Q19.156P - Chemistry: Molecular Nature Of Matter And Change

Question

EDTA binds metal ions to form complex ions (see Problem ), so it is used to determine the concentrations of metal ions in solution: 

${\text{M}}^{\text{n + }}{\text{(aq) + EDTA}}^{\text{4 - }}\text{(aq)}\to {\text{MEDTA}}^{\text{n - 4}}\text{(aq)}$

A $\text{50.0 - mL}$ sample of ${\text{0.048 M Co}}^{\text{2 + }}$is titrated with ${\text{0.050 M EDTA}}^{\text{4 - }}$.Find ${\text{[Co}}^{\text{2 + }}\text{]}$ and ${\text{[EDTA}}^{\text{4 - }}\text{]}$ after.

1. $\text{25.0 mL}$ and
2. $\text{75.0 mL}$of ${\text{EDTA}}^{\text{4 - }}$are added (${\text{log K}}_{\text{f}}$ of ${\text{CoEDTA}}^{\text{2 - }}\text{ = 16.31}$).
   

Step-by-Step Solution

Answer

1. The concentration of ${\text{[Co}}^{\text{2 + }}]$ and ${\text{[EDTA}}^{\text{4 - }}]$ after $\text{25 mL}$ is added is $\left[{\text{EDTA}}^{\text{4 - }}\right]{\text{ = 5.32×10}}^{\text{ - 17}}\text{ M}$ and $\left[{\text{Co}}^{\text{2 + }}\right]\text{ = 0.0153 M}$.
2. The concentration of ${\text{[Co}}^{\text{2 + }}]$ and ${\text{[EDTA}}^{\text{4 - }}]$after ${\text{75 mL [EDTA}}^{\text{4 - }}]$is added is $\left[{\text{EDTA}}^{\text{4 - }}\right]\text{ = 0.0108 M}$ and $\left[{\text{Co}}^{\text{2 + }}\right]{\text{ = 8.71×10}}^{\text{ - 17}}\text{ M}$. 

Step 1: Concept Introduction

Titration (also known as titrimetry and volumetric analysis) is a typical quantitative chemical analysis method used in laboratories to quantify the concentration of an analyte (a substance to be analysed).

Step 2: Concentrations after 25.0 mL

The volume of ${\text{Co}}^{\text{2 + }}$is: $\text{50 mL = } \text{0.05 L}$

Number of moles of ${\text{Co}}^{\text{2 + }}$is: $\text{0.048 M}$

Number of moles of ${\text{EDTA}}^{\text{4 - }}$: $\text{0.05 M}$

First, write the reaction between ${\text{Co}}^{\text{2 + }}$and ${\text{EDTA}}^{\text{4 - }}$-

$$\begin{gathered} {\text{Co}}^{\text{2 + }}{\text{ + EDTA}}^{\text{4 - }}\rightleftharpoons {\text{CoEDTA}}^{\text{2 - }} \\ \text{Kf = }\frac{{\displaystyle {\text{[CoEDTA}}^{\text{2 - }}\text{]}}}{{\displaystyle {\text{[Co}}^{\text{2 + }}{\text{][EDTA}}^{\text{4 - }}\text{]}}}{\text{=10}}^{\text{16.31}} \end{gathered}$$

Here calculate ${\text{[Co}}^{\text{2 + }}]$after adding $\text{25 mL EDTA}$

$\begin{array}{rcl}\left[{\text{Co}}^{\text{2 + }}\right]& =& \frac{{\displaystyle \text{0.05L×0.048 M - 0.025 L×0.05 M}}}{{\displaystyle \text{0.05 L + 0.025 L}}}\\ & =& \text{0.0153 M}\end{array}$

Do the same calculation for ${\text{[CoEDTA}}^{\text{2 - }}\text{]}$-

$\begin{array}{rcl}\left[{\text{CoEDTA}}^{\text{2 - }}\right]& =& \frac{{\displaystyle \text{0.025 L×0.05 M}}}{{\displaystyle \text{0.05 L + 0.025 L}}}\\ & =& \text{0.0167 M}\end{array}$

Now determine ${\text{[EDTA}}^{\text{4 - }}\text{]}$from the $\text{Kf}$ expression

$\begin{array}{rcl}\left[{\text{EDTA}}^{\text{4 - }}\right]& =& \frac{{\displaystyle \text{0.0167 M}}}{{\displaystyle {\text{0.0153 M×10}}^{\text{16.31}}}}\\ & =& {\text{5.32×10}}^{\text{ - 17}}\text{ M}\end{array}$

Therefore, the value for concentration is obtained as $\left[{\text{EDTA}}^{\text{4 - }}\right] \text{ = } {\text{5.32×10}}^{\text{ - 17}}\text{ M}$ and $\left[{\text{Co}}^{\text{2 + }}\right]\text{ = 0.0153 M}$.

Step 3: Concentrations after 75.0 mL EDTA 4 -  is added

(b)

Because the volume is post equivalence point, the calculations will be –

$\begin{array}{rcl}\left[{\text{CoEDTA}}^{\text{2 - }}\right]& =& \frac{{\displaystyle \text{0.05 L×0.048 M}}}{{\displaystyle \text{0.025 L}}}\\ & =& \text{0.0192 M}\\ \left[{\text{EDTA}}^{\text{4 - }}\right]& =& \frac{{\displaystyle \text{0.075 L×0.05 M - 0.05 L×0.048 M}}}{{\displaystyle \text{0.0125 L}}}\\ & =& \text{0.0108 M}\end{array}$

Now determine $\left[{\text{Co}}^{\text{2 + }}\right]$from the $\text{Kf}$ expression-

$\begin{array}{rcl}\left[{\text{Co}}^{\text{2 + }}\right]& =& \frac{{\displaystyle \text{0.0192 M}}}{{\displaystyle {\text{0.0108 M + 10}}^{\text{16.31}}}}\\ & =& {\text{8.71×10}}^{\text{ - 17}}\text{ M}\end{array}$

Therefore, the value for concentration is obtained as $\left[{\text{EDTA}}^{\text{4 - }}\right]\text{ = 0.0108 M}$ and $\left[{\text{Co}}^{\text{2 + }}\right] \text{ = } {\text{8.71×10}}^{\text{ - 17}}\text{ M}$.