Chemistry
posted by j .
If the initial concentration of NH3(g) is 4.643 mol/L, calculate the % of NH3(g) left over after the reaction reaches equilibrium according to the balanced equation. The value of Kc at 773.0 K is 16.70. The initial concentration of the reaction products is 0 mol/L.
2NH3(g) = N2(g)+3H2(g)
I know that we're supposed to do an ICE chart. I got (x^2)/ 6.7452x . But I don't know how to solve for the x and the rest I would appreciate if you could write out the steps to this :)

You need work on your ICE charts.
...............2NH3 ==> N2 + 3H2
initial.......4.643.....0......0
change........2x.......x......3x
equil.......4.6432x.....x......3x
Kc = 16.70 = (N2)(H2)^3/(NH3)2
16.70 = (x)(3x)^3/(4.6432x)^2
16.70 = 27x^4/(etc)
I didn't check my work (so I could have made a math error) but I expanded the denominator, multiplied by 16.70, and ended up with
27x^4 66.8x^2 +310.15x 360 = 0
First I ignored the 27x^4 and solved the quadratic and obtained an answer of 2.31, substituted 2.31 back into the equation to see if I obtained zero. I didn't; the value was quite positive. Several more trials and I think the answer is >1.279 but < 1.280. You can try your hand at the trial and error method or find a computer program at school that will solve a quartic or look on the web for a calculator that will do it. 
I looked on the web and found, and used, two calculators but I wasn't satisfied with either answer. One answer was 1.03 something but that didn't give me a zero when I substituted. The other one gave a value of 1.276 and that didn't give a zero either. Both showed negative numbers which means the answer is higher than 1.276.

Thank you so much :)
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