A gas is at a temperature of 326.0 K and pressure of 810.0 mm Hg. At constant volume, it is cooled down to 273.0 K. Showing and explaining each step, calculate the final pressure.

According to the Gay-Lussac's law, the pressure of a given amount of gas, held at a constant volume, is directly proportional to its temperature (in Kelvin scale).
In other words,

P alpha T

where, P and T are the pressure and temperature of the gas, respectively.
This relation can also be thought of as P/T = constant (at a constant volume).
This relation can be further extended to

P1/T1 = P2/T2

where P1 and P2 are the gas pressures at temperatures T1 K and T2 K, respectively.
In the given question, P1= 810 mm Hg, T1 = 326 K and T2 = 273 K.
Using the above relationship,

P2 = (P1/T1). T2
= (810/326). 273 = 678 mm Hg.

Thus, when the gas is cooled to 273 K at constant volume, its pressure will be 678 mm Hg.
Hope this helps!