Ideal gas graph question

Question

How will the qualitative graph of P versus molar mass of a 1-g sample of different gases at constant volume and temperature look like?

i am confused on how to derive the equation and then answer how will it look like

Answer 1

One gram of different gases represents different numbers of moles of each gas. For example, 1 g H2 =~0.5 moles, 1 g He =~0.25 moles, and 1 g Ne =~0.05 moles. So, the question really boils down to what is the relationship between pressure (P) and moles (n) at constant temperature and volume. This can further be viewed as the relationship between the number of gas particles (change in number of moles) and pressure. From the kinetic theory of gases, it can be seen that as the number of particles (moles) increases, the pressure increases if the volume and temperature are constant. Thus, a graph of P v molar mass would be linear with a negative slope, meaning inversely related to the molar mass.

From the ideal gas law, PV = nRT, and at constant T and V, you have P/n = k and P1/n1 = P2/n2. Doubling moles will double the pressure and vice versa.