When is a rate of reaction negative?

May 12, 2018

The rate of reaction is negative when it is defined by a reactant.

Explanation:

Rate of reaction can be defined in many ways, but the most common way is to measure the change in concentration of a species of the reaction over time. If the concentration of reactant is measured, it will decrease over time as it is consumed and so the rate will be recorded as negative (if a product is measured then the rate would be positive).

May 12, 2018

When you've gotten the sign backwards on the forward reaction.

A rate of reaction is defined to be equal to the change in concentration of the product with a coefficient of $1$ per unit time.

$a A + b B r i g h t \le f t h a r p \infty n s c C + \mathrm{dD}$

$r \left(t\right) = k {\left[A\right]}^{m} {\left[B\right]}^{n} = - \frac{1}{a} \frac{\Delta \left[A\right]}{\Delta t} = . . . = \frac{1}{c} \frac{\Delta \left[C\right]}{\Delta t}$

where $A$ and $B$ are reactants and $C$ and $D$ are products. $a \to d$ are stoichiometric coefficients.

By definition, since the product is being made, the rate of reaction is conventionally positive for the forward reaction.

If ever you calculate a negative rate of reaction, you've switched a sign. A negative rate, however, IS possible, but only if you are looking at the rate for a reactant, i.e.

$\frac{\Delta \left[A\right]}{\Delta t}$ or $\frac{\Delta \left[B\right]}{\Delta t}$.