On the surface of a hypothetical planet X, the atmospheric pressure is 4.16 x 10

Question

On the surface of a hypothetical planet X, the atmospheric pressure is 4.16 x 106 Pa, and the temperature is 526 K. On the earth's surface the atmospheric pressure is 1.00 x 105 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. Find the ratio (N/V)X/(N/V)Earth.

Please include units. Thank you so much in advance

Explanation / Answer

we use PV= n RT

for planet, Px Vx= Nx RTx , so (N/V)x= (Px/RTx)

for earth, Pe Ve = Ne R Te, so (N/V)e= (Pe/RTe)

(N/V)x/(N/V)e = (Px/RTx) /(Pe/RTe)

(N/V)x/(N/V)e =PxTe/PeTx

(N/V)x/(N/V)e =(4.16x106* 320)/(1x105*526)

(N/V)x/(N/V)e =25.3

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