a sample of nitrogen gas is placed into a container at 200k. if the temperature

Question

a sample of nitrogen gas is placed into a container at 200k. if the temperature of the container is reduced by 100 deg C and the measured pressure decreases by 50%, how does the volume of the container change?

a) the container volume increases by less than 50%.

b) the container volume increases by more than 50%

c) the container volume doesn't change.

d) the container volume increases by 50%.

e) the continaer volume decreases by 50%.

I know the answer but don't know how to get it. So, solve it in step by step order so that even a dumb person like me can understand...

Explanation / Answer

Ti = 200 K , Tf = 200 - 100 K = 100 K (either you reduce it by 100 C or 100 K, the result is same for t final)
Pi = x, Pf = x - x/2 = x/2

we know, PV = nRT, surely the n is the no. of moles of gas that is constant and R is also constant, so

PV/T will always remain the same
PiVi/Ti = PfVf/Tf
=> x Vi / 200 = x/2 Vf / 100
=> Vi = Vf

answer is C - the volume of container doesnt change

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