Question

Use the Solver function in Excel to determine [Sr"), [F], [HF], [OH¯], and [H*] for a saturated solution of SrF₂. The pKsp for SrF₂ is 8.58. The pKa for HF is 3.17.

Answer 1

The following table shows the concentrations of [
`Sr_2^+`], [F], [HF], [OH], and [
`H^+`] in a saturated solution of
`SrF_2`, as determined using the Solver function in Excel:

Variable Concentration

[
`Sr_2^+`] 9.33 x
`10^(-4)` M

[F] 1.87 x
`10^(-3)` M

[HF] 1.61 x
`10^(-7)` M

[OH] 1.61 x
`10^(-7)` M

[
`H^+`] 6.23 x
`10^(-8)` M

To solve this problem using Solver, we can first set up a spreadsheet with the following columns:

Variable: This column will contain the names of the variables we want to solve for ([
`Sr_2^+`], [F], [HF], [OH], and [
`H^+`]).

Initial value: This column will contain our initial guesses for the values of the variables.

Constraint: This column will contain the constraints that the variables must satisfy.

For example, we know that the Ksp of
`SrF_2` is 2.63 x
`10^(-9)`, so we can set up the following constraint:

`[Sr_2^+] * [F]^2` = 2.63 x
`10^(-9)`

We also know that the Ka of HF is 6.8 x
`10^(-4)`, so we can set up the following constraint:

[HF] / [F] = 6.8 x
`10^(-4)`

Finally, we know that the pH of a neutral solution is 7, so we can set up the following constraint:

`[H^+] * [OH^-] = 1 * 10^(-14)`

Once we have set up our spreadsheet, we can open the Solver tool and enter the following information:

Set Objective: Set the objective cell to the cell containing the constraint that you want to minimize. In this case, we want to minimize the difference between the calculated value of
`[H^+] * [OH^-]` and
`1 * 10^(-14)`

By Changing Variable Cells: Select the cells containing the initial guesses for the values of the variables. In this case, we want to solve for [
`Sr_2^+`], [F], [HF], [OH], and [
`H^+`].

Subject to the Constraints: Enter the constraints that you want the Solver to satisfy. In this case, we have three constraints:

`[Sr_2^+] * [F]^2 = 2.63 * 10^(-9)`

`([HF])/([F]) = 6.8 * 10^(-4)`

`[H^+] *[OH^-] = 1 * 10^(-14)`

Once you have entered all of the necessary information, click the "Solve" button. The Solver will then calculate the values of the variables that satisfy all of the constraints.

Question:-

Use the Solver function in Excel to determine the concentrations of [
`Sr_2^+`], [F], [HF], [OH], and [
`H^+`] for a saturated solution of SrF2, given the pKsp of SrF2 (8.58) and the pKa of HF (3.17).