I was having difficulty with the following problem. Can someone please tell me if it is correct?
Ethanol can be synthesized by the reaction of ethylene with water vapor. K = 3.4 x 102
C2H4 (g) + H2O (g) ⇌ C2H5OH (g)
If you start with 5.4 atm of ethylene and 5.4 atm of water vapor, what are the concentrations of each of the gases at equilibrium?
i 5.4 5.4 0 K = x = 3.4 x 102
c –x –x +x (5.4–x)2
e 5.4–x 5.4–x x x = (3.4 x 102)(29–10.8x+ x2)
x = 9.9 x 103–3.7 x 103 x+3.4 x 102 x2
3.4 x 102 x2– 3.7 x 103 x+9.9 x 103 = 0
Is it right that at this point I would use the quadratic formula where a= 3.4 x 10^2, b= -3.7 x 10^3, c=9.9 x 10^3? It says the answer is 4.0 but I get 4.7. What did I do wrong? Any input would be greatly appreciated.