Question

given the lewis structures provided in the image, which would you expect to have the larger heat capacity, oxygen or methane?
oxygen
methane
dont test me yet, i am trying to gain an understanding before attempting to answer this question.

Explanation:

Step1: Consider degrees of freedom

Methane (\(CH_4\)) is a poly - atomic molecule. Poly - atomic molecules have more degrees of freedom (translational, rotational, and vibrational). Oxygen (\(O_2\)) is a di - atomic molecule.

Step2: Relate degrees of freedom to heat capacity

The molar heat capacity (\(C_v\) or \(C_p\)) is related to the number of degrees of freedom (\(f\)). The formula for molar heat capacity at constant volume is \(C_v=\frac{f}{2}R\) (where \(R\) is the gas constant). Methane has more degrees of freedom. For a di - atomic molecule like \(O_2\), at moderate temperatures, \(f = 5\) (3 translational and 2 rotational). For a poly - atomic molecule like \(CH_4\), \(f> 5\) (3 translational, 3 rotational and some vibrational at higher temperatures).

Answer:

Methane