Chromium (iii) forms a complex with diphenylcarbazide whose molar absorptivity is 4.17x104 at 540 nm.

calculate the path length( in cm) needed to cause a 2.56x10-6m solution of the complex to have the same absorbance as a 7.68x10-6m solution measured in a 1.00-cm cell.

3.00 cm

Explanation:

The absorbance can be expressed using Beer-Lambert's law:

A = ε*b*c

Where ε is a constant for each compound, b is the optical path, and c is the molar concentration of the compound.

Now we match the absorbance values for both solutions, because we want the absorbance value to be the same for both solutions:

A = ε * 1.00 cm * 7.68x10⁻⁶M = ε * b * 2.56x10⁻⁶ M

And solve for b:

 ε * 1.00 cm * 7.68x10⁻⁶M = ε * b * 2.56x10⁻⁶ M

1.00 cm * 7.68x10⁻⁶M = b * 2.56x10⁻⁶ M

b = 3.00 cm