‘Q’

‘Q’ is a character in ‘Star Trek – The Next Generation’ –but please don’t worry, this blog post is not about him!

It is, however about the ‘Reaction Quotient’ (or to give its symbol, ‘Q’!)

You will come across the chemistry ‘Q’ in topic 7.1 which is to do with equilibrium. In this topic you will consider what an equilibrium is and how external influences can be used to move (shift, change) the position of the equilibria to make more products or more reactants.

It is also possible to determine a numerical value that will tell you how far the equilibria lies with regards to the products or reactants. This value is called K_c, the equilibrium constant. If K_c = 1, the reaction is in perfect equilibrium and there are equal concentrations of products and reactants. If K_c is less than 1, the concentration of reactants is less than the products and if K_c is greater than 1 the concentration of the products are more than the reactants.

Q is an way of representing the relative amounts of products and reactants at a point in time where equilibrium has not been reached. It allows you to decide if a reaction that is not at equilibrium is moving towards K_c (ie, equilibrium) or away from it.

If Q is greater than K_c there will be a greater concentration of products than is to be expected at equilibrium so the reverse reaction will be favoured.

Which therefore means that if Q is smaller than K_c there will be a greater concentration of reactants than is to be expected at equilibrium so the forwards reaction will be favoured.

It is possible to work out ‘Q’ when just the concentrations are given but really, this means nothing in terms of deciding which direction the reaction is moving in (in other words, if it is moving towards equilibrium (K_c) or away from it) unless the value of K_c is actually given.

A typical question may give you some concentration values for a reaction at equilibrium and ask you to determine K_c. The question may then be extended by giving you some different concentration values and asking you to decide if the second reaction is moving towards equilibrium or away from it.

For example, use the following concentrations to calculate K_c for the following reaction which is at equilibria.

3H₂ + N₂ == 2NH₃

[H₂] = 3.0 mol dm ^-3

[N₂] = 2.0 mol dm ^-3

[NH₃] = 0.5 mol dm ^-3

Answer:

K_c =  [NH₃]² /[H₂]³ x [N₂]¹

=  0.5 ²/ 3³ x 2¹=

= 0.25 / 54

K_c = 0.0046 (units not given)

In another reaction not at equilibria it was found the concentrations of products and reactants were:

[H₂] = 2.0 mol dm ^-3

[N₂] = 2.0 mol dm ^-3

[NH₃] = 1.0 mol dm ^-3

Use this information to determine the value of Q and decide which direction the equilibria is shifting.

Answer:

Q =[NH₃]² /[H₂]³ x [N₂]¹

Q =  1² / 2³ x 2¹= 0.0625

As Q is more than K_c, the concentration of reactants are less than what they would be at equilibrium and so the backwards reaction must be favoured. SO the reaction is moving (or shifting) in the direction of the reactants (or the LHS)

By the way, it should be noted that I have made up the value of K_c for this reaction for illustrative processes! Please don’t go quoting me on this!! That said, if you do watch Star Trek you will know Q has superhuman properties and he would have been able to change the value of Kc to be 0.0046…. But that is another story and maybe a blog post for TOK 😉