Problem 95 - Chemistry and Chemical Reactivity

Question

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

Step-by-Step Solution

Answer

You need 87.8 kg of \( \mathrm{Cl}_{2} \).

Step 1: Write Balanced Chemical Equations

Here are the balanced equations for the reaction steps:1. \( \mathrm{Cl}_{2}(\mathrm{g}) + 2 \mathrm{KOH}(\mathrm{aq}) \rightarrow \mathrm{KCl}(\mathrm{aq}) + \mathrm{KClO}(\mathrm{aq}) + \mathrm{H}_{2}\mathrm{O}(\ell) \)2. \( 3 \mathrm{KClO}(\mathrm{aq}) \rightarrow 2 \mathrm{KCl}(\mathrm{aq}) + \mathrm{KClO}_{3}(\mathrm{aq}) \)3. \( 4 \mathrm{KClO}_{3}(\mathrm{aq}) \rightarrow 3 \mathrm{KClO}_{4}(\mathrm{aq}) + \mathrm{KCl}(\mathrm{aq}) \)

Key Concepts

Balancing Chemical Equations

Balancing chemical equations is a fundamental skill in chemistry that ensures the law of conservation of mass is upheld. This means that the number of atoms of each element is the same on both sides of the equation. When balancing equations, start by listing the number of each type of atom present in the reactants and products. Adjust the coefficients, which are the numbers placed before compounds, to achieve balance.

• Start with compounds that contain the most atoms.
• Balance atoms found in only one reactant and one product first.
• Balance polyatomic ions as a unit if they appear unchanged on both sides.

In the steps of potassium perchlorate synthesis, each equation was systematically balanced to ensure the correct stoichiometry throughout the chemical process.

Stoichiometric Calculations

Stoichiometric calculations involve using the coefficients from balanced chemical equations to determine the relationships between amounts of reactants and products. These calculations allow chemists to predict how much product will form from a given amount of reactant or vice versa.
To perform stoichiometric calculations:

• Convert the mass of a substance to moles using its molar mass.
• Use the stoichiometric coefficients to relate the moles of reactants to the moles of products.
• Convert moles back to mass if needed.

In the case of potassium perchlorate synthesis, calculations begin with the determination of how much chlorine gas (\(\mathrm{Cl}_{2}\)) is needed to produce 234 kg of \(\mathrm{KClO}_{4}\). By converting this mass to moles, and tracing back through each balanced equation, the amount of \(\mathrm{Cl}_{2}\) is found.

Potassium Perchlorate Synthesis

Potassium perchlorate (\(\mathrm{KClO}_{4}\)) synthesis involves a series of reactions that transform chlorine gas (\(\mathrm{Cl}_{2}\)) and potassium hydroxide (\(\mathrm{KOH}\)) into \(\mathrm{KClO}_{4}\).
Each reaction step serves a specific purpose:

• First, chlorine reacts with potassium hydroxide to form \(\mathrm{KCl}\), \(\mathrm{KClO}\), and \(\mathrm{H}_{2}\mathrm{O}\).
• Then, several transformations involving different oxychlorides eventually lead to \(\mathrm{KClO}_{4}\).

Through these consecutive transformations, the intermediate compounds, \(\mathrm{KClO}\) and \(\mathrm{KClO}_{3}\), undergo further chemical reactions, yielding the target compound \(\mathrm{KClO}_{4}\). Each step requires precise control over reaction conditions to ensure maximum yield of \(\mathrm{KClO}_{4}\).