The decomposition of PH ₃ follows first order kinetics. The time required for 3 / 4^ th of PH ₃ to decompose is 75.76 s . Calculate the fraction of original amount of PH ₃ which will remain after 2.0 minutes.

Step-by-step solution

For a first order reaction, the rate constant k is given by k = 2.303 t ( [A]₀ [A]_t ) . Given that 3/4 of PH ₃ decomposes, the remaining amount [A]_t = [A]₀ - 3 4 [A]₀ = 1 4 [A]₀ . Substituting the values for t = 75.76 s: k = 2.303 75.76 ( [A]₀ [A]₀ / 4 ) = 2.303 75.76 (4) = 2.303 0.602 75.76 0.0183 s ⁻¹ . Now, calculate the fraction remaining after t = 2.0 minutes, which is 120 seconds. Using the integrated rate law: ( [A]₀ [A]_t ) = kt 2.303 . ( [A]₀ [A]_t ) = 0.0183 120 2.303 2.196 2.303 0.9535 . Therefore, [A]