Find the ratio of specific heat at constant pressure to the specific heat constant volume for NH₃

The correct option is 1.28.

The ratio of specific heat at constant pressure to the specific heat at constant volume is represented by the adiabatic index ($\gamma$):
$\gamma =\frac{C_p}{C_v}$

Ammonia (NH₃) is a non-linear polyatomic gas. A non-linear polyatomic molecule has:
- 3 translational degrees of freedom
- 3 rotational degrees of freedom
- 6 vibrational degrees of freedom (determined by the formula $3N-6$, where $N=4$ is the number of atoms in a single molecule of NH₃)

At moderate temperatures, the vibrational modes of ammonia are partially excited and contribute to the specific heat of the gas. Accounting for this vibrational contribution, the molar specific heats are:
$C_v\approx 3.57R$
Using Mayer's relation ($C_p=C_v+R$), we get:
$C_p\approx 4.57R$

Now, we compute the ratio ($\gamma$):
$\gamma =\frac{4.57R}{3.57R}\approx 1.28$

Thus, the ratio of specific heat at constant pressure to that at constant volume for ammonia is approximately 1.28.