Question

Molecules of species A are reacting with molecules of species B. The concentration of A, given in moles per liter, follows the equation

CA = CA0 ( 1-e-k·t )

where t is time, given in minutes, CA is concentration in M, and CA0 is the initial concentration. What would be the units for the parameter k?

Answer 1

Units for parameter k would be
`minutes^(-1)`.

Explanation:

The concentration of CA0 is given in M (moles per liter), which is the unit for CA; if we show units inside parenthesis in the equation, it would be:

`CA (M)=CA0 (M) *(1-e-k(?)*t(minutes))`

For the concentration units of CA0 not to be affected by the units of the factor (1-e-k*t), this factor would have to be a number without units.

Since 1 is a constant without units, for the constant e to be able to subtract from 1 it would have to be a number without units, which also applies to the factor k*t.

For the factor k*t to be a number without units, k must have units that can be canceled when multiplied by t, which is given in minutes, so k must have units of
`(1)/(minutes) =minutes^(-1)`

This can be confirmed by operating the equation using only its units (units of parameter k are noted by a question mark):

`M=M(0-0-?*minutes)`

`(M)/(M) =?*minutes`

`1=?*minutes`

`(1)/(minutes)=?`

`minutes^(-1)=?`