The rate constant for the gas phase decomposition of t-butyl acetate at 527 K is approximately 2.76×10^−9 s^−1.
The rate constant (k) for a chemical reaction can often be temperature-dependent and is commonly expressed using the Arrhenius equation, which relates k to temperature. When ln k is plotted against the reciprocal of the Kelvin temperature (1/T), the resulting graph should yield a straight line. In the given scenario for the gas phase decomposition of t-butyl acetate, the slope of this line is provided as -2.04×10⁴ K, and the y-intercept is 30.7.
These parameters are part of the linearized form of the Arrhenius equation, ln k= -Ea/r+(1/t) +ln (A), where Ea is the activation energy, R is the gas constant, T is the temperature, and A is the pre-exponential factor. From the given information, the slope −Ea /R can be equated to the provided value, allowing for the determination of Ea. Subsequently, the value of k at 527 K can be calculated using the Arrhenius equation with the obtained activation energy and the given y-intercept. The resulting rate constant at 527 K is approximately 2.76×10^−9 s^−1.