How to Calculate the Most Probable Speed of CO2 at 305 K?

[6021023]

Homework Statement

Diatomic carbon dioxide gas (CO2 has molar mass of 44.0 g/mol) is at a temperature of 305 K.

Calculate the most probable speed v_mp.

Homework Equations

v_mp = sqrt(2kT/m)

The Attempt at a Solution

v_mp = sqrt(2 * 1.3801 * 10^-23 * 305 / 44)

v_mp = 1.383 * 10^-11

 

[naresh]

How about you write down the units of all the numerical values you substituted? It is always good practice to do this, and cancel out the units.

 

[6021023]

I can see that m is not simply 44 mol. It needs to be in kg. m = M/N_A. The units for M is g/mol. What are the units for N_A, Avogadro's number?

 

[naresh]

well, it's a number...

6.023E23 particles/mole

 

[6021023]

Then

v_mp = sqrt(2 * 1.3801 * 10^-23 (m^2 * kg / (s^2 * K) * 305 K / (44 g/mol / (6.02E23 particles/mol) * kg/1000g)

This ends up with the units being sqrt(m^2/s^2 * particles)

Is that correct?

 

[naresh]

heh, well particles isn't really a physical unit (neither is mol). So what you really have is sqrt(m^2/s^2).

 

[6021023]

Got it. The answer was 339 m/s. Thanks!

 

[naresh]

Looks like molecules should be moving a little faster than that. Check your math. The approach is correct, however.