Question

We have a sample of gas characterised by P, V, and T and another sample of gas characterized by 2P, V/4, and 2T. What is the ratio of the number of molecules in the first and second samples?

Options

• 2: 1

• 16: 1

• 8: 1

• 4: 1

Answer 1

4: 1

Explanation:

PVT 

2P, V/4, 2T

`"P"_1"V"_1 = "n"_1"RT"_1  ; "P"_2"V"_2 = "n"_2"RT"_2`

`"n"_1/"n"_2 = (("P"_1"V"_1)/"RT"_1)/(("P"_2"V"_2)/"RT"_2) =( "P"_1"V"_1)/("T"_1) xx "T"_2/("P"_2"V"_2)`

`= "PV"/"T" xx (2"T" xx 2)/(2"P" xx "V"/4)` = 4:1