alleryStart learning →A plot of ln k against 1/T is drawn for a reaction. What does its slope equal?
AIt equals the activation energy divided by R
BIt equals minus the activation energy over R
CIt equals the natural log of frequency factor
DIt equals minus the frequency factor over R
Answer & Solution
Correct answer: B. It equals minus the activation energy over R
1. Taking natural logarithms of k = A times e to the minus Ea over RT gives ln k = (-Ea/R)(1/T) + ln A.
2. That is the straight line form y = mx + b with ln k as y and 1/T as x.
3. The slope m is therefore minus Ea divided by R.
4. So Ea is found as minus the slope multiplied by R, which keeps Ea positive since the slope is negative.
5. The intercept b is ln A, so the natural log of the frequency factor is read off the intercept and not the slope.
6. Dropping the minus sign is the usual error and would give a negative activation energy.
_Source: OpenStax Chemistry (CC BY 4.0), Ch 12 "Kinetics", section 12.5 Collision Theory_
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