Final answer:
The rate constant for the gas phase decomposition of t-butyl acetate at 533 K is calculated using the Arrhenius equation, given the slope and y-intercept from a ln(k) versus 1/T plot. The calculated rate constant at 533 K is approximately 0.0005 s⁻¹.
Step-by-step explanation:
The question involves using the Arrhenius equation to find the rate constant for the gas phase decomposition of t-butyl acetate at a specific temperature. The Arrhenius equation in its logarithmic form is ln(k) = -Ea/(R*T) + ln(A), where k is the rate constant, Ea is the activation energy, R is the gas constant, and T is the temperature in Kelvin. The slope from the plot of ln(k) versus 1/T is equivalent to -Ea/R, and the y-intercept corresponds to ln(A), where A is the frequency factor.
Given the slope of the line (-2.04x10⁴ K) and the y-intercept (30.7), we can use the equations to calculate the rate constant at 533 K. First, multiply the slope by the negative of the gas constant in its appropriate units, which is -8.314 J/(mol*K), and then by the temperature (533 K). Add the product to the y-intercept, and take the exponential to obtain k in s⁻¹:
ln(k) = (-2.04x10⁴ / 533) + 30.7
= -38.29 + 30.7
= -7.59
k = e^(-7.59)
k = 0.0005 s⁻¹
Therefore, the rate constant at 533 K is approximately 0.0005 s⁻¹.