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The \(\mathrm{SO}_{2}\) content in air may be determined by passing the air through water to produce a solution of sulfurous acid, \(\mathrm{H}_{2} \mathrm{SO}_{3}\). The subsequent reaction of this solution with potassium permanganate, \(\mathrm{KMnO}_{4}\), establishes the amount of \(\mathrm{SO}_{2}\) absorbed from the air. (a) Write the balanced equation for the reaction of \(\mathrm{SO}_{2}\) with water to produce \(\mathrm{H}_{2} \mathrm{SO}_{3}\). (b) Write the balanced equation for the reaction of \(\mathrm{H}_{2} \mathrm{SO}_{3}\) (or \(\mathrm{SO}^{2-}{ }_{3}\) ) with \(\mathrm{KMnO}_{4}\) (or \(\mathrm{MnO}^{-}{ }_{4}\) ) to form \(\mathrm{MnSO}_{4}, \mathrm{~K}^{+}\) and \(\mathrm{H}_{2} \mathrm{SO}_{4}\), among other products, (c) If 1000 liters of air are passed through water and the resulting solution requires \(2.5 \times 10^{-5}\) moles of \(\mathrm{KMnO}^{5}\) for complete reaction (part b), what is the concentration (in ppm) of SO2 in the air. Assume STP conditions.

Step by step solution

01

(a) Write the balanced equation for the reaction of SO鈧� with water to produce H鈧係O鈧�

First, let's write the unbalanced equation for the reaction of SO鈧� with water: SO鈧� + H鈧侽 -> H鈧係O鈧� Now we need to balance it. In this case, the equation is already balanced. Therefore, the balanced equation is: SO鈧� + H鈧侽 -> H鈧係O鈧�

02

(b) Write the balanced equation for the reaction of H鈧係O鈧� (or SO鈧兟测伝) with KMnO鈧� (or MnO鈧勨伝) to form MnSO鈧�, K鈦�, and H鈧係O鈧�, among other products

Let's write the unbalanced equation for the reaction: H鈧係O鈧� + KMnO鈧� -> MnSO鈧� + K鈦� + H鈧係O鈧� To balance this equation, we will use the half-reaction method. Let's separate the reduction and oxidation reactions Oxidation : SO鈧兟测伝 -> SO鈧劼测伝 + 2e鈦� Reduction : MnO鈧勨伝 + 8H鈦� + 5e鈦� -> Mn虏鈦� + 4H鈧侽 Now, we need to balance the electrons in the two half-reactions. Multiply the oxidation reaction by 5 to balance the number of electrons and then add the two half-reactions. 5*(SO鈧兟测伝 -> SO鈧劼测伝 + 2e鈦�) -> 5SO鈧兟测伝 -> 5SO鈧劼测伝 + 10e鈦� MnO鈧勨伝 + 8H鈦� + 5e鈦� -> Mn虏鈦� + 4H鈧侽 Combining the half-reactions: 5SO鈧兟测伝 + 2MnO鈧勨伝 + 16H鈦� -> 5SO鈧劼测伝 + 2Mn虏鈦� + 4H鈧侽 Now, let's rewrite the equation with the original reactants and products: 5H鈧係O鈧� + 2KMnO鈧� + 6H鈧侽 -> 5H鈧係O鈧� + 2MnSO鈧� + K鈧係O鈧� This is the balanced equation for the reaction of H鈧係O鈧� with KMnO鈧� to form MnSO鈧�, K鈦�, and H鈧係O鈧�, among other products.

