Question

Calculate the concentration of Cl- remain in solution?

you are given a 1.00 mL solution of .1 M Cl- and told to verify the chloride concentration by gravimetric analysis. 1mL of .5M Ag+ is added to this solution and the resultant AgCl quantitatively precipitated. Based on the Ksp expression, calculate the concentration of Cl- that remains in solution.

Any help, answers, or suggestions would be greatly appreciated

Answer 1

The concentration of chloride remaining is `9 × 10^"-10"color(white)(l) "mol/L"`.

Explanation:

Step 1. Calculate the amounts of substances present at the end of the reaction

`color(white)(mmmmmm)"Ag"^"+" + "Cl"^"-" → "AgCl"`
`"I/mmol": color(white)(mll)0.50 color(white)(ml)0.10`
`"C/mmol": color(white)(m)"-0.10"color(white)(m)"-0.10"`
`"E/mmol": color(white)(ml)0.40color(white)(mm)0`

`"Moles of Cl"^"-" = 1.00 color(red)(cancel(color(black)("mL Cl"^"-"))) × "0.1 mmol Cl"^"-"/(1 color(red)(cancel(color(black)("mL Cl"^"-")))) = "0.10 mmol Cl"^"-"`

`"Moles of Ag"^"+" = 1 color(red)(cancel(color(black)("mL Ag"^"+"))) × "0.5 mmol Ag"^"+"/(1 color(red)(cancel(color(black)("mL Ag"^"+")))) = "0.50 mmol Ag"^"+"`

So, you have a solution of 0.40 mmol `"Ag"^+"` in 2 mL solution in equilibrium with solid `"AgCl"`.

`["Ag"^"+"] = "0.40 mmol"/"2 mL" = "0.20 mol/L"`

Step 2. Calculate the concentration of `"Cl"^"-"`

`color(white)(mmmmmm)"AgCl" → "Ag"^"+" + "Cl"^"-"`
`"E/mol·L"^"-1": color(white)(mmmmm)0.20color(white)(mm)x`

`K_text(sp) = ["Ag"^"+"]["Cl"^"-"] = 0.20x = 1.77 ×10^"-10"`

`x = (1.77 × 10^"-10")/0.20 = 9 × 10^"-10"`

`["Cl"^"-"] = x color(white)(l)"mol/L" = 9 × 10^"-10"color(white)(l) "mol/L"`

Note: The answer can have only one significant figure because that is all you gave for the concentrations of the ions.