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Chapter 18: Problem 72

Oxalic acid \(\left(\mathrm{H}_{2} \mathrm{C}_{2} \mathrm{O}_{4}\right)\) is present in many plants and vegetables. (a) Balance the following equation in acid solution: $$\mathrm{MnO}_{4}^{-}+\mathrm{C}_{2} \mathrm{O}_{4}^{2-} \longrightarrow \mathrm{Mn}^{2+}+\mathrm{CO}_{2}$$ (b) If a 1.00-g sample of \(\mathrm{H}_{2} \mathrm{C}_{2} \mathrm{O}_{4}\) requires \(24.0 \mathrm{~mL}\) of \(0.0100 \mathrm{M} \mathrm{KMnO}_{4}\) solution to reach the equivalence point, what is the percent by mass of \(\mathrm{H}_{2} \mathrm{C}_{2} \mathrm{O}_{4}\) in the sample?

Short Answer

Expert verified
The balanced redox equation is \(2\mathrm{MnO}_{4}^{-} + 16H^{+} + 5\mathrm{C}_{2} \mathrm{O}_{4}^{2-} \longrightarrow 2\mathrm{Mn}^{2+} + 10CO_{2}+ 8 H_{2}O \). The percent by mass of \( H_{2}C_{2}O_{4} \) in the sample is 5.4%.

Step by step solution

01

Balancing the redox reaction

Reduction half reaction: \( \mathrm{MnO}_{4}^{-} + 8H^{+} + 5e^{-} \longrightarrow \mathrm{Mn}^{2+} + 4H_{2}O \).\nOxidation half reaction: \( \mathrm{C}_{2} \mathrm{O}_{4}^{2-} \longrightarrow 2\mathrm{CO}_{2}+2e^{-}\).\nTo balance, multiply the oxidation half reaction by 5 and reduction half reaction by 2, and add both reactions: \(2\mathrm{MnO}_{4}^{-} + 16H^{+} + 5\mathrm{C}_{2} \mathrm{O}_{4}^{2-} \longrightarrow 2\mathrm{Mn}^{2+} + 10CO_{2}+ 8 H_{2}O \).
02

Determine moles of KMnO4

Using the definition of molarity (moles per liter), calculate the moles of KMnO4 used in the titration. Apply the formula \( M = n / V \), but rearrange to \( n = M * V \), where \( M = 0.01 \)M, \( V = 24.0 / 1000 \)L gives moles of KMnO4, \( n = 0.01*0.024 = 0.00024 \) moles.
03

Calculate moles of H2C2O4

From the balanced chemical equation, 2 moles of KMnO4 react with 5 moles of H2C2O4. Thus, for 0.00024 moles of KMnO4, moles of H2C2O4 required= \( (5 / 2)*0.00024 = 0.0006 \) moles.
04

Determine mass of H2C2O4

Calculate the mass of H2C2O4 using the formula \( \text{mass} = \text{moles} * \text{Molar mass} \). The molar mass of \( H_{2}C_{2}O_{4} = 2 + 2*12 + 4*16 = 90 \) g/mol. Therefore, mass of \( H_{2}C_{2}O_{4} = 0.0006 * 90 = 0.054 \) g.
05

Calculate percent by mass of H2C2O4

The percent by mass of H2C2O4 = \( (\text{Mass of} H_{2}C_{2}O_{4} / \text{Total sample mass}) * 100 = (0.054 / 1) * 100 = 5.4 \% \).

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Most popular questions from this chapter

A \(9.00 \times 10^{2}-\mathrm{mL} 0.200 \mathrm{M} \mathrm{MgI}_{2}\) was electrolyzed. As a result, hydrogen gas was generated at the cathode and iodine was formed at the anode. The volume of hydrogen collected at \(26^{\circ} \mathrm{C}\) and \(779 \mathrm{mmHg}\) was \(1.22 \times 10^{3} \mathrm{~mL}\). (a) Calculate the charge in coulombs consumed in the process. (b) How long (in min) did the electrolysis last if a current of \(7.55 \mathrm{~A}\) was used? (c) A white precipitate was formed in the process. What was it and what was its mass in grams? Assume the volume of the solution was constant.

Predict whether \(\mathrm{Fe}^{3+}\) can oxidize \(\mathrm{I}^{-}\) to \(\mathrm{I}_{2}\) under standard-state conditions.

Calcium oxalate \(\left(\mathrm{CaC}_{2} \mathrm{O}_{4}\right)\) is insoluble in water. This property has been used to determine the amount of \(\mathrm{Ca}^{2+}\) ions in blood. The calcium oxalate isolated from blood is dissolved in acid and titrated against a standardized \(\mathrm{KMnO}_{4}\) solution as described in Problem \(18.72 .\) In one test, it is found that the calcium oxalate isolated from a 10.0 -mL sample of blood requires \(24.2 \mathrm{~mL}\) of \(9.56 \times 10^{-4} \mathrm{M} \mathrm{KMnO}_{4}\) for titration. Calculate the number of milligrams of calcium per milliliter of blood.

The diagram here shows an electrolytic cell consisting of a Co electrode in a \(2.0 \mathrm{M} \mathrm{Co}\left(\mathrm{NO}_{3}\right)_{2}\) solution and a Mg electrode in a \(2.0 \mathrm{M} \mathrm{Mg}\left(\mathrm{NO}_{3}\right)_{2}\) solution. (a) Label the anode and cathode and show the halfcell reactions. Also label the signs \((+\) or \(-)\) on the battery terminals. (b) What is the minimum voltage to drive the reaction? (c) After the passage of \(10.0 \mathrm{~A}\) for \(2.00 \mathrm{~h}\) the battery is replaced with a voltmeter and the electrolytic cell now becomes a galvanic cell. Calculate \(E_{\text {cell. }}\) Assume volumes to remain constant at \(1.00 \mathrm{~L}\) in each compartment.

Which species in each pair is a better oxidizing agent under standard-state conditions: (a) \(\mathrm{Br}_{2}\) or \(\mathrm{Au}^{3+} ?\) (b) \(\mathrm{H}_{2}\) or \(\mathrm{Ag}^{+} ?\) (c) \(\mathrm{Cd}^{2+}\) or \(\mathrm{Cr}^{3+} ?\) (d) \(\mathrm{O}_{2}\) in acidic media or \(\mathrm{O}_{2}\) in basic media?
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