Heat Capacity of a Monoatomic Ideal Gas (9.13)

[Nivi Ahlawat 3I]

If the heat capacity of a monoatomic ideal gas is Cp = 5/2 R, then for question 9.13, why don't we use this value, as used in 9.7 for part a? Similarly, why is the Cv = 3/2 R value for monoatomic ideal gas used for 9.7, and not for 9.13?

[Ronald Yang 2F]

I'm looking at question 9.13, and it seems like the gas is nitrogen gas. Nitrogen gas isn't a monoatomic gas. It's a linear molecule, since it's N₂. I'm guessing that's why we don't use the heat capacities for a monoatomic ideal gas.

[Chem_Mod]

Nitrogen N2 is diatomic. For diatom, Cv=5/2R instead of 3/2R.

[Kayti Luu 2B]

Hi, I'm a bit lost as to where the formula 5/2R and 3/2R is derived from. Is it something we are just given to memorize? Could someone explain that please? Thank you!

[Chem_Mod]

The heat capacity of an ideal gas is given 1/2 R for each "degree of freedom" corresponding to its translational, rotational, and vibrational(at high temperature only) motions. The reason it is 1/2 R is derived from something called the kinetic theory of ideal gas. For example, a monatomic ideal gas has 3 translational freedoms and 0 others, so it gets 3/2 R for Cv. and Cp = Cv+R which is another thing that can be proved mathematically.

For this class, the values 3/2 R and 5/2 R can simply be memorized though (with the understanding that they only apply to monatomic ideal gas)

[Emma McGinnis 1G]

when applying these formulas, the R is always 8.314 correct?

[204643643]

As far as I understand, R is not necessarily always going to be 8.314. We use that value when we are solving a problem that deals with Joules. But if we are solving a problem that has to do with atm and Liters, the value 0.082 is used.

[Hayley Hammons 1L]

Referring to the original question, the solution manual should have used Cv=5/2R instead of just R when calculating part b for ∆T. This correction is listed under solution manual errors on the Chemistry 14B website.