Solving for the correct X value

[Sydney Rohan 3G]

Can someone please help me on the following problem:

At a certain temperature, the equilibrium constant, Kc, for this reaction is 53.3.

H2(g)+I2(g) <--------> 2HI(g) Kc=53.3

At this temperature, 0.300 mol H2 and 0.300 mol I2 were placed in a 1.00 L container to react. What concentration of HI is present at equilibrium?

When I set up the ICE table and then I solved for x. In the end, I found that x= 0.413 and 0.235. BUt both of these numbers are positive so how do you determine which one is the correct x value?

[Gabriel McDonald 1J]

You don't actually need to use the quadratic equation for this problem!

After setting up your ICE box, you should get Kc = (2x)²/(0.3-x)². Since both the numerator and the denominator are squared, we can take the square root of both sides to get √Kc = (2x)/(0.3-x). Then, plug in your value for Kc and solve for x. I got 0.471 for x.

[Sohan Talluri 1L]

In general, if solving the quadratic results in two positive values for x, the correct value can be found by plugging x back into the expressions for the equilibrium concentrations. Even if x itself is not negative, if the initial concentration of one of the reactants minus x results in a negative value for the equilibrium concentration, that solution would be incorrect.

Hopefully this helps and please correct me if there are any mistakes.

[Rainy Liu Ruoshui_2K]

In this case, the initial concentration of H2 and I2 is 0.3. So x=0.413 couldn't be the x value, because in this case, the equilibrium concentration of H2 would be negative.