variation of the rate constant with temperature for the first order reaction 2N2O(g) = 2N2O4(g) + O2(g) is given in the following table. determine graphically the activation energy for the reaction. |t(k)|273 298 318 338 |k(second)| 7.87 x 10^3. 3.46 x 10^5. 4.98 x 10^6. 4.87 x 10^7.

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What is the order of reaction

To determine the activation energy for the given reaction, we can use the Arrhenius equation, which relates the rate constant (k) to the temperature (T) and the activation energy (Ea):

k = Ae^(-Ea/RT)

Where:
k is the rate constant
A is the pre-exponential factor (a constant)
Ea is the activation energy
R is the gas constant (8.314 J/(mol·K))
T is the absolute temperature

To determine the activation energy graphically, we need to plot ln(k) against 1/T and calculate the slope of the resulting graph, which is equal to -Ea/R.

Let's start by calculating the values of ln(k) for the given temperatures:

| t(k) | 273 | 298 | 318 | 338 |
|------|-----|-----|-----|-----|
| ln(k) |value of ln(k) can be calculated by taking the natural logarithm (ln) of each k value.|
| | | | | |

Now, we will plot ln(k) against 1/T (in Kelvin) on a graph with ln(k) on the y-axis and 1/T on the x-axis.

Next, draw a best-fit line through the data points.

Finally, calculate the slope of the line, which is equal to -Ea/R. Rearrange the equation to solve for Ea:

Ea = -slope * R

Substitute the value of R (8.314 J/(mol·K)) into the equation to find the activation energy.