Certain amount of gas occupies 400 ml at 17 degree C. At what temperature would the volume be reduced to half.

Let us assume the gas can be considered to be an ideal
gas. The relation between pressure P, temperature T and volume V of an ideal gas is: P*V
= n*R*T, where n is the amount of gas in moles and R is a
constant.

Here, the amount of gas is not changing and as R
is a constant we can write the ideal gas equation as P*V/T =
constant

V1 = 400 ml and T1 = 17 C or 290
K.

We need to determine the change in temperature to
decrease the volume by half. The pressure is assumed to remain constant in both the
cases.

400/290 =
(400/2)/T2

=> T2 =
290/2

=> 145 K

or -128
degree Celsius

The gas has to be cooled to -128 degree
Celsius to reduce the volume to half.