9701 MCQ Solution 8

Question 8: [Physical > States of Matter]:

A 2g sample of hydrogen at temperature T and of volume V exerts a pressure p.

Deuterium, ₁²H, is an isotope of hydrogen.

Which of the following would also exert a pressure p at the same temperature T?

A 2g of deuterium of volume V

B 4g of deuterium of volume V/2

C a mixture of 1g of hydrogen and 2g of deuterium of total volume V

D a mixture of 2g of hydrogen and 1g of deuterium of total volume 2V

Reference: Past Exam Paper – November 2002 Paper 1 Q8

Solution 8:

Answer: C.

Find the relation between the initial pressure and initial temperature using the ideal gas equation.

pV = nRT

Substitute the known information

pV = (2/2)(8.31)T

Therefore: pV = 8.31T

One of the given final scenarios must match the initial equation

A: pV = (2/4)(8.31)T : pV = 4.16T thus is incorrect

B: p(V/2) = (4/4)(8.31)T: pV = 16.62T thus is incorrect

C: pV = (1/2)(8.31)T + (2/4)(8.31)T: pV = 8.31T thus is correct

D: p(2V) = (2/2)(8.31)T + (1/4)(8.31)T: pV = 8.63T thus is incorrect