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Chapter 18: Problem 69

The \(\mathrm{SO}_{2}\) present in air is mainly responsible for the phenomenon of acid rain. The concentration of \(\mathrm{SO}_{2}\) can be determined by titrating against a standard permanganate solution as follows: \(5 \mathrm{SO}_{2}+2 \mathrm{MnO}_{4}^{-}+2 \mathrm{H}_{2} \mathrm{O} \longrightarrow \overrightarrow{5 \mathrm{SO}_{4}^{2-}+2 \mathrm{Mn}^{2+}+4 \mathrm{H}^{+}}\) Calculate the number of grams of \(\mathrm{SO}_{2}\) in a sample of air if \(7.37 \mathrm{~mL}\) of \(0.00800 \mathrm{M} \mathrm{KMnO}_{4}\) solution are required for the titration.

Short Answer

Expert verified
The grams of \(\mathrm{SO2}\) present in the sample of air is approximately 0.00944 g.

Step by step solution

01

Calculate moles of KMnO4

Firstly, use the concentration and volume of the \(\mathrm{KMnO_{4}}\) solution to find the number of moles of \(\mathrm{KMnO_{4}}\) used. The formula is simply: Molarity = moles / Volume(L), therefore moles = Molarity x Volume(L). Here, the molarity of \(\mathrm{KMnO_{4}}\) is 0.00800 M and the volume is 7.37 mL (or 7.37 x 10^-3 L). Hence, moles of \(\mathrm{KMnO_{4}}\) = 0.00800 M x 7.37 x 10^-3 L = 5.896 x 10^-5 moles.
02

Use stoichiometry to find moles of SO2

Now, from the chemical reaction, one can see that the ratio of \(\mathrm{KMnO_{4}}\) to \(\mathrm{SO2}\) moles is 2:5. Therefore, the moles of \(\mathrm{SO2}\) will be (5 / 2) times the moles of \(\mathrm{KMnO_{4}}\). So, moles of \(\mathrm{SO2}\) = 5 / 2 x 5.896 x 10^-5 moles = 1.474 x 10^-4 moles.
03

Calculate mass of SO2

Finally, the mass of \(\mathrm{SO2}\) can be obtained by multiplying the number of moles by the molar mass of \(\mathrm{SO2}\) (which is approximately 64.07 g/mol). Hence, mass of \(\mathrm{SO2}\) = 1.474 x 10^-4 moles x 64.07 g/mol = 0.00944 grams.

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Most popular questions from this chapter

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?

Which species in each pair is a better reducing agent under standard-state conditions: (a) Na or Li? (b) \(\mathrm{H}_{2}\) or \(\mathrm{I}_{2} ?(\mathrm{c}) \mathrm{Fe}^{2+}\) or \(\mathrm{Ag} ?\) (d) \(\mathrm{Br}^{-}\) or \(\mathrm{Co}^{2+} ?\)

Balance the following redox equations by the ionelectron method: (a) \(\mathrm{H}_{2} \mathrm{O}_{2}+\mathrm{Fe}^{2+} \longrightarrow \mathrm{Fe}^{3+}+\mathrm{H}_{2} \mathrm{O}\) (in acidic solution) (b) \(\mathrm{Cu}+\mathrm{HNO}_{3} \longrightarrow \mathrm{Cu}^{2+}+\mathrm{NO}+\mathrm{H}_{2} \mathrm{O}\) (in acidic solution) (c) \(\mathrm{CN}^{-}+\mathrm{MnO}_{4}^{-} \longrightarrow \mathrm{CNO}^{-}+\mathrm{MnO}_{2}\) (in basic solution) (d) \(\mathrm{Br}_{2} \longrightarrow \mathrm{BrO}_{3}^{-}+\mathrm{Br}^{-}\) (in basic solution) (e) \(\mathrm{S}_{2} \mathrm{O}_{3}^{2-}+\mathrm{I}_{2} \longrightarrow \mathrm{I}^{-}+\mathrm{S}_{4} \mathrm{O}_{6}^{2-}\) (in acidic solution)

A galvanic cell is constructed by immersing a piece of copper wire in \(25.0 \mathrm{~mL}\) of a \(0.20 \mathrm{M} \mathrm{CuSO}_{4}\) solution and a zinc strip in \(25.0 \mathrm{~mL}\) of a \(0.20 \mathrm{M} \mathrm{ZnSO}_{4}\) solution. (a) Calculate the emf of the cell at \(25^{\circ} \mathrm{C}\) and predict what would happen if a small amount of concentrated \(\mathrm{NH}_{3}\) solution were added to (i) the \(\mathrm{CuSO}_{4}\) solution and (ii) the \(\mathrm{ZnSO}_{4}\) solution. Assume that the volume in each compartment remains constant at \(25.0 \mathrm{~mL}\). (b) In a separate experiment, \(25.0 \mathrm{~mL}\) of \(3.00 \mathrm{M} \mathrm{NH}_{3}\) are added to the \(\mathrm{CuSO}_{4}\) so- lution. If the emf of the cell is \(0.68 \mathrm{~V},\) calculate the formation constant \(\left(K_{\mathrm{f}}\right)\) of \(\mathrm{Cu}\left(\mathrm{NH}_{3}\right)_{4}^{2+}\)

A sample of iron ore weighing \(0.2792 \mathrm{~g}\) was dissolved in an excess of a dilute acid solution. All the iron was first converted to Fe(II) ions. The solution then required \(23.30 \mathrm{~mL}\) of \(0.0194 \mathrm{M} \mathrm{KMnO}_{4}\) for oxidation to Fe(III) ions. Calculate the percent by mass of iron in the ore.
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