5.1.1 (c) Using the rate equation

Syllabus

(c) Using the rate equation

• calculation of the rate constant, k, and related quantities, from a rate equation including determination of units

What does this mean?

Calculating the rate constant.

This is a firm favourite question from examiners.

Given a rate equation such as Rate = k[Br₂][NO]²

And given data such as:

It's possible to calculate the rate constant by re-arranging the rate equation.

k =[Br₂][NO]² /Rate

k = 0.02 x (0.04)²/0.352

k = 0.000032 / 0.352 = = 0.00091

If we had data from more than one experiment it wouldn't matter which we chose, we should still calculate the same number.

Units of Rate Constant.

If an examiner asks you to calculate the rate constant then (s)he will almost always also ask you to work out its units.

These can vary depending on the rate equation so there's no point trying to just learn them.

The easiest way is to re-arrange the rate equation for k and then cancel units.

eg 1.

Rate = k[A]

k = Rate/[A]

Units: k = moldm^-3s^-1/moldm^-3

So, the units are s^-1

eg 2.

Rate = k[A][B] (or Rate = k[A]2)

k = Rate/[A][B]

Units: k = moldm^-3s^-1/moldm^-3 x moldm^-3

So, the units are s^-1/moldm^-3 = mol^-1dm³s^-1

eg 3.

Rate = k[A][B][C] (or Rate = k[A]2[B])

k = Rate/[A][B][C]

Units: k = moldm^-3s^-1/moldm^-3 x moldm^-3x moldm^-3

So, the units are s^-1/mol²dm^-6 = mol^-2dm⁶s^-1

Note that unlike the equilibrium constant (K_c) it is impossible for the rate constant to have no units.

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