Question

Ammonia Equilibrium treated by solver. We now use the solve spreadsheet introduced in Figure 8 - 9 for ${\mathrm{TIN}}_3$ solubility to find the concentration of species in 0.01 M ammonia solution, neglecting activity coefficient. In the systematic treatment of equilibrium of ${\mathbf{NH}}_{\mathbf{3}}$hydrolysis, we have four unknowns $\left(\left[{\mathrm{NH}}_3\right],\left[{\mathrm{NH}}_4^{+}\right],\left[H^{+}\right],\left[{\mathrm{OH}}^{-}\right]\right)$ and two equilibrium (8-13) , (8-14). Therefore we will estimate the concentration of 4unknowns - 2equilibirum = 2species, for which I choose localid="1663566766281" ${\mathrm{NH}}^{+}\mathrm{and}{\mathrm{OH}}^{-}$. Setup the spreadsheet shown below, in which the estimate localid="1663566820791" ${\mathrm{pNH}}_4^{+}=3.{\mathrm{pOH}}^{-}$= 3 appears in B6andB7 . (Estimates comes from the ${\mathrm{K}}_{\mathrm{b}}$equilibrium 8-17 with $\left[{\mathrm{NH}}_4^{+}\right]\mathbf{=}\left[{\mathrm{OH}}^{-}\right]\mathbf{=}\sqrt{{\mathbf{K}}_{\mathbf{b}}\left[{\mathrm{NH}}_3\right]}\mathbf{\approx }\sqrt{{\mathbf{10}}^{\mathbf{-}\mathbf{4}\mathbf{.}\mathbf{755}}\left[0.01\right]}\mathbf{\Rightarrow }{\mathbf{pNH}}_{\mathbf{4}}^{\mathbf{+}}\mathbf{=}{\mathbf{pOH}}^{\mathbf{-}}\mathbf{\approx }\mathbf{3}$. Estimate donot have to be very good for Solver to work. The formula in cell C8 is $\left[{\mathrm{NH}}_3\right]=\mathbf{\left[}{\mathbf{NH}}_{\mathbf{4}}^{\mathbf{}\mathbf{}\mathbf{+}}\mathbf{\right]}$.

$\left[{\mathrm{OH}}^{-}\right]\mathbf{/}{\mathbf{K}}_{\mathbf{b}}$ and the formula in the cell C9 is $\left[H^{+}\right]\mathbf{=}{\mathbf{K}}_{\mathbf{w}}\mathbf{/}\left[{\mathrm{OH}}^{-}\right]$. The mass balance ${\mathbf{b}}_{\mathbf{1}}$appears in cell F6 and the charge balance ${\mathbf{b}}_{\mathbf{2}}$ appears in cell F7 . Cell F8 has the sum ${\mathbf{b}}_{\mathbf{1}}^{\mathbf{}\mathbf{2}}\mathbf{+}{\mathbf{b}}_{\mathbf{2}}^{\mathbf{}\mathbf{2}}$. As described for ${\mathbf{TIN}}_{\mathbf{3}}$on page 176, open the solver window and set the Solver Option. Then use the Solver to set the target cell F8 Equal to Min by changing cells B6 : B7 . What are the concentrations of the species? What fraction of ammonia $\left(=\left[{\mathrm{NH}}_4^{+}\right]/\left[{\mathrm{NH}}_4^{+}\right]+\left[{\mathrm{NH}}_3\right]\right)$ is hydrolyzed. Your answer should agree with those from Goal Seek in Figure 8-8

Short answer

Ammonia Equilibrium treated by Solver: Here one use the Solver spreadsheet from in Figure8 - 9for ${\mathrm{TIN}}_3$ solubility in order to find the concentration of species in 0.01 M${\mathrm{NH}}_3$solution.

This is also a task for practicing in Excel so one need to follow the instructions from the task and the result would be same as in the Figure 8 - 8 found by Goal Seek.

Step-by-step solution

Step 1:

Ammonia Equilibrium treated by Solver: Here one use the Solver spreadsheet from in Figure8 - 9for ${\mathrm{TIN}}_3$ solubility in order to find the concentration of species in 0.01 M${\mathrm{NH}}_3$solution.

This is also a task for practicing in Excel so one need to follow the instructions from the task and the result would be same as in the Figure 8 - 8 found by Goal Seek.

Step 2:

Setup the spreadsheet shown below,

Estimate ${\mathrm{pNH}}_4^{+}=3$appears in B6 and B7 . (Estimates comes from the ${\mathrm{K}}_{\mathrm{b}}$equilibrium 8 - 17 with

$\left[{\mathrm{NH}}_4^{+}\right]=\left[{\mathrm{OH}}^{-}\right]=\sqrt{{\mathrm{K}}_{\mathrm{b}}\left[{\mathrm{NH}}_3\right]}\approx \sqrt{{10}^{-4.755}[0.01]}\Rightarrow {\mathrm{pNH}}_4^{+}={\mathrm{pOH}}^{-}\approx 3$.

The formula in cell C8 is $\left[{\mathrm{NH}}_3\right]=\left[{\mathrm{NH}}_4^{+}\right]$.

$\left[{\mathrm{OH}}^{-}\right]/{\mathrm{K}}_{\mathrm{b}}$ and the formula in the cell C9 is $\left[{\mathrm{H}}^{+}\right]={\mathrm{K}}_{\mathrm{w}}/\left[{\mathrm{OH}}^{-}\right]$.

The mass balance ${\mathrm{b}}_1$appears in cell ${\mathrm{F}}_6$and the charge balance ${\mathrm{b}}_2$appears in cell ${\mathrm{F}}_7$.

Cell $\mathrm{F}8$ has the sum ${\mathrm{b}}_1^2+{\mathrm{b}}_2^2$.

As described for ${\mathrm{TIN}}_3$on page 176, open the solver window and set the Solver Option.

Then use the Solver to set the target cell${\mathrm{F}}_8$ Equal to Min by changing cells ${\mathrm{B}}_6:{\mathrm{B}}_7$.