Question

Spectroscopic data for the indicators thymol blue (TB),semithymol blue (STB), and methylthymol blue (MTB) are shown in the table. A solution ofTB,STB,MTB in a1.000-cm cuvet had absorbances of 0.412at455nm,0.350 at485nm, and 0.632 at545nm. Modify the spreadsheet in Figure 19-4 to handle three simultaneous equations and find$\mathbf{\left[}\mathbf{TB}\mathbf{\right]}\mathbf{,}\mathbf{\left[}\mathbf{STB}\mathbf{\right]}$and$\left[\mathrm{MTB}\right]$in the mixture.

Short answer

$$\begin{gathered} \mathrm{The}\left[\mathrm{TB}\right],\left[\mathrm{STB}\right],\left[\mathrm{MTB}\right]\mathrm{in}\mathrm{the}\mathrm{mixture}\mathrm{are}, \\ \left[\mathrm{TB}\right]=1.22·{10}^{-5}\mathrm{M} \\ \left[\mathrm{STB}\right]=9.30·{10}^{-6}\mathrm{M} \\ \left[\mathrm{MTB}\right]=1.32·{10}^{-5}\mathrm{M} \end{gathered}$$

Step-by-step solution

Modify a spreadsheet and use a formula to find the values:

Make a spreadsheet,

Hence, highlight the cells G4,G5 and G6.

Use the formula in the cells,

=MMULT(MINVERSE(B4:D6);E4:E6)

Thus, the values of $\left[\mathrm{TB}\right],\left[\mathrm{STB}\right],\left[\mathrm{MTB}\right]$are,

$$\begin{gathered} \left[\mathrm{TB}\right]=1.22·{10}^{-5}\mathrm{M} \\ \left[\mathrm{STB}\right]=9.30·{10}^{-6}\mathrm{M} \\ \left[\mathrm{MTB}\right]=1.32·{10}^{-5}\mathrm{M} \end{gathered}$$