Find the ratio (N/V)x/(N/V)Earth.?

Question

On the surface of a hypothetical planet X, the atmospheric pressure is 9.72 x 10^6 Pa, and the temperature is 702 K. On the earth's surface the atmospheric pressure is 1.00 x 10^5 Pa, while the surface temperature can reach 320 K. These data imply that the planet X has a "thicker" atmosphere at its surface than does the earth, which means that the number of molecules per unit volume (N/V) is greater on the surface of planet X than on the earth.

Answer 1

Use the ideal gas law.

PV = NkT

We are looking for the quantity (N/V) in both cases to set up a ratio (N/V)x / (N/V)e, so solve the Ideal Gas Law for N/V

N/V = P/(kT)

Now we will plug this into our ratio to get.

(N/V)x / (N/V)e = (Px / (kTx)) / (Pe / (kTe))

We can cancel Boltzmann's Constant k from both terms and get the following ratio.

(N/V)x / (N/V)e =(Px / Tx) / (Pe / Te)

Now simply, plug in your numbers and compute. You can do this step on your own as this is an online assignment from the book maker Wiley, possibly Chapter 14 Problem 17.

Answer 2

Ideal gas law: PV = nRT

so n/V is proportional to P/T.

So your ratio (n/V)x/(n/V)Earth = (Px Tearth) / (Tx Pearth).

They give you both temps and pressures. Plugnchug.