Question

A solution containing a mixture of the compounds X and Y had an absorbance of 1.00 at 443 nm and an absorbance of 0.861 at 520 nm when measured with a 1.00 cm cell. The molar absorptivities (ε) of X and Y at each wavelength are shown in the table below. 443 16410 3871. 520 3993 6425

Answer 1

We have to use Beer's law to determine the concentration of each substance in the solution.

A = εcl                  [where A = absorbance; ε = absorption coefficient; c = concentration; l = length of the                                              cell]

Beer’s law is additive, so for the mixture we can write:

(A_mix)_λ = (ε_X)_λC_Xl + (ε_Y)_λC_Yl

Now we can form two equations:

1. (A_mix)₄₄₃ = (ε_X)_λ1C_Xl + (ε_Y)_λ1C_Yl

or, 1 = 16410*C_X*1 + 3871*C_Y*1

or, C_X = (1-3871C_Y)/16410

2. (A_mix)₅₂₀ = (ε_X)_λ2C_Xl + (ε_Y)_λ2C_Yl

0.861 = 3993*C_X*1 + 6425*C_Y*1

or, 0.861 = 3993*[(1-3871C_Y)/16410]*1 + 6425*C_Y*1

= 0.243(1-3871 C_Y) + 6425 C_Y

= 0.243 - 941.9 C_Y + 6425 C_Y

= 0.243 + 5483 C_Y

or, C_Y = 1.127 * 10^-4 M

From equation 1, we get C_X = 3.435 * 10^-5 M