Decomposition of a certain substance Y at 45 °C was found to be zero order. What is the half-life of substance Y if it took 15.5 minutes to decompose 67% of this substance? [Y]₀ = 0.25 M.

• A. 0.058 min
• B. 0.029 min
• C. 12 min
• D. 23.5 min

Answer: (C)

Verified step by step guidance

1. Identify that the reaction is zero order, which means the rate of decomposition is constant and independent of the concentration of substance Y.
2. Recall the integrated rate law for a zero-order reaction: \[ [Y] = [Y]_0 - k t \] where \[ [Y]_0 \] is the initial concentration, \[ k \] is the rate constant, and \[ t \] is time.
3. Use the information that 67% of the substance decomposes in 15.5 minutes. Calculate the remaining concentration after 15.5 minutes: \[ [Y] = [Y]_0 \times (1 - 0.67) \].
4. Substitute the known values into the zero-order rate law to solve for the rate constant \[ k \]: \[ k = \frac{[Y]_0 - [Y]}{t} \].
5. Use the formula for the half-life of a zero-order reaction: \[ t_{1/2} = \frac{[Y]_0}{2k} \] to calculate the half-life of substance Y.