The problem states that there are initially 21 liters of a gas at a pressure of 78 atm. and the temperature of the gas is 900 K. The pressure is decreased to 45 atm. and the temperature is decreased to 750 K. The new volume as a result of the changes in the pressure and temperature has to be found.
This can be done using the ideal gas law. We have P*V = n*R*T, where P is the pressure, V is the volume, n is the amount of substance, R is a constant and T is the temperature. As the amount of the substance making up the gas n is a constant, the equation can be written as n*R = P*V/ T
Now the initial values and the final values that are known are substituted. Let the final volume be V.
21*78/900 = V*45/750
=> V = 21*78*750/900*45
=> V = 91/3 L
The required volume of the gas after the changes in pressure and temperature are made is 30.33 L.