How Do You Calculate the Average Square Speed of Argon Molecules?

In summary, the average square speed of argon molecules can be calculated using the formula derived from the kinetic theory of gases. This involves determining the average kinetic energy of the molecules, which is given by the equation \( \langle v^2 \rangle = \frac{3kT}{m} \), where \( k \) is the Boltzmann constant, \( T \) is the absolute temperature in Kelvin, and \( m \) is the mass of an argon molecule. By substituting the appropriate values for these variables, one can compute the average square speed of argon molecules in a gas sample.
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petar rezek
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Homework Statement
3. a) Calculate the mass of argon that at 13°C, in a volume of 50 liters, presses the walls with a pressure of 5.10¹ Pa.
b) What is the internal energy of the gas at that temperature?
c) What is the average square speed of the molecules? A, (Ar) = 39,948
needed help with question C)
Relevant Equations
pv=nRT
U=NEk=3/2NkT=3/2nRT
In the images you can see what I did I need someone to check answers and show me how to do C part of question
 

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In addition to being annoyingly sideways, your images are unreadable. If you are going to ask people to do you the favor of helping you with something, you should make it easy for them, not hard.
 
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petar rezek said:
Homework Statement: 3. a) Calculate the mass of argon that at 13°C, in a volume of 50 liters, presses the walls with a pressure of 5.10¹ Pa.
b) What is the internal energy of the gas at that temperature?
c) What is the average square speed of the molecules? A, (Ar) = 39,948
needed help with question C)
Relevant Equations: pv=nRT
U=NEk=3/2NkT=3/2nRT

In the images you can see what I did I need someone to check answers and show me how to do C part of question
Welcome to PF.

Please start a new thread in the Homework Help, Introductory Physics forum, and type your work into the forum window using LaTeX for the equations. I will send you a Private Message (PM) now with some hints on how to use LaTeX.

When you repost, please also use a more descriptive thread title -- the title should reflect the question being asked in the thread. Thank you.
 

FAQ: How Do You Calculate the Average Square Speed of Argon Molecules?

What is the formula for calculating the average square speed of Argon molecules?

The formula to calculate the average square speed (or mean square speed) of Argon molecules is given by the equation: \( \langle v^2 \rangle = \frac{3k_B T}{m} \), where \( \langle v^2 \rangle \) is the mean square speed, \( k_B \) is the Boltzmann constant, \( T \) is the absolute temperature in Kelvin, and \( m \) is the mass of a single Argon molecule.

How do you find the mass of a single Argon molecule?

The mass of a single Argon molecule can be found by dividing the molar mass of Argon by Avogadro's number. The molar mass of Argon is approximately 39.95 g/mol. Therefore, the mass of a single Argon molecule is \( m = \frac{39.95 \, \text{g/mol}}{6.022 \times 10^{23} \, \text{molecules/mol}} \approx 6.63 \times 10^{-26} \, \text{kg} \).

What is the Boltzmann constant and its value?

The Boltzmann constant (\( k_B \)) is a physical constant that relates the average kinetic energy of particles in a gas with the temperature of the gas. Its value is approximately \( 1.38 \times 10^{-23} \, \text{J/K} \).

How does temperature affect the average square speed of Argon molecules?

The average square speed of Argon molecules is directly proportional to the absolute temperature. As the temperature increases, the average square speed of the molecules also increases. This relationship is expressed in the formula \( \langle v^2 \rangle = \frac{3k_B T}{m} \).

Can you provide an example calculation for the average square speed of Argon molecules at room temperature?

Sure! Let's calculate the average square speed at room temperature (298 K). Using the formula \( \langle v^2 \rangle = \frac{3k_B T}{m} \), where \( k_B = 1.38 \times 10^{-23} \, \text{J/K} \), \( T = 298 \, \text{K} \), and \( m \approx 6.63 \times 10^{-26} \, \text{kg} \):\[ \langle v^2 \rangle = \frac{3 \times 1.38 \times 10^{-23} \times 298}{6.63 \times 10^{-26

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