⚛️ Physics · Kinetic Theory · NEET & JEE

The number of molecules per unit volume of an ideal gas at 300 K and pressure 1.0 × 10⁵ Pa is about (k = 1.38 × 10^-23 J/K):

Answer: 2.4 × 10²⁵ m^-3.

A 2.4 × 10²³ m^-3
B 2.4 × 10²⁵ m^-3
C 6.0 × 10²³ m^-3
D 1.2 × 10²⁵ m^-3

Correct answer: B. 2.4 × 10²⁵ m^-3

Explanation: From P = nkT, n = P/(kT) = 10⁵/(1.38 × 10^-23 × 300) ≈ 2.4 × 10²⁵ per m³.

Not all gas molecules move at the same speed - the Maxwell-Boltzmann distribution shows the spread, with the most probable speed v_p slightly less than the average v_avg, which is slightly less than the root-mean-square speed v_rms used in the pressure formula.

Concept context

Kinetic theory of gases connects molecular motion to pressure and temperature, explaining gas laws, specific heats, and molecular speeds.

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The number of molecules per unit volume of an ideal gas at 300 K and pressure 1.0 &times; 105 Pa is about (k = 1.38 &times; 10-23 J/K):

Concept context

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The number of molecules per unit volume of an ideal gas at 300 K and pressure 1.0 × 10⁵ Pa is about (k = 1.38 × 10^-23 J/K):