Please help me understand this homework problem, Any one who can explain it to m
ID: 817516 • Letter: P
Question
Please help me understand this homework problem, Any one who can explain it to me in an understandable way will get 15000 points. Please include units and significant figures for the points thank you.
Consider a system consisting of two connected containers with a valve between the two containers. Assume that the volume of the valve itself can be ignored. Initially, the valve is closed. One container, designated A, having a volume of 100.0 L, holds only gaseous nitrogen; the pressure in the container is 0.300 atm. The second container, designated B, having a volume of 50.0 L, holds only gaseous methane; the pressure in the second container is 0.450 atm. The two containers are at the same temperature. The valve is then opened. Assume that there is no reaction which occurs between methane and nitrogen, and assume that the system's temperature does not change after opening the valve. Describe what happens after the valve is opened, connecting the two sides. After opening the valve and when no further change is occurring: What is the total pressure inside Container A? What is the partial pressure of nitrogen in Container A? Sketch a picture of a small representative volume of Container A. Indicate the meaning of each symbol you use.Explanation / Answer
a) After the valve is opened the two gases mix, but do not react. The whole container now acts as a single volume instead of the two volumes separated by the valve. Valve volume is negligible. Due to two different gases of different amounts and different pressures mixing, the overall pressure changes in the system.
b) Initially,
P1V1= n1*R*T
=> 0.3*100 = n1*0.0821* T
=> n1 = 30/(0.0821*T)
The temperaures in both is same at T Kelvin.
Similarly, P2V2 = n2*R*T
=> n2 = (0.45*50)/(0.0821*T) = 22.5/(0.0821*T)
Now after valve is released, total number of moles = n1 + n2
Total volume V = V1 + V2 = 100 L + 50L =150 L
=> P = ((n1+n2)*R*T)/V
= (((52.5)/0.0821*T)*0.0821*T)/150
This is because the system's temperature does not change after valve is released (given in question)
=> P = 52.5/150 = 0.35 atmospheres.