Calculating a particles most probable speed

In summary, the most probable speed of a particle in Diatomic carbon dioxide gas (CO2) with a molar mass of 44.0 g/mol at a temperature of 281 Kelvin can be calculated using the equation V_m_p = \sqrt{\frac{2*k_B*t}{m}}. The mass should be converted to kg before plugging it into the equation, as it represents the mass of an individual particle, not per mol.
  • #1
TFM
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[SOLVED] Calculating a particles most probable speed

Homework Statement



Diatomic carbon dioxide gas (CO2) has molar mass of 44.0 g/mol is at a temperature of 281 Kelvin.

Calculate the most probable speed .

Homework Equations



[tex] V_m_p = \sqrt{\frac{2*k_B*t}{m}} [/tex]

The Attempt at a Solution



[tex] V_m_p = \sqrt{\frac{2*(1.3807*10^-^2^3)*281}{44}} [/tex]

I have also tried with

[tex] V_m_p = \sqrt{\frac{2*(1.3807*10^-^2^3)*281}{0.044}} [/tex]

with m in kg/mol, but to no avail. I am sure this is the right equation,

TFM
 
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  • #2
The m stands for mass, not mass per mol!

Convert the 44g/mol to kg first.
 
  • #3
It doesn't specify the number of moles, so is it the mass of an individual particle?

TFM
 
  • #4
I've just checked and it is.

thanks Nick89 :smile:
 

What is the equation for calculating a particle's most probable speed?

The equation for calculating a particle's most probable speed is vmp = √(2kT/m), where vmp is the most probable speed, k is the Boltzmann constant, T is the temperature in Kelvin, and m is the mass of the particle.

What is the significance of calculating a particle's most probable speed?

Calculating a particle's most probable speed can provide valuable information about the behavior and characteristics of the particle, such as its average kinetic energy and its distribution within a system.

What units are typically used for the variables in the equation for calculating a particle's most probable speed?

The units used for the variables in the equation are as follows: vmp in meters per second (m/s), k in joules per Kelvin (J/K), T in Kelvin (K), and m in kilograms (kg).

How is the most probable speed different from the average speed of a group of particles?

The most probable speed is the speed at which the largest number of particles in a group are moving, while the average speed is the overall average of all the particles' speeds in the group. This means that the most probable speed may not necessarily be the same as the average speed, as it depends on the distribution of speeds within the group.

Can the equation for calculating a particle's most probable speed be used for any type of particle?

Yes, the equation can be used for any type of particle, as long as the mass of the particle and the temperature of the system are known. However, it is most commonly used for gas particles in kinetic theory or statistical mechanics.

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