Question

Consider two samples of gas. Sample A consists of n moles and is kept at temperature T in container of volume V. Gas B consists of 2n moles, and is kept under the temperature T/2 in a container of volume V/2. What is the pressure of gas B in terms of pressure of gas A, P?
a. 2P
b. 4P
c. 8P
d. P
e. P/2
f. P/4
g. P/8

Answer 1

Answer: e. P/2

Explanation:

For ideal gases, we have the relation:

P*V = n*R*T

where:

n =  number of mols

R = Gas constant

T = temperature

V = volume

P = pressure.

We know that for sample A, we have n moles, a temperature T and a volume V, then the pressure of this sample will be:

Pa = (n*R*T)/V.

For sample B, we have:

n/2 moles, temperature T/2 and a volume V/2, then the pressure will be:

Pb = (n/2)*R*(T/2)*(2/V) = (n*R*T/V)*(2/4)

and:

(n*R*T/V) = Pa

Then we can replace it and we get:

Pb = (n*R*T/V)*(2/4) = Pa*(2/4) = Pa*(1/2) = Pa/2.

Then the correct option is e.