03

(c) Determine the concentration of SO鈧� in the air

First, let's calculate the moles of H鈧係O鈧� generated from the 2.5x10鈦烩伒 moles of KMnO鈧� used in the reaction. From the balanced equation in part (b), we know that: 5 moles of H鈧係O鈧� reacts with 2 moles of KMnO鈧� Therefore, moles of H鈧係O鈧� = (5/2) * moles of KMnO鈧� moles of H鈧係O鈧� = (5/2) * (2.5x10鈦烩伒) = 6.25x10鈦烩伒 moles Now we know that 1 mole of SO鈧� produces 1 mole of H鈧係O鈧� from the balanced equation in part (a). So, there are 6.25x10鈦烩伒 moles of SO鈧� in 1000 liters of air. At STP conditions, 1 mole of a gas occupies 22.4 liters. Therefore, the volume of air containing 6.25x10鈦烩伒 moles of SO鈧� is: Volume = (6.25x10鈦烩伒) * (22.4) = 0.0014 liters Now, calculate the concentration of SO鈧� in ppm (parts per million): Concentration of SO鈧� (ppm) = (volume of SO鈧� / total volume of air) * 10^6 Concentration of SO鈧� (ppm) = (0.0014 / 1000) * 10^6 = 1.4 ppm The concentration of SO鈧� in the air is 1.4 ppm.

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Key Concepts

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

Sulfur Dioxide Analysis

Sulfur Dioxide (\(\text{SO}_2\)) is a common air pollutant, mainly produced from burning fossil fuels and from volcanic eruptions. Its presence in the air is problematic because it can form acid rain and respiratory problems in humans. To measure \(\text{SO}_2\) in the atmosphere, air is bubbled through water to create a solution called sulfurous acid (\(\text{H}_2\text{SO}_3\)). This method effectively captures \(\text{SO}_2\) because it promptly reacts with water.
By analyzing this sulfurous acid, we can infer the quantity of \(\text{SO}_2\) in the sampled air. Monitoring sulfur dioxide levels is crucial for effective air quality management and ensuring the health of both the environment and the population.

Balanced Chemical Equations

Balanced chemical equations are essential for understanding chemical reactions because they show the exact proportions of reactants and products. This exercise involves two reactions: the formation of \(\text{H}_2\text{SO}_3\) from \(\text{SO}_2\) and water, and the reaction of \(\text{H}_2\text{SO}_3\) with potassium permanganate (\(\text{KMnO}_4\)).
Ensuring these equations are balanced is key to accurately determining the amounts of each substance involved. In the case of the first reaction:

• \(\text{SO}_2 + \text{H}_2O \rightarrow \text{H}_2\text{SO}_3\) is already balanced, since there is one sulfur atom, two oxygen atoms, and two hydrogen atoms on each side of the equation.

Equations in chemistry must obey the law of conservation of mass, meaning atoms are neither created nor destroyed during a reaction; this is why balanced equations are crucial.

Stoichiometry

Stoichiometry is a fundamental concept in chemistry that involves calculating the relative quantities of reactants and products in chemical reactions. It鈥檚 a powerful tool used to convert between the mass of one substance and the mass, volume, or number of particles of another substance.
In this problem, stoichiometry helps determine the concentration of \(\text{SO}_2\) in the air. We use the balanced equation \(5\text{H}_2\text{SO}_3 + 2\text{KMnO}_4 \rightarrow 5\text{H}_2\text{SO}_4 + 2\text{MnSO}_4 + \text{K}_2\text{SO}_4\) to find out the amount of \(\text{H}_2\text{SO}_3\) that reacted with the known quantity of \(\text{KMnO}_4\). Knowing that 5 moles of \(\text{H}_2\text{SO}_3\) react with 2 moles of \(\text{KMnO}_4\), we calculate the amount of \(\text{SO}_2\) originally present in 1000 liters of air.
This calculation relies heavily on the principles of stoichiometry to provide accurate results.

Air Pollutants Detection

Detecting air pollutants like sulfur dioxide is crucial for environmental and public health. Various methods are used, depending on the specific pollutants and required sensitivity.
In this problem, \(\text{SO}_2\) is detected by converting it into sulfurous acid \(\text{H}_2\text{SO}_3\), followed by quantifying it through a reaction with \(\text{KMnO}_4\). This chemical detection method allows not only identification but also provides quantitative data on concentration levels. Monitoring \(\text{SO}_2\) is particularly important as it contributes to smog and can lead to acid rain formation, affecting both ecosystems and human-made structures.
By understanding and implementing these detection methodologies, environmental agencies can set air quality standards and mitigate the adverse effects of pollutants.