**The rate constant of a reaction
can be expressed as**

**k = Ae ^{-Ea/RT} **

** which is called the Arrhenius
equation. Taking the natural log of both sides of the Arrhenius equation gives**

**ln k = -Ea/R(1/T) + ln A **

The equation above is of the form y = mx + b, where y = ln k, m = -Ea/RT, x = 1/T, and b = ln A. For a reaction whose rate constant obeys the Arrhenius equation, a plot of ln k vs 1/T gives a straight line and it's slope can be used to determine Ea.

Sample data shown in the following table was used to produce the two graphs.

Temp |
Temp ^{-1} |
Average Time |
Rate Of Reaction |
Rate Constant (k) |
ln k |
---|---|---|---|---|---|

(K) |
(K^{-1}) |
(s) |
(M/s) |
(M^{-3}s^{-1}) |
() |

277 |
3.61 x 10 ^{-3} |
289 |
4.8 x 10 ^{-8} |
15 |
2.7 |

295 |
3.39 x 10 ^{-3} |
173 |
8.1 x 10 ^{-8} |
25 |
3.2 |

311 |
3.22 x 10 ^{-3} |
74 |
1.9 x 10 ^{-7} |
58 |
4.1 |

Using the slope from the graph displaying the trendline:

Slope = -3.2549 K x 1000 = -3300 K

Slope = -Ea/R

Ea = -Slope x R = -(-3300

~~K~~x 8.314 J mol^{-1}~~K~~)^{-1}Ea = 27000 J mol

^{-1}= 27 kJ mol^{-1}

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