Calculate the kinetic energy of F 2 , Cl 2 , and Br 2 at 298 K.

Identify the formula for kinetic energy of a gas molecule: $$ KE = \frac{3}{2}kT $$, where $$ k is $$the Boltzmann constant and $$ T is $$the temperature in Kelvin.. Recognize that the kinetic energy formula $$ KE = \frac{3}{2}kT $$ applies to each molecule of the gas, regardless of the type of diatomic molecule (F_{2}, Cl_{2}, Br_{2}).. Use the given temperature $$ T = 298 \text{ K} in $$the kinetic energy formula.. Substitute the value of the Boltzmann constant $$ k = 1.38 \times 10^{-23} \text{ J/K} $$ into the formula.. Calculate the kinetic energy for each molecule type using the formula $$ KE = \frac{3}{2} \times 1.38 \times 10^{-23} \times 298 .$$

Calculate the kinetic energy of F2, Cl2, and Br2 at 298 K.

Identify the formula for kinetic energy of a gas molecule: $$ KE = \frac{3}{2}kT $$, where $$ k is $$the Boltzmann constant and $$ T is $$the temperature in Kelvin. Recognize that the kinetic energy formula $$ KE = \frac{3}{2}kT $$ applies to each molecule of the gas, regardless of the type of diatomic molecule (F_{2}, Cl_{2}, Br_{2}). Use the given temperature $$ T = 298 \text{ K} in $$the kinetic energy formula. Substitute the value of the Boltzmann constant $$ k = 1.38 \times 10^{-23} \text{ J/K} $$ into the formula. Calculate the kinetic energy for each molecule type using the formula $$ KE = \frac{3}{2} \times 1.38 \times 10^{-23} \times 298 .$$

Ch.5 - Gases

Tro - Chemistry: A Molecular Approach 4th Edition

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Tro 4th Edition

Ch.5 - Gases

문제 83b

5장, 문제 83b

Calculate the kinetic energy of F₂, Cl₂, and Br₂ at 298 K.

검증된 단계별 안내

Identify the formula for kinetic energy of a gas molecule: $ KE = \frac{3}{2}kT $, where $ k $ is the Boltzmann constant and $ T $ is the temperature in Kelvin.

Recognize that the kinetic energy formula $ KE = \frac{3}{2}kT $ applies to each molecule of the gas, regardless of the type of diatomic molecule (F₂, Cl₂, Br₂).

Use the given temperature $ T = 298 \text{ K} $ in the kinetic energy formula.

Substitute the value of the Boltzmann constant $ k = 1.38 \times 10^{-23} \text{ J/K} $ into the formula.

Calculate the kinetic energy for each molecule type using the formula $ KE = \frac{3}{2} \times 1.38 \times 10^{-23} \times 298 $.

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주요 개념

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Kinetic Energy

Kinetic energy is the energy possessed by an object due to its motion. In the context of gases, it is directly related to the temperature of the gas, as higher temperatures correspond to greater molecular speeds. The formula for kinetic energy (KE) is KE = 1/2 mv², where m is the mass and v is the velocity of the particles.

Temperature and Molecular Motion

Temperature is a measure of the average kinetic energy of the particles in a substance. At 298 K (approximately 25°C), the molecules of gases like F₂, Cl₂, and Br₂ are in constant motion, and their kinetic energy can be calculated using the ideal gas law and the principles of statistical mechanics, which relate temperature to molecular speed.

Molar Mass and Gas Properties

The molar mass of a gas affects its kinetic energy and behavior under various conditions. For diatomic molecules like F₂, Cl₂, and Br₂, the molar mass is crucial for calculating their kinetic energy at a given temperature. The heavier the molecule, the lower its average speed at the same temperature, which influences its kinetic energy.