A textbook first-order continuous gaseous decomposition happens exclusively confined inside an isoth — Chemical Kinetics Chemistry Question
Question
A textbook first-order continuous gaseous decomposition $A(g) \rightarrow B(g) + C(g)$ happens exclusively confined inside an isothermal, inflexible flask. The starting reading consists solely of pure reactant gas $A$ sitting at a robust pressure of $100 \text{ torr}$. Carefully recorded exactly $50 \text{ minutes}$ later, the overall gross atmospheric pressure inside has surged significantly to $150 \text{ torr}$. Deduce the definitive integer value representing the half-life of this gas reaction in minutes.
💡 Solution & Explanation
Operating the stoichiometry table: Initially $P_A = 100$. Post reaction $t=50$: $P_A = 100 - x$, $P_B = x$, $P_C = x$. Total pressure sum equates $100 + x = 150$, solving instantly to $x = 50 \text{ torr}$. Consequently, evaluating the residual unreacted target gas provides $P_A = 100 - 50 = 50 \text{ torr}$. Because the residual pressure of $A$ has strictly dropped uniformly to exactly $50\%$ of its origin boundary ($100 \rightarrow 50$), the elapsed block of $50 \text{ minutes}$ formally represents precisely one whole fundamental half-life.