/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 125 The \(\mathrm{SO}_{2}\) present ... [FREE SOLUTION] | 91影视

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Chapter 19: Problem 125

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: \(5 \mathrm{SO}_{2}+2 \mathrm{MnO}_{4}^{-}+2 \mathrm{H}_{2} \mathrm{O} \longrightarrow 5 \mathrm{SO}_{4}^{2-}+2 \mathrm{Mn}^{2+}+4 \mathrm{H}^{+}\) 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 is required for the titration.

Short Answer

Expert verified
0.00944 grams of \( \mathrm{SO}_{2} \) are in the sample.

Step by step solution

01

Identify the Problem and Information

We are given a chemical reaction where \( \mathrm{SO}_{2} \) reacts with \( \mathrm{KMnO}_{4} \) in a titration process. We need to find the mass of \( \mathrm{SO}_{2} \) in a sample using the given volume and concentration of \( \mathrm{KMnO}_{4} \). The chemical reaction is: \[5\ \mathrm{SO}_{2}+2\ \mathrm{MnO}_{4}^{-}+2\ \mathrm{H}_{2} \mathrm{O}\longrightarrow 5\ \mathrm{SO}_{4}^{2-}+2\ \mathrm{Mn}^{2+}+4\ \mathrm{H}^{+}\] So, 2 moles of \( \mathrm{MnO}_{4}^{-} \) react with 5 moles of \( \mathrm{SO}_{2} \).
02

Calculate Moles of KMnO4 Used

Use the concentration and volume of \( \mathrm{KMnO}_{4} \) to calculate moles: \[ moles\ of\ \mathrm{KMnO}_{4} = 0.00800\ \mathrm{M} \times \frac{7.37\ \mathrm{mL}}{1000\ \mathrm{mL/L}} = 5.896\times 10^{-5}\ \mathrm{mol} \]
03

Determine Moles of SO2 Using Stoichiometry

From the reaction equation, the ratio of \( \mathrm{SO}_{2} \) to \( \mathrm{KMnO}_{4} \) is \( \frac{5}{2} \). So, moles of \( \mathrm{SO}_{2} \) is \[ moles\ of\ \mathrm{SO}_{2} = 5.896\times 10^{-5}\ \mathrm{mol}\ \times \frac{5}{2} = 1.474\times 10^{-4}\ \mathrm{mol} \]
04

Calculate Mass of SO2

Use the molar mass of \( \mathrm{SO}_{2} \) (64.07 g/mol) to calculate the mass: \[ mass\ of\ \mathrm{SO}_{2} = 1.474\times 10^{-4}\ \mathrm{mol} \times 64.07\ \mathrm{g/mol} = 0.009441\ \mathrm{g} \]
05

Final Solution

Summarize the final calculation: The mass of \( \mathrm{SO}_{2} \) in the sample is approximately \( 0.00944 \) grams.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Understanding Acid Rain
Acid rain is a harmful environmental phenomenon caused primarily by emissions of sulfur dioxide (SO鈧�) and nitrogen oxides. These gases react with water vapor in the atmosphere to form acids, such as sulfuric acid (H鈧係O鈧�), which then fall to the ground as rain. This type of precipitation can damage plants, aquatic life, and infrastructure. Reducing emissions of SO鈧�, which is often produced by burning fossil fuels, can help mitigate acid rain.
Exploring Chemical Reactions
Chemical reactions involve the transformation of substances through the breaking and forming of bonds. In the given exercise, sulfur dioxide (SO鈧�) reacts with potassium permanganate (KMnO鈧�) in a titration. This particular reaction converts SO鈧� into sulfate ions (SO鈧劼测伝) and manganese ions (Mn虏鈦�). Understanding these processes helps us see how substances change, often transforming harmful compounds into less damaging ones. In industrial applications, such reactions can be used to reduce pollutants.
Deep Dive into Stoichiometry
Stoichiometry is the study of quantitative relationships in chemical reactions. It allows us to calculate how much of each substance is needed or produced. In the exercise, the reaction ratio is 5 moles of SO鈧� to 2 moles of KMnO鈧�. By knowing this ratio, we can calculate the exact amount of reactants required, ensuring no wastage and accurate results. Stoichiometry enables chemists to scale reactions efficiently, which is crucial in both laboratory and industrial settings.
Mastering Molar Mass Calculation
Calculating the molar mass is essential for converting moles into grams. Molar mass is the weight of one mole of a substance and is expressed in grams per mole. For SO鈧�, the molar mass is determined by adding the atomic masses: 32.07 g/mol for sulfur and 2 脳 16.00 g/mol for oxygen, totaling 64.07 g/mol. Using this value, we can find the mass of SO鈧� involved in the reaction from the number of moles calculated, bridging the gap between theoretical chemistry and practical application.

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