Problem 70 - Chemistry and Chemical Reactivity

Question

Potassium perchlorate is prepared by the following sequence of reactions: $$\begin{aligned}\mathrm{Cl}_{2}(\mathrm{g})+& 2 \mathrm{KOH}(\mathrm{aq}) \longrightarrow \mathrm{KCl}(\mathrm{aq})+\mathrm{KClO}(\mathrm{aq})+\mathrm{H}_{2} \mathrm{O}(\ell) \\\& 3 \mathrm{KClO}(\mathrm{aq}) \longrightarrow 2 \mathrm{KCl}(\mathrm{aq})+\mathrm{KClO}_{3}(\mathrm{aq}) \\\& 4 \mathrm{KClO}_{3}(\mathrm{aq}) \longrightarrow 3 \mathrm{KClO}_{4(\mathrm{aq})+\mathrm{KCl}(\mathrm{aq}) \end{aligned}$$ What mass of \(\mathrm{Cl}_{2}(\mathrm{g})\) is required to produce \(234 \mathrm{kg}\) of \(\mathrm{KClO}_{4} ?\)

Step-by-Step Solution

Answer

479.80 kg of \( \mathrm{Cl}_{2} \) is required to produce 234 kg of \( \mathrm{KClO}_{4} \).

Step 1: Identify the main reaction

The final product of interest is potassium perchlorate (\( \text{KClO}_4 \)). We need to calculate the amount of \( \text{Cl}_2 \) required for its production according to the series of reactions, with a starting focus on the third step: 4 \( \text{KClO}_3 \rightarrow 3 \text{KClO}_4 + \text{KCl} \).

Step 2: Calculate molar masses

Determine the molar masses:- \( \text{KClO}_4 \) has a molar mass of \( 39.1 + 35.5 + 4(16) = 138.55 \text{ g/mol} \)- \( \text{KClO}_3 \) has a molar mass of \( 39.1 + 35.5 + 3(16) = 122.55 \text{ g/mol} \)- \( \text{Cl}_2 \) has a molar mass of \( 2(35.5) = 70.9 \text{ g/mol} \)

Step 3: Convert mass of KClO4 to moles

Using the molar mass, convert 234 kg of \( \text{KClO}_4 \) to moles:\[ 234,000 \text{ g} \, \div \, 138.55 \text{ g/mol} = 1,689.5 \text{ moles of } \text{KClO}_4 \]

Step 4: Relate moles of KClO4 to KClO3

Based on the third reaction, 4 moles of \( \text{KClO}_3 \) produce 3 moles of \( \text{KClO}_4 \). The moles of \( \text{KClO}_3 \) required are:\[ \frac{4}{3} \times 1,689.5 = 2,252.67 \text{ moles of } \text{KClO}_3 \]

Step 5: Relate moles of KClO3 to KClO

The second reaction shows 3 moles of \( \text{KClO} \) produce 1 mole of \( \text{KClO}_3 \). Hence, moles of \( \text{KClO} \) needed:\[ 3 \times 2,252.67 = 6,758.01 \text{ moles of } \text{KClO} \]

Step 6: Relate moles of KClO to Cl2

From the first reaction, 1 mole of \( \text{Cl}_2 \) produces 1 mole of \( \text{KClO} \). Thus, moles of \( \text{Cl}_2 \) required are:\[ 6,758.01 \text{ moles} \]

Step 7: Convert moles of Cl2 to mass

Using the molar mass of \( \text{Cl}_2 \), convert moles to grams:\[ 6,758.01 \text{ moles} \times 70.9 \text{ g/mol} = 479,801.309 \text{ g} \]Then convert grams to kilograms:\[ 479,801.309 \text{ g} \div 1,000 = 479.80 \text{ kg} \]

Key Concepts

Stoichiometry

Stoichiometry is a fundamental concept in chemistry involving the calculation of reactants and products in chemical reactions. When dealing with stoichiometry, it's crucial to understand the balanced chemical equations. These equations provide the relationships between the amounts of reactants and products, typically measured in moles.

In the sequence of reactions for producing potassium perchlorate, stoichiometry allows us to determine the amount of chlorine gas needed to obtain the desired quantity of potassium perchlorate. By examining the coefficients in the balanced equations, we can relate moles of one substance to another.

This foundational skill is pivotal for predicting how much of each chemical is required or produced. Understanding stoichiometry ensures that chemical reactions are efficient and cost-effective, which is essential in both educational settings and industrial applications.

Chlorine Gas

Chlorine gas, represented as \( \mathrm{Cl}_2 \), is a diatomic molecule and plays a vital role in many chemical processes. It is often used as a reactant in chemical reactions due to its reactivity.

In the production of potassium perchlorate, chlorine gas is one of the initial reactants. In the first reaction of the sequence, chlorine gas reacts with potassium hydroxide to eventually form potassium chlorate. Understanding the properties and reactions of chlorine gas helps explain why it is chosen for this reaction.

Due to its highly reactive nature, chlorine can attack other molecules, breaking bonds and forming new compounds. In practical applications, handling chlorine requires careful management due to its toxic nature and potential hazards.

Molar Mass Calculations

Calculating molar mass is a critical step in understanding and working with chemical reactions. The molar mass is the weight of one mole of a substance and is expressed in grams per mole. It is calculated by adding up the atomic masses of all atoms in a molecule.

For instance, in this exercise, it's necessary to calculate the molar masses of \( \mathrm{KClO}_4 \), \( \mathrm{KClO}_3 \), and \( \mathrm{Cl}_2 \) to convert mass to moles and vice versa.

This conversion is elementary yet essential for balancing equations, determining proportions, and ensuring that measurements in a chemical reaction are precise. Being proficient in molar mass calculations enables chemistry students to solve complex problems and verify their results.

Potassium Perchlorate

Potassium perchlorate \( (\mathrm{KClO}_4) \) is a chemical compound frequently used in fireworks, explosives, and other pyrotechnics due to its oxidizing properties.

In this sequence of reactions, the goal is to produce potassium perchlorate starting from chlorine gas. The process involves multiple steps and intermediate compounds such as potassium chlorate \( (\mathrm{KClO}_3) \). Understanding both its chemical structure and how it is chemically synthesized is important for both practical applications and theoretical comprehension.

Potassium perchlorate is highly valued for its ability to release oxygen when decomposed, making it a vital component in industries requiring rapid combustion. Knowledge of its production process and properties is vital for ensuring safety and efficacy in various applications.