The standard solution of FeSCN2+ (prepared by combining 9.00 mL of 0.200 M Fe(NO3)3 w/1.00 mL of 0.0020 M KSCN) has an absorbance of 0.500. If a trial's absorbance is measured to be 0.310 and its initial concentration of SCN– was 0.0010 M, the equilibrium concentration of SCN– will be

It seems to me the answer depends upon what species or ion is doing the absorbing. If it is SCN- and the absorbance has dropped from 0.500 to 0.310, then the concentration of that absorbing material has increased.

Absorbance = 0.500 = e^-0.6931
changes to
0.310 = e^-1.171
It is the exponents that are proportional to the amount of absorbing material, assuming the path length through the sample is the same. The amount of absorber has increased by a factor of 1.171/0.6931 = 1.69

Ignore my previous answer. I was using the transmittance equation instead of absorbance. I should have known better.

Absorbance = 1 - e^-kX
If absorbance = 0.50, kX = 0.6931
If absorbance = 0.31, e^-kX = 0.69 and
kX = 0.3711
X is the path length which stays the same, so k decreases by a factor .3711/.6931 = 0.534
That would make the amount of SCN- 0.000534 M

i don't think it's correct if we take the ratio of the absorbance because both are not from one concentration.

To determine the equilibrium concentration of SCN– in the solution, we can use the Beer-Lambert Law, which states that there is a linear relationship between the concentration of a solution and its absorbance.

The Beer-Lambert Law can be expressed as:

A = εbc

where A is the absorbance, ε is the molar absorptivity (a constant), b is the path length (usually the width of the cuvette), and c is the concentration of the solution.

In this case, we have the initial absorbance (A1) and concentration of SCN– (c1), and we want to find the equilibrium concentration of SCN– (c2).

The absorbance is given by:

A = εbc

We can rearrange this equation to solve for concentration:

c = A / (εb)

Now we can substitute the values into the equation.

For the standard solution:
A1 = 0.500 (given)
c1 = 0.0020 M (given)

Therefore, the initial concentration of SCN– is 0.0010 M.

For the trial solution:
A2 = 0.310 (given)
c2 = ?

Using the equation above and substituting the values:
c2 = A2 / (εb)

We don't have the values of ε (molar absorptivity) and b (path length) given in the problem statement. These values are usually determined experimentally, so we need them to calculate the equilibrium concentration of SCN– accurately.

Therefore, without knowing the values of ε and b, we cannot determine the equilibrium concentration of SCN– in the solution.