Chapter ST, Problem 24PQ

Interpretation Introduction

Interpretation:

The volume of $\text{0}\text{.100}\text{M}$${\text{Cr}}_2{\text{O}}_7{}^{2-}$ required to oxidize $60\text{mL}$ of $\text{0}\text{.25}\text{M}$${\text{Fe}}^{2+}$ has to be determined.

Concept Introduction:

Mole is S.I. unit. The number of moles is calculated as ratio of mass of compound to molar mass of compound.

Molar mass is sum of the total mass in grams of all atoms that make up mole of particular molecule that is mass of 1 mole of compound. The S.I unit is $\text{g/mol}$.

The expression to relate number of moles, mass and molar mass of compound is as follows:

  $\text{Number of moles}=\frac{\text{mass of the compound}}{\text{molar mass of the compound}}$

Answer to Problem 24PQ

Option (A) is the correct one.

Explanation of Solution

Reason for correct option:

The formula to calculate molarity of ${\text{Fe}}^{2+}$ is as follows:

  ${\text{molarity of Fe}}^{2+}=\frac{{\text{moles of Fe}}^{2+}}{{\text{volume of Fe}}^{2+}}$        (1)

Rearrange equation (1) to calculate moles of ${\text{Fe}}^{2+}$.

  ${\text{moles of Fe}}^{2+}=\left({\text{molarity of Fe}}^{2+}\right)\left({\text{volume of Fe}}^{2+}\right)$        (2)

Substitute $60\text{mL}$ for moles of ${\text{Fe}}^{2+}$ and $\text{0}\text{.25}\text{M}$ for volumes of ${\text{Fe}}^{2+}$ in equation (2).

  $\begin{array}{c}{\text{moles of Fe}}^{2+}=\left(\text{0}\text{.25}\frac{\text{mol}}{\text{L}}\right)\left(60\text{mL}\right)\left(\frac{{10}^{-3}\text{L}}{1\text{mL}}\right)\\ =0.015\text{mol}\end{array}$

The given reaction is as follows:

  ${\text{Cr}}_2{\text{O}}_7{}^{2-}\left(aq\right)+6{\text{Fe}}^{2+}\left(aq\right)+14{\text{H}}^{+}\left(aq\right)\to 2{\text{Cr}}^{3+}\left(aq\right)+6{\text{Fe}}^{3+}\left(aq\right)+{\text{7H}}_2\text{O}\left(l\right)$

The ratio between ${\text{Fe}}^{2+}$ and ${\text{Cr}}_2{\text{O}}_7{}^{2-}$ is 6:1.

Moles of ${\text{Cr}}_2{\text{O}}_7{}^{2-}$ can be calculated as follows:

  $\begin{array}{c}\text{moles of}{\text{Cr}}_2{\text{O}}_7{}^{2-}=\left(\frac{{\text{moles of Fe}}^{2+}}{6}\right)\\ =\frac{0.015\text{mol}}{6}\\ =0.0025\text{mol}\end{array}$

The formula to calculate molarity of ${\text{Cr}}_2{\text{O}}_7{}^{2-}$ is as follows:

  ${\text{molarity of Cr}}_2{\text{O}}_7{}^{2-}=\frac{{\text{moles of Cr}}_2{\text{O}}_7{}^{2-}}{{\text{volume of Cr}}_2{\text{O}}_7{}^{2-}}$        (3)

Rearrange equation (3) to calculate volume of ${\text{Cr}}_2{\text{O}}_7{}^{2-}$.

  ${\text{volume of Cr}}_2{\text{O}}_7{}^{2-}=\frac{{\text{moles of Cr}}_2{\text{O}}_7{}^{2-}}{{\text{molarity of Cr}}_2{\text{O}}_7{}^{2-}}$        (4)

Substitute $0.0025\text{mol}$ for moles of ${\text{Cr}}_2{\text{O}}_7{}^{2-}$ and $0.100\text{M}$ for molarity of ${\text{Cr}}_2{\text{O}}_7{}^{2-}$ in equation (4).

  $\begin{array}{c}{\text{volume of Cr}}_2{\text{O}}_7{}^{2-}=\frac{0.0025\text{mol}}{0.100\frac{\text{mol}}{\text{L}}}\\ =0.025\text{L}\left(\frac{{10}^3\text{mL}}{1\text{L}}\right)\\ =25\text{mL}\end{array}$

The volume of $\text{0}\text{.100}\text{M}$${\text{Cr}}_2{\text{O}}_7{}^{2-}$ required to oxidize $60\text{mL}$ of $\text{0}\text{.25}\text{M}$${\text{Fe}}^{2+}$ is $25\text{mL}$. Hence, correct option is (A).

Reason for incorrect option:

Since the volume of $\text{0}\text{.100}\text{M}$${\text{Cr}}_2{\text{O}}_7{}^{2-}$ required to oxidize $60\text{mL}$ of $\text{0}\text{.25}\text{M}$${\text{Fe}}^{2+}$ is $25\text{mL}$ so option (B), (C) and (D) are incorrect.

Conclusion

Volume of $\text{0}\text{.100}\text{M}$${\text{Cr}}_2{\text{O}}_7{}^{2-}$ required to oxidize $60\text{mL}$ of $\text{0}\text{.25}\text{M}$${\text{Fe}}^{2+}$ is $25\text{mL}$. Hence, correct option is (A).