Calculate equilibrium concentrations of W, Y, Z, and N?

Question

This is a problem in my textbook:
Consider the reaction W + 3Y = 2N + 4Z
A solution was prepared by mixing 100.0 mL of 8.04 x 10^-3 M W and 200.0 mL of 4.63 x 10^-3 M Y. After the system had come to equilibrium, the absorbance, A, of the solution was measured at a wavelength (600nm) where only Z absorbs light. The value of A (absorbance) was found to be 0.422.

The following data were also collected for known solutions of pure Z at 600nm:
[Z]-------------------A (absorbance)
2.00x10^-4---------0.100
5.00x10^-4---------0.240
8.00x10^-4---------0.390
18.0x10^-4---------0.880

I just don't know where to start with this one. Not even sure I understand what it's asking me to do! Thanks for the help.

Answer 1

The change of concentrations of the components due to a chemical reaction are related to each other by the stoichiometry of the reaction.
For this reaction the relations are:
([W]-[W]₀)/(-1) = ([Y]-[Y]₀)/(-3) = ([N]-[N]₀)/2 = ([Z]-[Z]₀)/4
where [X] stands for the concentration and [X]₀ for the initial concentration

1 calculate initial concentrations
Simple mixing rule
[X]mix = ([X]1*V1+[X]V2)/(V1+V2) where V1, V2 are the volumes mixed
Hence
[W]₀=(8.04x10^-3 mol/l x 0.2 l + 0 x 0.1 l) / (0.1l +0.2l)
= 5.36x10^-3 mol/l
and
[Y]₀= 1.54x10^-3 mol/l
[Z]₀ = 0
[N]₀= 0

2. Calculate concentration of Z in equilibrium
According to Beer-Lambert law the absorbance is proportional to the concentration:
A = c x [Z]
You can evaluate the constant c fitting of the data of known solutions to the equation above. You can do it graphically or numerically by linear regression.
I get c= 488.25 l/mol
Therefore the concentration of Z at the equilibrium is
[Z] = A/c = 0.422 / 488.25l/mol = 8.64x10^-4 mol/l

3. Calculate the other concentrations
Just apply the relations above and solve for the unknown concentrations:
[W] = [W]₀-[Z]/4 = 5.14x10^-3 mol/l
[Y] = [Y]₀ - 3/4 x [Z] = 8.95x10^-4 mol/l
[N] = 2/4 x [Z] = 4.32x1o^-4 mol/l

Answer 2

i think "pr!n(e$$" needs to go take some English as a Second Language classes.