The activation energy, Ea, for a zeroth-order reaction, X-->products, is most readily obtained from the slope of a plot of: (choose from below)

-[X] vs time
-ln k vs time
-rate vs time
-[X]^2 vs time
-ln[X] vs time
-1/[X] vs time
-ln k vs 1/T, where T is temperature in
-ln k vs T, where T is temperature in K
-k vs 1/T, where T is temp in K

I thought it was the 3rd last answer but im not too sure.

Thanks!

If plot ln k vs 1/T

then slope = -Ea/RT

To determine the activation energy, Ea, for a zeroth-order reaction, you need to plot ln k (the natural logarithm of the rate constant) against 1/T (the reciprocal of the temperature in Kelvin). The correct answer is "ln k vs 1/T, where T is the temperature in K."

Here's an explanation of how to arrive at this answer:

1. Understand the reaction order: For a zeroth-order reaction like X -> products, the rate of the reaction does not depend on the concentration of the reactant X. In a zeroth-order reaction, the rate equation is: rate = k, where k is the rate constant.

2. Arrhenius equation: The Arrhenius equation is widely used to relate the rate constant (k) with the activation energy (Ea), temperature (T), and other factors. The equation is written as: k = Ae^(-Ea/RT), where A is the pre-exponential factor, R is the ideal gas constant, and e is Euler's number.

3. Linearize the Arrhenius equation: To obtain the activation energy, Ea, we need to linearize the Arrhenius equation. Taking the natural logarithm of both sides of the equation gives: ln k = ln A - (Ea/RT). This equation is of the form y = mx + c, where y = ln k, x = 1/T, m = -Ea/R, and c = ln A.

4. Plotting the linearized equation: By plotting ln k on the y-axis and 1/T on the x-axis, the graph would appear as a straight line. The slope of the line will be -Ea/R, where R is the ideal gas constant. Therefore, the slope of the plot gives the activation energy (Ea).

In summary, to obtain the activation energy, Ea, for a zeroth-order reaction, you need to plot ln k against 1/T, where T is the temperature in Kelvin. The slope of this plot will give you the activation energy.