Question

In the planet Mars, the average temperature is around −53°C and atmospheric pressure is 0.9 kPa. Calculate the number of moles of the molecules in unit volume in the planet Mars? Is this greater than that in earth?

Answer 1

Average temperature of mass = −53°C

∴ T_mars = T₁ = 273 − 53 = 220 K

Atmospheric pressure = P₁ = 0.9 kPa = 0.9 × 10³Pa

PV = NkT .......(1)

Since volume is unity V = 1

Equation (1) becomes P = NkT

Where k is Boltzmann constant

N = `"P"/"kT"`

= `(0.9 xx 10^3)/(1.381 xx 10^-23 xx 220)`

= `(0.9 xx 10^3)/303.6`

N = 2.964 × 10²³

∴ μ = `(2.964 xx 10^23)/(6.023 xx 10^23)` = 0.4921

μ_mass = 0.49 mol

N_A = Avogadro number

No. of moles in unit volume in Mars = μ = `"N"/"NA"`

No. of moles in unit volume in Earth = μ_Earth = 40 mol