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!

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