.4L)(361.2K/298.2K)(1atm/1atm)
The ratio of the temperatures clearly tells us that the final volume should increase, by around 20% (about 60K higher than 300K). Now do the calculation and see if the volume change is indeed around 20% higher.
V2 = 44.1L
This is around a 20% increase and is higher than the initial volume, so let's claim our work is done.