What's the rms speed of nitrogen (N2) molecules at 273 K ? (a) 465 m / s (b) 492 m / s (c) 51

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What's the rms speed of nitrogen (N2) molecules at 273 K ?...

What's the rms speed of nitrogen $\left(\mathrm{N}_{2}\right)$ molecules at $273 \mathrm{~K} ?$ (a) $465 \mathrm{~m} / \mathrm{s}$ (b) $492 \mathrm{~m} / \mathrm{s}$ (c) $510 \mathrm{~m} / \mathrm{s}$ (d) $560 \mathrm{~m} / \mathrm{s}$.

Key Concepts

Root Mean Square Speed

The root mean square (rms) speed is a measure used in the kinetic theory of gases to quantify the average speed of gas particles. It is computed as the square root of the average of the squares of the individual speeds of the molecules. This concept is fundamental in connecting the microscopic motions of the particles to the macroscopic property of temperature, with the rms speed being directly proportional to the square root of the temperature.

Kinetic Theory of Gases

The kinetic theory of gases explains how the properties of gases, such as pressure and temperature, emerge from the motions and collisions of their individual molecules. This theory lays the groundwork for relating microscopic particle behavior to macroscopic observables by using statistical methods. It introduces concepts like average kinetic energy and rms speed, establishing formulas that link temperature, molecular mass, and speed of the particles.

Molar Mass and Unit Conversion

In problems involving gas particle speeds, it is essential to ensure that mass units are consistent. Often, the mass of a single molecule is derived from the molar mass by converting from grams per mole to kilograms per molecule using Avogadro’s number. This unit conversion is crucial for accurately applying formulas from kinetic theory, such as the equation for rms speed, to real-world calculations.

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