Question

For the reaction H2(g) + I2(g) <===> 2HI(g), Kc=54.9 at 699K. A system was charged with 2.50 moles of H2 ans 2.50 moles of I2 and 5.00 moles of HI initially in a 5.00 liter vessell. How many moles of H2 should there be present at equilibrium?
(Answer my teacher gave: 0.2127mol in 1L)

My ICE TABLE

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

I-(0.500)---(0.500)-----(1.00)

C-(-x)------(-x)--------(2x)

E-(0.500-x)-(0.500-x)---(1.00+2x)

54.9=(1.00+2x)^2/(0.500-x)^2

54.9=4x^2+4x+1 / x^2-x+0.25

54.9x^2-54.9x+13.725=4x^2+4x+1

50.9x^2-58.9x+12.725=0

Then I used the quadratic formula to get my answer

(using + root)x=0.8697
(uding - root)x=0.2874

0.500-0.2874=0.2126

My Issue:
I get the correct answer but I get the answer using the using root. I thought this should never happen. I also know another method to solve this question and when I do it I get x=0.2874.

Answer 1

Well, you should have proofed your post. The first sentence at the end of your post says "I get the correctanswer but I the answers using the USING ROOT".I don't know what a using root is I assume you meant to say you get the correct answer using the negative root and .... The 0.2874 is the correct answer for x(based on your numbers--I didn't solve the quadratic) BECAUSE it gives you 0.500 - 0.2874 = 0.2126 and that is a reasonable answer for the H2 and I2 after equilibrium is attained. What do you get for H2 and I2 if you use the + root of 0.8697? That would be 0.5-0.8697 and that is a negative concentration for H2 and I2 and you know that can't be right. #1 ruleis you shouldn't worry about it because you KNOW which is the right answer and #2 I would forget about that rule about the negative root NEVER being right. In this case the FINAL answer is what counts and not an intermediate result In fact, I
NEVER pay any attention to which root is being used because it doesn't matter.