Chapter 13, Problem 13.1P

(a)

Interpretation Introduction

Interpretation:

Milliliters of $\text{0}\text{.0500 M EDTA}$ required to react with $50.0\text{ mL}$ of $0.0100{\text{ M Ca}}^{2+}$ have to be determined.

Concept Introduction:

EDTA or ethylenediaminetetraacetic acid is used for titration of majority of metals with help of formation of strong metal complexes in the ratio of $1:1$. It is utilized to bind metals, most commonly used in industrial processes. It is also used for prevention of food oxidation and in environmental chemistry.

Formula to calculate molarity of solution is as follows:

  $\text{Molarity of solution}\left(\text{M}\right)=\frac{\text{Moles of solute}}{\text{Volume }\left(\text{L}\right)\text{ of solution}}$        (1)

Answer to Problem 13.1P

Volume of $\text{0}\text{.0500 M EDTA}$ required to react with $50.0\text{ mL}$ of $0.0100{\text{ M Ca}}^{2+}$ is $10\text{ mL}$.

Explanation of Solution

Rearrange equation (1) for moles of solute.

  $\text{Moles of solute}=\left[\begin{array}{c}\left(\text{Molarity of solution}\left(\text{M}\right)\right)\\ \left(\text{Volume }\left(\text{L}\right)\text{ of solution}\right)\end{array}\right]$        (2)

Substitute $0.0100\text{ M}$ for molarity of solution and $50.0\text{ mL}$ for volume of solution in equation (2) to calculate moles of ${\text{Ca}}^{2+}$.

  $\begin{array}{c}{\text{Moles of Ca}}^{2+}=\left(0.0100\text{ M}\right)\left(50.0\text{ mL}\right)\left(\frac{{10}^{-3}\text{ L}}{1\text{ mL}}\right)\\ =0.0005\text{ mol}\end{array}$

Since EDTA always forms complexes with metals in ratio of $1:1$, 0.0005 moles of ${\text{Ca}}^{2+}$ will react with same number of moles of EDTA.

Rearrange equation (1) for volume of solution.

  $\text{Volume}\left(\text{L}\right)\text{ of solution}=\frac{\text{Moles of solute}}{\text{Molarity}\left(\text{M}\right)\text{ of solution}}$        (3)

Substitute $0.0005\text{ mol}$ for moles of solute and $\text{0}\text{.0500 M}$ for molarity of solution in equation (3) to calculate volume of EDTA solution.

  $\begin{array}{c}\text{Volume of EDTA solution}=\left(\frac{0.0005\text{ mol}}{\text{0}\text{.0500 M}}\right)\left(\frac{{10}^3\text{ mL}}{1\text{ L}}\right)\\ =10\text{ mL}\end{array}$

Hence, required volume of EDTA solution is $10\text{ mL}$.

(b)

Interpretation Introduction

Interpretation:

Milliliters of $\text{0}\text{.0500 M EDTA}$ required to react with $50.0\text{ mL}$ of $0.0100{\text{ M Al}}^{3+}$ have to be determined.

Concept Introduction:

EDTA or ethylenediaminetetraacetic acid is used for titration of majority of metals with help of formation of strong metal complexes in the ratio of $1:1$. It is utilized to bind metals, most commonly used in industrial processes. It is also used for prevention of food oxidation and in environmental chemistry.

Formula to calculate molarity of solution is as follows:

  $\text{Molarity of solution}\left(\text{M}\right)=\frac{\text{Moles of solute}}{\text{Volume }\left(\text{L}\right)\text{ of solution}}$        (1)

Answer to Problem 13.1P

Volume of $\text{0}\text{.0500 M EDTA}$ required to react with $50.0\text{ mL}$ of $0.0100{\text{ M Al}}^{3+}$ is $10\text{ mL}$.

Explanation of Solution

Rearrange equation (1) for moles of solute.

  $\text{Moles of solute}=\left[\begin{array}{c}\left(\text{Molarity of solution}\left(\text{M}\right)\right)\\ \left(\text{Volume }\left(\text{L}\right)\text{ of solution}\right)\end{array}\right]$        (2)

Substitute $0.0100\text{ M}$ for molarity of solution and $50.0\text{ mL}$ for volume of solution in equation (2) to calculate moles of ${\text{Al}}^{3+}$.

  $\begin{array}{c}{\text{Moles of Al}}^{3+}=\left(0.0100\text{ M}\right)\left(50.0\text{ mL}\right)\left(\frac{{10}^{-3}\text{ L}}{1\text{ mL}}\right)\\ =0.0005\text{ mol}\end{array}$

Since EDTA always forms complexes with metals in ratio of $1:1$, 0.0005 moles of ${\text{Al}}^{3+}$ will react with same number of moles of EDTA.

Rearrange equation (1) for volume of solution.

  $\text{Volume}\left(\text{L}\right)\text{ of solution}=\frac{\text{Moles of solute}}{\text{Molarity}\left(\text{M}\right)\text{ of solution}}$        (3)

Substitute $0.0005\text{ mol}$ for moles of solute and $\text{0}\text{.0500 M}$ for molarity of solution in equation (3) to calculate volume of EDTA solution.

  $\begin{array}{c}\text{Volume of EDTA solution}=\left(\frac{0.0005\text{ mol}}{\text{0}\text{.0500 M}}\right)\left(\frac{{10}^3\text{ mL}}{1\text{ L}}\right)\\ =10\text{ mL}\end{array}$

Hence, required volume of EDTA solution is $10\text{ mL}$.