A vessel with a volume of 125 cm ^3 holds tritium ( ³ H , t_ 1/2 = 12.3 y ) gas at a pressure of 500 kPa and a temperature of 300 K . Determine the activity of the gas.

Step-by-step solution

Using the ideal gas equation, the number of moles of tritium gas is: n = PV RT = 500 10^3 125 10⁻⁶ 8.314 300 0.025 mol Since tritium gas ( ³ H ₂ ) is diatomic, the total number of radioactive tritium atoms is: N = 2nN_A = 2 0.025 6.022 10²³ 3.01 10²² The decay constant is: = 2 t_ 1/2 = 0.693 12.3 365.25 24 3600 1.786 10⁻⁹ s ⁻¹ The activity A of the gas is: A = N = (1.786 10⁻⁹) (3.01 10²²) 5.38 10¹³ Bq Converting the activity to Curies ( 1 Ci = 3.7 10¹⁰ Bq ): A = 5.38 10¹³ 3.7 10¹⁰ 1454 Ci The closest value among th