To solve this we assume that the sample gas is an ideal gas. Then, we can use the ideal gas equation which is expressed as PV = nRT. At a constant pressure and number of moles of the gas, the ratio T/V is equal to some constant. At another set of condition of temperature, the constant is still the same. Calculations are as follows:
T1 / V1 = T2 / V2
V2 = T2 x V1 / T1
V2 = 350 K x 500 mL / 150 K
V2 = 1166.67 mL
Therefore, the new volume of the system from the temperature change would be 1166.67 mL or about 1.2 L.