# Does the equilibrium constant have units?

1. Jan 27, 2012

### jetwaterluffy

According to my teacher in my chemistry lesson, the equilibrium constant has different units depending on how many moles of reactant and product there are. But the idea of a constant which changes it's units depending on the situation seems a bit dodgy to me, especially as it seems to be related to ratios, and I though ratios are meant to be dimensionless.
Also, the units seem to be based on which power the concentration is to, but seeing as that depends on the moles of the reactants, which is a variable in itself, I would have thought it wouldn't change the units, so I think it is dimensionless. I did some research on this, and some websites confirm my idea, some confirm my teacher's. (I'm going with my teacher's viewpoint for the sake of the exam, anyway, but I want to know which is right.)
So which is true? Is it dimensionless, or do the units change depending on the situation?
(If this would be more appropriate in the homework help section, please move it.)

2. Jan 27, 2012

### chemisttree

Nope. Expressing the ratio of a certain distance traveled within a certain time can be expressed as a ratio, for example (km/hr).

The molar ratio between reactants and products is always fixed. This is referred to as the reaction stoichiometry. The amount of the reactant can change (#moles) but the ratio of the #moles of reactant to the #moles of product will remain fixed for a particular reaction.

So if you look at the definition of equilibrium (expressed as a mathematical equation) you will see the answer, regardless of how counterintuitive it may seem to you. Teacher is right.

3. Jan 27, 2012

### asym

Your teacher is NOT right. However your arguments are not valid either. It's a bit obscure, read carefully.

Proper definition of equilibrium constant involves ratio of activities, not concentrations, and activities are dimensionless by definition.

Ex.:
$$K = \frac{a_{{\rm H}^+} a_{{\rm A}^-}}{a_{\rm HA}}$$

Activity may be expresed as a product of an activity coefficient and the relative concentration, which is dimensionless as well, because it is calculated as molar concentration divided by standard concentration, which is conventionaly chosen to be $$c_0 = 1~{\rm mol/l}$$.

Ex.:
$$a_{{\rm H}^+} = \gamma_{{\rm H}^+}[{\rm H}^+] = \gamma_{{\rm H}^+}c_{{\rm H}^+}/c_0$$

In textbook examples we usually simplify calculations by setting activity coefficients to unity, thus equilibrium constant is expressed in relative concentrations

$$K = \frac{[{\rm H}^+][{\rm A}^-]}{[{\rm HA}]}$$

At this step people (even specialists and authors of textbooks) often forget, than concentrations are still relative = dimensionless.

This is the contemporary view - you might find different and less consistent approach in historical books.

Last edited: Jan 27, 2012
4. Jan 28, 2012

### jetwaterluffy

So basically neither of us are right? Good to know.

5. Jan 28, 2012

### Amok

Equilibrium constant, as it is properly defined (through the mass action law), has no units. What asym said is correct. Chemistry teachers deliberately teach the "wrong" definition to avoid talking about activities or fugacities divided by standard pressure (a dimension-less ratio). Even with your teacher's definition, the equilibrium constant does not depend on how many moles of reactant are there. Do not confuse stoichiometric coefficients with number of moles

Last edited: Jan 28, 2012
6. Feb 8, 2012

### chemisttree

Be careful here! The teacher was obviously referring to the number of moles as the stoichiometric coefficient since the context was in the determination of units. And in that case the equilibrium expression, whether defined in terms of concentration or activity, most certainly depends upon the 'number of moles'.

Since the teacher chooses to express the equilibrium constant in terms of concentration, THE EQUILIBRIUM CONSTANT WILL HAVE UNITS... it doesn't matter if it is used as a dimensionless quantity. If the teacher expresses it in terms of concentration, you must use units for full marks. Teacher is right.

7. Feb 8, 2012

### Amok

The teacher is right about a wrong definition, that's what I'm saying, and I think that's what the OP wanted to know.

8. Feb 8, 2012

### DrDu

That's exactly why students soon start to hate chemistry and physicists make jokes about it.

9. Feb 8, 2012

### Amok

Well, sometimes you have to simplify chemistry since it deals with very complex system. But I understand what you are saying. Having been TA for a chemistry class given to physics students, I totally get that. I think there are some very weird things about how chemistry is taught, especially considering how close to physics Chemistry 101 subjects actually are.