Equilibrium constants help Enough work for 8 marks?

[westy6711]

Activation energy from a decomposition.

Homework Statement

. The rate constant for the decomposition of C2H6 is given in the table below. Calculate the activation energy.

105 k/s Temperature/K
2.5 823
4.7 833
8.2 843
12.3 853
23.1 863
35.3 873
57.6 883
92.4 893
141.5 903

The Attempt at a Solution

This is what i have so far...

Ea = R x (("T1" x "T2") / ("T2" - "T1")) x ln("k2" / "k1")

8.314 x (823 x 903) / (903 – 823) x In(141.5 / 823) = ?

I haven't a clue if this is even right, am i meant to plot a graph?

Any help would be very much appreciated.

 

[cheme101]

I don't quite follow your table, but here's a general solution.

For rate laws, the equation relating k to temperature is k = A * exp(-ΔE/RT).

So you need to use your existing data and fit it to the equation by finding the constants A & ΔE (A is an arbitrary constant & ΔE is the activation energy).

If you take the natural log of both sides, you will get

ln k = ln A + (-ΔE/R)(1/T)

That can be graphed:
y-coordinate= ln k
y-intercept= ln A
x-coordinate = 1/T
slope = -ΔE/R

SO: If you graph ln k vs 1/T from your data, then multiply the slope by R, you will get your activation energy.

 

[westy6711]

Thank you so much, That did it :)