## Contribution to the heat capacity by molecular motions

K Honeychurch 1K
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Joined: Fri Sep 26, 2014 2:02 pm

### Contribution to the heat capacity by molecular motions

Problem 7.29 asks you to predict the contribution to the linear heat capacity CV/m made by molecular motions of the following atoms and molecules: (a) HCN (b) C2H6 (c) Ar (d) HBr.
Can someone please explain how to go about doing this problem? Thank you.

Anuk Burli 2C
Posts: 29
Joined: Fri Sep 26, 2014 2:02 pm

### Re: Contribution to the heat capacity by molecular motions

Hi
I believe that the larger the molecule for similar types of bonding such as HCN and HBR the larger the molecule the higher the heat capacity. You also have to take into account that certain equations can predict heat capacities. For example Cp for monatomics is 5/2 R where R is the ideal gas constant, for linear it's 7/2R and for non linear it's 4R. This should help for approaching this question.

Chem_Mod
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### Re: Contribution to the heat capacity by molecular motions

The contributions to heat capacity from molecular motion are tabled on page 255, I believe.

These arise from "degrees of freedom" of a molecule, which is the number of ways it can store energy in its movements. Molecules have translational (moving around) and rotational (changing orientation) degrees of freedom.

-All molecules have 3 translational degrees, from the 3 dimensions of space.
-Monatomic substances have no rotational degrees, since no matter how you rotate a sphere it stays the same.
-Nonlinear molecules have 3 rotational degrees, from the 3 axes of rotation.
-Linear molecules have only 2 rotational degrees, since there is symmetry about one axis.

Every degree of freedom contributes R/2 to $c_{v,m}$ of the ideal gas.

Justin Le 2I
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### Re: Contribution to the heat capacity by molecular motions

The size of the molecule doesn't affect the heat capacity of atoms or molecules, the complexity of the atom or molecule does. On page 255 there is a table that gives the molar heat capacity at constant volume and constant pressure for three types: atoms, linear molecules such as CO2 and nonlinear molecules such as H2O.

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