Introduction to reaction quotient Qc | Chemical equilibrium | Chemistry | Khan Academy

- [Voiceover] Today we
are going to be talking

about the Reaction Quotient, Q.

In this video, I'm going to go over,

how you calculate Q and how you use it.

We're gonna start with
and example reaction

between sulfur dioxide,

S02 gas,

which will react with oxygen gas,

and this is a reversible reaction

that makes

sulfur trioxide

or SO3.

We should make sure this
is a balanced reaction.

We have two sulfur dioxdes
reacting with one O2

to give

2S03.

At equilibrium we can calculate

the equilibrium constant, Kc.

So, at equilibrium

we know the concentrations

should be constant because the rate of the

forward and backward
reactions are the same.

And if we plug those concentrations in

to this expression, we will get Kc.

So,

Kc is

the product concentration raised

to the second power so that's from

this stoichiometric coefficient.

And then our reactant concentrations,

so S02

squared

and the concentration of O2.

So we know at some temperature,

if you plug in the
equilibrium concentrations,

Kc is equal to 4.3.

But what if we're interested in looking

at the reaction and it's not

at equilibrium yet or
maybe we just don't know

if it's at equilibrium.

In that case,

when you're not sure it's

at equilibrium or really at any point

in your reaction or any time,

we can calculate the Reaction Quotient, Q.

So Qc

is equal to

the concentration of our product

squared,

so the concentration of the product

raised to

the stoichiometric coefficient

times the reactant concentrations,

also raised to their
stoichiometric coefficients.

So S02 squared

and O2.

So you may be wondering at this point,

what's the difference?

The equation for Qc and Kc will

always look exactly the same

and the main difference
is when you use them.

The equilibrium constant K you calculate

only with the equilibrium concentrations.

So the c means everything

is in terms of the molar concentration.

And for the reaction quotient, Q,

again everything is in terms of molar

concentration but we can calculate it

with any concentrations and we don't

have to be at equilibrium.

Molar concentration...

So let's calculate this

for a set of example concentrations.

At some point in our reaction we have

the following concentrations.

We have 0.10

molar

S02,

0.30

molar

O2,

and 3.5

molar of our product.

So if we plug these numbers into

our expression for Qc,

we get

3.5 molar

squared

in the numerator

and 0.10 squared

times 0.3

in the denominator.

So if I plug this into my calculator,

I get that Qc

with this set of concentrations

is 4,083.

So now we know how to calculate Qc.

So next we're going to talk about

what it tells you.

So there are three possible scenarios.

So when Q

is equal to K,

that tells us we're at equilibrium.

So, if at any point you're not sure

if your concentrations are the

equilibrium concentrations,

you can calculate Q

and check if it's equal to K.

And in this case, it's not.

So the other two possibilities are

that Q is greater than K,

which is the case here.

Or Q can be less than K.

So let's go through both
of those possibilities.

We can draw all of the
possible values of Q

on a number line

or a Q line.

So Q can have values anywhere

from zero

to infinity.

When you have no product

your numerator is zero

and Q is equal to zero.

So that tells us

Q equals zero

when you have all reactants

and no products.

And then if you have no reactants left

and all products,

we have zero in the denominator

and that gives us a Q value of infinity.

So that means at Q equals infinity,

we have all products.

Then we have a bunch of values in between.

And I'm gonna just write
some intermediate values

in here

but the actual intermediate values here

aren't super important.

We're mostly gonna wanna
compare the relative

values of our Q and K.

So Q here is equal to 4,083,

which I will place

right around here.

So that's Qc

and our K

in yellow

is 4.3.

So we'll place that right around here.

So we can see that

our Q is larger than K

and it's closer to having all products.

At the concentrations we have up here,

we have way more products than we should

at equilibrium.

So our reaction is gonna try to adjust

the concentrations to get to equilibrium.

And what that means in
terms of our number line

is that our concentrations are gonna shift

so that Q can get closer to K.

Since our shift is to the right,

and it's moving towards all reactants,

our reaction is going to favor reactants

to get to equilibrium.

So when Q is greater than K, like here,

we're going to favor

reactants...

reactants.

And then the last scenario
when Q is less than K

our reaction will

favor products.

And we can show that
also on our number line.

If we had a different
set of concentrations,

where Q was less than K,

which I will show

using this color here.

If we had, say, a Q value around here

then our shift would be

to the right

towards making more products

and therefore that would mean our reaction

is gonna try to reach equilibrium

by favoring the forward reaction.

So that's how you calculate
Q and how you use it

to see how the reaction concentrations

will shift to get to equilibrium.

In our next video, we'll go over

an example problem using Q and trying

to figure out how the
reactant concentrations

will shift for another reaction.