## Units for K

$K = \frac{k_{forward}}{k_{reverse}}$

Emma Randolph 1J
Posts: 65
Joined: Fri Sep 28, 2018 12:29 am

### Units for K

Why do units change for k depending on the order of the reaction?

Celine Cheng 1H
Posts: 33
Joined: Fri Sep 28, 2018 12:21 am
Been upvoted: 1 time

### Re: Units for K

Rate is usually expressed in M/s (though I've seen it expressed with different time units)

Since you have rate = k [reactant] [reactant] ...
Every [reactant] must have a concentration with unit M
If you have 1 reactant, you have rate = k [reactant] so the units are M/s = k (M), so k's units are 1/s (or s^(-1))
Is you have 2 reactants, you have rate = k [reactant] [reactant] so the units are M/s = k (M) (M), so k's units are 1/( M s )
and so on for diff order reactions

Arshiya
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Joined: Fri Sep 28, 2018 12:16 am
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### Re: Units for K

Because the units for the rate is Molarity/second, the different ordered reactions will have different units for k in order to have the M/s rate unit. Therefore for first-order reactions, k is 1/s. For second order reactions, k is 1/M*s.

Margaret Akey
Posts: 80
Joined: Fri Sep 28, 2018 12:18 am

### Re: Units for K

zero order: rate = k
first order: rate = k[A]
second order: rate=k[A]^2

rate is always Molarity/second or Moles*Second^-1*Liters^-1

so when you have just rate = k for zero order.. Molarity/second needs to equal k, so k is Molarity/second (easy!)

Now, when you have rate= k[A] for first order.. Molarity/second needs to equal Concentration*k which is also just saying Molarity*k so k needs to be Seconds^-1 so that [A]*k equals Molarity/Second to equal rate units. (still fairly straight forward)

finally, when you have rate=K[A]^2 you still have Molarity/second which is the units for rate.. but now you have Molarity^2*k, you need to divide Molarity^2 by Molarity to get just one Molarity on the top, and you need to divide by seconds also to get seconds on the bottom. therefore k=molarity^-1*seconds^-1, this is also equal to L*mol^-1*sec^-1 if you expand molarity units

Nicholas Le 4H
Posts: 74
Joined: Fri Sep 28, 2018 12:24 am

### Re: Units for K

The units for k change depending on the order so that it can produce the correct units for the rate which is always in molarity per second.