Question

What is the average kinetic energy and rms speed of N₂ molecules at STP? Compare these values with those of H₂ molecules at STP. [Use R = 8.314 J/(mol·K) and M in kg/mol.]

Answer 1

The average kinetic energy and rms speed of N₂ molecules at STP is $5.65686 \times 10^{-21}$ and $493 \mathrm{~m} / \mathrm{s}$

Given,

$\begin{aligned}&\mathrm{P}=1.013 \times 10^{5} \mathrm{~Pa} \\&\mathrm{~T}=273.15 \mathrm{~K} \\&\rho=1.25 \mathrm{~kg} / \mathrm{m}^{3}\end{aligned}$

The average kinetic energy of a molecule is given by, $K . E .=\frac{3}{2} k T$ where k is the Boltzmann constant and Tis the absolute temperature of the gas.

$K . E .=\frac{3}{2} \times 1.380649 \times 10^{-23} \times 273.15 K$

$K.E= 5.65686 \times10^{-21}$

The rms speed of $\mathrm{N}_{2}$ molecules is given by

$\begin{aligned}&\mathrm{V}_{\mathrm{rms}}=\sqrt{\frac{3 \mathrm{RT}}{\mathrm{M}}}=\sqrt{\frac{3 \mathrm{P}}{\rho}} \\&\mathrm{V}_{\mathrm{rms}}=\sqrt{\frac{3 \mathrm{P}}{\rho}} \\&\mathrm{V}_{\mathrm{rms}}=\sqrt{\frac{3 \times 1.013 \times 10^{5}}{1.25}}=493 \mathrm{~m} / \mathrm{s}\end{aligned}$

The average kinetic energy of a gas's particles is inversely related to its temperature. As the gas warms, the particles must travel more quickly since their mass is constant.

The average kinetic energy (K) is equal to one half of the mass (m) of each gas molecule times the RMS speed (vrms) squared.

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