Calculating the energy used during electrolysis of NaCl
Let's reformulate your equations a little bit.
The ideal gas law was just fine:
$$n = \frac{p V}{RT}$$
A problem lies in your formulation of Faradays law.
We are not interested in masses, but in moles. Of course it is interchangeable by using the molar mass, but why make things complicated. As a rule of thumb you can remember for such tasks: Convert from mass in the beginning and convert to mass in the end (if needed). Nearly all equations in "the middle" are based on the concept of fixed relationsships between the number of involved particles and all equations are much easier to understand if you use $n$.

Faradays law means that the overall charge is just the product of charge per particle times the number of particles:
$$
Q = nzF
$$

The energy is just the product of $Q$ and $U$ divided by $\mu$. You don't need time and amperage. 
This gives:
$$
E = \frac{QU}{\mu} = \frac{zFpVU}{RT\mu}
$$

Unfortunately when putting values into these equations you get another result. The following python code will give 448.4 kWh as result. I think that your result is correct and our difference results from differently used constants...:

constants = {}
constants['F'] = 96485.33289
constants['R'] = 8.314
conversion = {}
conversion['to kWh'] = 2.7777e-07

n = lambda p, V, T : p * V / (constants['R'] * T)
Q = lambda n, z : n * z * constants['F']
E = lambda Q, U, mu : Q * U / mu
# Using p=1.01325*10^5 Pa, V=100m^3, T=298K, z=1, U=3.6V, mu=0.88
print(E(Q(n(1.01325e5, 100, 298), 1), 3.6, 0.88) * conversion['to kWh'], 'kWh')