The gas-phase decomposition of sulfuryl chloride is a first-order reaction: SO ₂ Cl ₂(g) SO ₂(g) + Cl ₂(g) The initial pressure of SO ₂ Cl ₂ is 0.5 atm . After 100 s , the total pressure of the reaction mixture becomes 0.75 atm . The rate constant for the reaction is:

Step-by-step solution

For the first-order gas-phase reaction: SO ₂ Cl ₂(g) SO ₂(g) + Cl ₂(g) Let the initial pressure be P_i and the decrease in pressure at time t be x . At t = 0 : P_i , 0 , 0 At t = 100 s : P_i - x , x , x Total pressure at time t , P_t = (P_i - x) + x + x = P_i + x Therefore, x = P_t - P_i The partial pressure of the reactant at time t is: P_A = P_i - x = P_i - (P_t - P_i) = 2P_i - P_t Given P_i = 0.5 atm and P_t = 0.75 atm : P_A = 2(0.5) - 0.75 = 1.0 - 0.75 = 0.25 atm The first-order rate constant is: k = 2.303 t P_