Could someone please correct my answer to the Equilibrium reaction question?

Consider the equilibrium reaction.
H2(g) + I2(g) ⇌ 2 HI(g)
In this case, 1.000 M H2 reacts with 2.000 M of I2 at a temperature of 441°C. The value of Kc = 67.
Determine the equilibrium concentrations of H2, I2, and HI.

These were MY answers, but, they are wrong.
[H2] = 1.896 M
[I2] = 0.052
[HI] = 1.052 M

Any teaching is Much Appreciated. Thank you.

1 Answer
Truong-Son N.
Feb 24, 2018

Maybe your process was correct? Check which concentration is which.

#["H"_2] = "0.0511 M"#
#["I"_2] = "1.0511 M"#
#["HI"] = "1.898 M"#

Construct the ICE table:

#"H"_2(g) + "I"_2(g) rightleftharpoons 2"HI"(g)#

#"I"" "1.000" "2.000" "" "0#
#"C"" "-x" "" "-x" "+2x#
#"E"" "1-x" "2-x" "" "2x#

This gives:

#K_c = 67 = (["HI"]^2)/(["H"_2]["I"_2])#

#= (2x)^2/((1.000 - x)(2.000 - x))#

This #K_c# is not small enough to make any approximation, so we have to do this in full.

#67(1.000 - x)(2.000 - x) = 4x^2#

#67(2.000 - 3.000x + x^2) = 4x^2#

#134.000 - 201.000x + 67x^2 = 4x^2#

#63x^2 - 201.000x + 134.000 = 0#

This quadratic formula is set up as:

#x = (-(-201.000) pm sqrt(201.000^2 - 4(63)(134.000)))/(2(63))#

Once you solve this, you should get

#x = "2.242 M", "0.9489 M"#

The physically reasonable solution is #x = "0.9489 M"#, which gives:

#color(blue)(["H"_2]) = 1.000 - 0.9489 = color(blue)("0.0511 M")#

#color(blue)(["I"_2]) = 2.000 - 0.9489 = color(blue)("1.0511 M")#

#color(blue)(["HI"]) = 2(0.9489) = color(blue)("1.898 M")#

Keep your answers in order, is all.

Related questions
Impact of this question
195 views around the world
You can reuse this answer
Creative Commons License