Question

For the gas phase decomposition of t-butyl bromide,

(CH₃)₃CBr(CH₃)₂C=CH₂ + HBr

the rate constant in s-1 has been determined at several temperatures. When ln k is plotted against the reciprocal of the Kelvin temperature, the resulting linear plot has a slope of -2.04×10⁴ K and a y-intercept of 30.6.

The value of the rate constant for the gas phase decomposition of t-butyl bromide at 542 K is _______ s⁻¹.

(Enter your answer to one significant figure.)

Answer 1

The rate constant for the gas phase decomposition of t-butyl bromide at 542 K is determined using the Arrhenius equation with a given slope and y-intercept from the ln(k) versus 1/T plot. The calculation results in a rate constant of approximately 0.0009 s-1 when rounded to one significant figure.

Step-by-step explanation:

The rate constant for the gas phase decomposition of t-butyl bromide at a given temperature can be determined using the Arrhenius equation, which in its linear form is ln(k) = -Ea/R(1/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 of the plot of ln(k) versus 1/T is -Ea/R, and the y-intercept is ln(A).

In this case, we are given that the slope of the linear plot is -2.04×104 K and the y-intercept is 30.6. To find the rate constant at 542 K, we use these values in the linear form of the Arrhenius equation:

ln(k) = (-2.04×104 K)(1/542 K) + 30.6

ln(k) = -37.6397 + 30.6

ln(k) ≈ -7.0397

Taking the exponential of both sides gives us k:

k = e-7.0397

k ≈ 0.000881

Since we need to provide the answer to one significant figure, the rate constant is approximately 0.0009 s-1 at 542 K.