Answer to Question #179877 in Organic Chemistry for Emma

Question

 If 0.500 mol of iodine and 0.500 mol of chlorine are initially placed into a 2.00-L reaction vessel at 25°C, find the concentrations of all entities at equilibrium.

I2(g)     +     Cl2(g)    ⇌    2 ICl(g)          K = 81.9 at 25°C

Answer 1

$I_{2(g) } + Cl_{2(g) }⇌ 2 ICl_{(g) }$

I: 0.500mol + 0.500mol = 0mol

C: -xmol + -xmol = +xmol

E: 0.500-x mol + 0.500-x = x

$K_c =\dfrac{x²}{(0.500-x)(0.500-x)}$

$81.9 =\dfrac{x²}{(0.500-x)(0.500-x)}$

$81.9 ( 0.250- x +x²) = x²$

$20.475 -81.9x+ 81.9x² = x²$

$80.9x²- 81.9x +20.475 = 0$

x = 0.45 or 0.56, but the value of K is greater than 1, so product conc. > reactant conc.

$\therefore x=0.56M$