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Ch.10 - Gases
Brown - Chemistry: The Central Science 14th Edition
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Capitolo 10, Problema 82c1

(c) Calculate the most probable speeds of CO molecules at 300 K.

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Identify the formula for the most probable speed, which is given by \( v_{mp} = \sqrt{\frac{2kT}{m}} \), where \( k \) is the Boltzmann constant, \( T \) is the temperature in Kelvin, and \( m \) is the mass of a molecule.
Convert the molar mass of CO to kilograms per molecule. The molar mass of CO is approximately 28.01 g/mol. Use the conversion factor \( 1 \text{ mol} = 6.022 \times 10^{23} \text{ molecules} \) to find the mass of one molecule in kilograms.
Substitute the values into the formula: \( k = 1.38 \times 10^{-23} \text{ J/K} \), \( T = 300 \text{ K} \), and the mass of one CO molecule in kilograms.
Calculate the expression under the square root to find the most probable speed.
Interpret the result in the context of molecular speeds, understanding that the most probable speed is the speed at which the largest number of molecules are moving at a given temperature.

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Kinetic Molecular Theory

Kinetic Molecular Theory explains the behavior of gases in terms of particles in constant motion. It posits that gas molecules are in rapid, random motion and that their kinetic energy is directly related to the temperature of the gas. This theory helps in understanding how temperature affects the speed of gas molecules, which is crucial for calculating the most probable speed.
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Kinetic Molecular Theory

Maxwell-Boltzmann Distribution

The Maxwell-Boltzmann Distribution describes the distribution of speeds among molecules in a gas. It shows that at a given temperature, molecules have a range of speeds, with a specific speed being the most probable. This concept is essential for determining the most probable speed of CO molecules at a specific temperature, such as 300 K.
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Maxwell-Boltzmann Distribution

Most Probable Speed Formula

The most probable speed of gas molecules can be calculated using the formula v_mp = sqrt((2kT)/m), where v_mp is the most probable speed, k is the Boltzmann constant, T is the temperature in Kelvin, and m is the mass of a gas molecule. This formula allows for the calculation of the speed of CO molecules at 300 K, providing a quantitative measure of their motion.
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Most Probable Speed Example
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