Question:

The average kinetic energy of an ideal gas per molecule in SI unit at $25^{\circ} C$ will be

Updated On: Jan 30, 2025
  • $6.17 \times 10^{-21} kJ$
  • $6.17 \times 10^{-21} J$
  • $6.17 \times 10^{-20} J$
  • $7.16 \times 10^{-20} J$
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The Correct Option is B

Solution and Explanation

The average kinetic energy of an ideal gas per molecule in SI units at $25^{\circ} C$ will be $6.17 \times$ $10^{-21} J$ The average kinetic energy of an ideal gas per molecule is given by the expression Average kinetic energy $=\frac{3}{2} kT$ Here, $k$ is boltzmann constant and $T$ is absolute temperature. $k =1.36 \times 10^{-23} J / K$ $T =25+273=298\, K$ Average kinetic energy $=\frac{3}{2} \times 1.36 \times 10^{-23} J / K \times 298\, K $ $=6.17 \times 10^{-21} J$
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Concepts Used:

Ideal Gas Equation

An ideal gas is a theoretical gas composed of a set of randomly-moving point particles that interact only through elastic collisions.

What is Ideal Gas Law?

The ideal gas law states that the product of the pressure and the volume of one gram molecule of an ideal gas is equal to the product of the absolute temperature of the gas and the universal gas constant.

PV=nRT

where,

P is the pressure

V is the volume

n is the amount of substance

R is the ideal gas constant

Ideal Gas Law Units

When we use the gas constant R = 8.31 J/K.mol, then we have to plug in the pressure P in the units of pascals Pa, volume in the units of m3 and the temperature T in the units of kelvin K.