Problem 6 - Chemistry Matter and Change

Question

State how many mole ratios can be written for a chemical reaction involving three substances.

Step-by-Step Solution

Answer

There are \(3\) mole ratios that can be written for a chemical reaction involving three substances, A, B, and C as follows: A:B, A:C, and B:C. The mole ratios are based on the stoichiometric coefficients of the substances in the balanced chemical equation.

Step 1: Understand the concept of a mole ratio

A mole ratio compares the moles of one substance to the moles of another substance in a balanced chemical equation. A given chemical reaction may involve more than one mole ratio, depending on the number of substances reacting and the stoichiometric coefficients of each substance.

Step 2: Consider a generic chemical reaction

Let's consider a generic chemical reaction involving three substances, A, B, and C, with stoichiometric coefficients x, y, and z, respectively: \[x\mathrm{A} + y\mathrm{B} \rightarrow z\mathrm{C}\]

Step 3: Identify possible mole ratios

In this reaction, we can establish the following mole ratios: A:B, A:C, and B:C. We can write each of these mole ratios in terms of the stoichiometric coefficients of the balanced chemical equation: 1. Mole ratio of A to B: \(\frac{x}{y}\) 2. Mole ratio of A to C: \(\frac{x}{z}\) 3. Mole ratio of B to C: \(\frac{y}{z}\)

Step 4: Count the mole ratios

We have identified three mole ratios for a chemical reaction involving three substances. Thus, there are \(3\) mole ratios that can be written for this reaction.

Key Concepts

Stoichiometric Coefficients

Stoichiometric coefficients are numbers that appear before the formulas of substances in a chemical equation. They indicate the ratio in which the substances react or are produced. For example, in the equation \(xA + yB \rightarrow zC\), the coefficients \(x\), \(y\), and \(z\) tell us the molar proportions of substances A, B, and C.
The coefficients show how many moles of each substance participate in the chemical reaction.

• If \(x = 2\), \(y = 3\), and \(z = 1\), it means 2 moles of A react with 3 moles of B to produce 1 mole of C.


• This makes the stoichiometric coefficients crucial for calculating the mole ratios, letting us understand how much of each substance is involved.

Understanding stoichiometric coefficients helps seize the quantitative essence of a chemical reaction. This is essential for anyone working with chemical reactions, from students to professionals.

Balanced Chemical Equation

A balanced chemical equation represents a chemical reaction where the number of atoms for each element is the same on both sides of the equation. Balancing is crucial for making accurate mole ratio calculations.
Consider the equation \(2H_2 + O_2 \rightarrow 2H_2O\). Here:

• Two molecules of hydrogen (\(2H_2\)) react with one molecule of oxygen (\(O_2\)) to yield two molecules of water (\(2H_2O\)).


• Each element's count is balanced: 4 hydrogens and 2 oxygens on both sides of the equation.

Balancing is achieved by adjusting stoichiometric coefficients until the number of atoms for each element is equal on both sides. This ensures the law of conservation of mass is satisfied, a fundamental principle of chemistry.
Importantly, balanced equations allow chemists to use mole ratios effectively, making stoichiometry calculations feasible and accurate.

Chemical Reaction

Chemical reactions involve the transformation of substances through breaking and forming of chemical bonds. In a reaction, reactants (starting materials) are converted into products (new substances).
For example, in \(xA + yB \rightarrow zC\), A and B are reactants that react to form product C. These transformations are described using chemical equations, which are essential tools in chemistry.

• Chemical reactions can be classified into types like synthesis, decomposition, single and double displacement based on how the reactants interact.


• Reactions must obey conservation laws, which means mass and energy should be conserved during the process.

Mole ratios, derived from stoichiometric coefficients, are an integral part of understanding the quantities involved in reactions. They enable chemists to predict the amounts of reactants consumed and products formed, enhancing the grasp of chemical processes and their practical applications.