The ideal gas law can be used to find the initial volume
of the gas. This law provides the relation between volume V, pressure P, temperature T
and the amount of substance n as P*V = n*R*T, with R being the gas
constant.
The information we have gives the initial
pressure as 0.5 atm, initial temperature as 325 K, the final pressure as 1.2 atm, final
temperature as 320 K and final volume as 48 L. Let the initial volume of the gas be V.
Substitute these values in the gas equation
0.5*V =
n*R*325
=> 0.5*V/325 =
n*R
and 48*1.2 =
n*R*320
=> 48*1.2/320 =
n*R
Equate the terms that are equal to n*R as that is a
constant here.
0.5*V/325 =
48*1.2/320
=> V =
48*1.2*325/320*0.5
=> V = 117
L
The initial volume of the gas was 117
L.
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