After 41.0 min, 41.0% of a compound has decomposed. what is the half-life of this reaction assuming first-order kinetics?

To solve this we assume that the gas inside the balloon 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 = 293.15 x 300 / 333.15

V2 = 263.98 cm^3