In this problem, we're asked to find the Kc or the equilibrium constant for

this particular reaction.

We're given some information about the initial concentrations of our reactants,

H2 and I2, and

information about the equilibrium concentration of HI, our product.

So we know this is an equilibrium process because we see we have our equilibrium

arrow here.

We know that because it's an equilibrium reaction,

we are not going to completely convert from our reactants to our products.

So what we need to find is, what are the equilibrium concentrations of the H2 and

I2, so that we can solve for the value of Kc.

For equilibrium problems, the way that we kind of organize and

sort our data is through the use of an ICE table.

And I stands for initial, change, and equilibrium.

We can also set up a column here that says H2, I2, and HI.

So now we can take the information given in our problem and

sort it into this table.

So the first thing I notice is that my initial concentrations of H2 and

I2 are both 0.100, so I can put this in.

And in this case, they happen to be the same, they don't have to be.

Sometimes, you'll see different values.

We also see that there's no mention of our initial concentration of H!, so

we can assume that that is 0.

The next thing we need to look at is our change row, and

we do this in terms of x, so I know that if I lose some x amount of H2,

I'm going to lose the same amount of I2.

And I'm going to gain twice as much of my HI because as we lose reactants,

we're going to products.

And if I look back at the stoichiometry of my equation,

what I see is that it's a 1 to 1 to 2 ratio in my balanced chemical equation.

Now I can look at my equilibrium row, and

all I need to do is sum the initial and change rows.

So my equilibrium concentration of H2 is 0.100-x.

It's the same for I2, and for HI, it's equal to 2x.

So now I can go back and say, well, wait a minute, in the initial problem,

it gave me what the actual equilibrium concentration of HI was.

So I can use that, along with my value of 2x, to determine my value of x.

So I can say HI is, at equilibrium,

is equal to 0.134, and it's also equal to 2x.

And so I can solve for x, and find that it equals to 0.0670.

Now I can use that value of x to figure out what my

equilibrium concentrations are for H2 and I2.