A canister of 1.20 mol of nitrogen gas (28.0 g/mol) at 9.1°C is left on Jupiter\

Question

A canister of 1.20 mol of nitrogen gas (28.0 g/mol) at 9.1°C is left on Jupiter's satellite after completion of a future space mission. Europa has no appreciable atmosphere, and the acceleration due to gravity at its surface is 1.30 m/s2. After some time, the canister springs a small leak, allowing molecules to escape through a small hole. What is the maximum height (in km) above Europa's surface that a N2 molecule having speed equal to the rms speed will reach if it is shot straight up out of the hole in the canister? Ignore the variation in g with altitude. (In km)

Explanation / Answer

we know,

molar mass of nitrogen, M = 28 gram/mole

= 28*10^-3 kg/mole

T = 9.1 + 273 = 282.1 k

now apply, Vrms = sqrt(3*R*T/M)

= sqrt(3*8.314*282.1/(28*10^-3))

= 501 m/s

given g = 1.3 m/s^2

maximum height reached by nitrogen molecules, Hmax = Vrms^2/(2*g)

= 501^2/(2*1.3)

= 96538 m

= 96.538 km <<<<<<<<<-------------Answer

= 29.7

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