Problem 11 - Chemistry in 30 days

Question

For the reaction \(A+2 B \rightarrow C, 5\) moles of \(A\) and 8 moles of \(B\) will produce (a) 5 moles of \(\bar{C}\) (b) 4 moles of \(\vec{C}\) (c) 8 moles of \(\mathrm{C}\) (d) 13 moles of \(C\)

Step-by-Step Solution

Answer

4 moles of \(C\) will be produced.

Step 1: Identify the Reaction Stoichiometry

The given chemical reaction is \(A + 2B \rightarrow C\). This means that one mole of A reacts with two moles of B to produce one mole of C.

Step 2: Determine Limiting Reactant

We are given 5 moles of A and 8 moles of B. According to the stoichiometry, we need 2 moles of B for each mole of A. For 5 moles of A, we would need \(5 \times 2 = 10\) moles of B. Since we only have 8 moles of B, B is the limiting reactant.

Step 3: Calculate Maximum Formation of C

Since B is the limiting reactant, it will determine how much C can be produced. For every 2 moles of B, 1 mole of C is produced. Therefore, \(\frac{8}{2} = 4\) moles of C can be produced with the given amount of B.

Key Concepts

Limiting Reactant

In chemical reactions, the limiting reactant is the substance that is entirely consumed first, preventing further reaction from occurring. Imagine you're mixing ingredients for a cake; if you run out of flour, you can't make any more cake, regardless of how many eggs you have left—flour is your limiting ingredient.
This principle applies to chemical reactions as well.

• The limiting reactant dictates the maximum amount of product that can be formed.
• To identify it, compare the mole ratio in the balanced equation with the available reactants.
• Usually, calculations are required to identify which reactant will run out first.

In our exercise, the reaction is described by the equation: \[A + 2B \rightarrow C\]Given 5 moles of \(A\) and 8 moles of \(B\), we need 10 moles of \(B\) to react with all of \(A\). Since only 8 moles of \(B\) are available, \(B\) is the limiting reactant. Once those 8 moles of \(B\) are used, the reaction stops regardless of any excess \(A\).

Chemical Reactions

A chemical reaction involves the transformation of reactants into products. Key characteristics include the breaking and forming of bonds and the conservation of mass. When you bake cookies, mixing flour, eggs, and sugar results in new substances: delicious cookies. Likewise, in a chemical equation, reactants come together to form new products with distinct properties.

• Chemical equations show which substances react together and the quantities involved.
• They're presented in the form: Reactants \(\rightarrow\) Products, indicating the direction of the reaction.
• The numbers before chemicals (coefficients) simplify the amounts needed for a reaction to go to completion.

For the reaction \(A + 2B \rightarrow C\), it shows one mole of \(A\) reacts with two moles of \(B\) to produce one mole of \(C\). This equation describes the specific recipe needed for \(C\) to materialize, offering vital information for predicting the amounts of products formed.

Mole Concept

The mole is a fundamental concept in chemistry that allows scientists to count particles at a macroscopic level, comparable to using a dozen to count eggs.

• A mole is defined as exactly \(6.022 \times 10^{23}\) entities (Avogadro's number).
• It provides a bridge between the atomic and macroscopic worlds.
• Moles are based on the amount of a substance, often measured in grams, that contains the same number of entities as there are in 12 grams of carbon-12.

By using the mole concept, we can relate the mass of a substance to the number of particles it contains, enabling accurate stoichiometric calculations in reactions. For instance, knowing \(A + 2B \rightarrow C\), allows us to calculate how much of each participant is necessary to achieve the desired reaction outcomes, like determining the limiting reactant and theoretical yield of products. Understanding the mole concept helps demystify chemical equations, making chemistry more accessible and intuitive.