# Thread: Is This Algebra Correct?

1. ## Is This Algebra Correct?

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.

2. Originally Posted by confused20
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.
Your chart makes this practically impossible to read. However when you "quote" your original post everything lines back up again. I'd like to know, though how this line
x = (3.4 x 102)(29–10.8x+ x2)
becomes this line?
x = 9.9 x 103–3.7 x 103 x+3.4 x 102 x2

Also, to save confusion in the future, when you want to write 3.4 times 102, don't write 3.4 x 102 because the multiplication symbol is an x just like your variable. Use 3.4 * 102.

-Dan