Suppose that the average velocity (vrms) of carbon dioxide molecules (molecular mass is equal to

step 1 So we know that the average velocity, the VRMS, is 1 .05 into 10 .5 meter per second. We also kn

Suppose that the average velocity (vrms) of carbon dioxide...

Suppose that the average velocity $\left(v_{\mathrm{rms}}\right)$ of carbon dioxide molecules (molecular mass is equal to $44.0 \mathrm{g} / \mathrm{mol}$ ) in a flame is found to be $1.05 \times 10^{5} \mathrm{m} / \mathrm{s}$. What temperature does this represent?

Key Concepts

Root-Mean-Square Speed

The root-mean-square (rms) speed is a statistical measure of the speed of particles in a gas and is directly related to the temperature of the system. It is defined as the square root of the average of the squares of the individual speeds and is used to link thermal energy with the motion of particles.

Molar Mass and Molecular Mass Conversion

In gas behavior calculations, it is often necessary to convert the molar mass of a substance into the mass of a single molecule. This conversion is performed using Avogadro's number, allowing the application of formulas derived from kinetic theory on a per-particle basis.

Boltzmann Constant

The Boltzmann constant is a fundamental physical constant that relates the average kinetic energy of particles in a gas with the temperature of the gas. It serves as a bridge between the macroscopic and microscopic worlds by linking temperature with energy at the molecular level.

Kinetic Molecular Theory

This theory explains the behavior of gases by considering them as a collection of moving particles, where temperature is directly related to the average kinetic energy of the molecules. It establishes connections between the microscopic motion of particles and macroscopic properties such as pressure and temperature.

Equipartition of Energy

The equipartition theorem states that energy is equally distributed among all available degrees of freedom in a system at thermal equilibrium. For translational motion in three dimensions, this implies that each molecule has an average kinetic energy proportional to the temperature, typically expressed as (3/2)kT.

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