ideal gas law, word question

Question

Which of the following changes in state will increase the density of a gas? A. Heating at constant pressure. B. Heating at constant volume. C. Compression at constant temperature. correct D. The density of a gas never changes.

i came up with,

 ρ=m/V

PV=nRT

PV=(m/M) RT

m=PVM/RT

ρ=m/V=PM/RT

I do not know what to do after this to pick the right answer. (Correct answer is c)

Answer 1

Look at your formula: p=PM/RT.

1. M (Molar Mass) is a constant. The gas is not changing.
2. R (Ideal Gas Constant) is a universal constant.
3. Therefore, the density p is controlled entirely by the ratio of Pressure (P) to Temperature (T).

To increase density p, the ratio P/T must increase.