Question

Write all the mole-mole factors for each of the following equations: a. \(2 \mathrm{SO}_{2}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{SO}_{3}(g)\) b. \(4 \mathrm{P}(s)+5 \mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{P}_{2} \mathrm{O}_{5}(s)\)

Short answer

Mole-mole factors for (a): 2 SO\textsubscript{2} : 1 O\textsubscript{2}, 2 SO\textsubscript{2} : 2 SO\textsubscript{3}, and 1 O\textsubscript{2} : 2 SO\textsubscript{3}. For (b): 4 P : 5 O\textsubscript{2}, 4 P : 2 P\textsubscript{2}O\textsubscript{5}, and 5 O\textsubscript{2} : 2 P\textsubscript{2}O\textsubscript{5}.

Step-by-step solution

- Understand Mole-Mole Factors

Mole-mole factors describe the ratio of moles of each substance involved in a chemical reaction, based on the coefficients in the balanced equation.

- Identify Mole-Mole Factors for Equation (a)

For the reaction \(2 \text{SO}_{2}(g) + \text{O}_{2}(g) \rightarrow 2 \text{SO}_{3}(g)\): The mole-mole factors are:- 2 moles of SO\textsubscript{2} react with 1 mole of O\textsubscript{2}- 2 moles of SO\textsubscript{2} produce 2 moles of SO\textsubscript{3}- 1 mole of O\textsubscript{2} produces 2 moles of SO\textsubscript{3}

- Identify Mole-Mole Factors for Equation (b)

For the reaction \(4 \text{P}(s) + 5 \text{O}_{2}(g) \rightarrow 2 \text{P}_{2} \text{O}_{5}(s)\): The mole-mole factors are:- 4 moles of P react with 5 moles of O\textsubscript{2}- 4 moles of P produce 2 moles of P\textsubscript{2}O\textsubscript{5}- 5 moles of O\textsubscript{2} produce 2 moles of P\textsubscript{2}O\textsubscript{5}

Key concepts

Chemical Equations

Chemical equations are symbolic representations of chemical reactions. They show the reactants (substances that start the reaction) on the left side, and the products (substances formed from the reaction) on the right side. The arrow between them indicates the direction of the reaction.
For example, in the equation for sulfur dioxide reacting with oxygen to form sulfur trioxide:
\(2 \text{SO}_{2}(g) + \text{O}_{2}(g) \rightarrow 2 \text{SO}_{3}(g)\), the reactants are \(\text{SO}_{2}\) and \(\text{O}_{2}\), and the product is \(\text{SO}_{3}\).
Chemical equations must be balanced, meaning the number of atoms for each element must be the same on both sides. This is necessary due to the Law of Conservation of Mass, which states that matter cannot be created or destroyed.
Balancing helps us understand the relationship between different substances in a reaction, which is vital for calculating amounts in stoichiometry.

Stoichiometry

Stoichiometry is the study of the quantitative relationships between reactants and products in a chemical reaction. It involves calculations that use the balanced chemical equation to predict the amount of reactants needed or products formed.
To perform stoichiometric calculations, you use mole ratios derived from the coefficients in the balanced chemical equation. These ratios tell us how much of one substance will react with or produce a certain amount of another substance.
For example, in the equation \(2 \text{SO}_{2}(g) + \text{O}_{2}(g) \rightarrow 2 \text{SO}_{3}(g)\), the coefficients indicate that 2 moles of \(\text{SO}_{2}\) react with 1 mole of \(\text{O}_{2}\) to produce 2 moles of \(\text{SO}_{3}\). This information can be used to calculate how many moles or grams of a substance are needed or produced.

Molar Ratios

Molar ratios are fractions derived from the coefficients of a balanced chemical equation. They indicate the proportions of reactants and products involved in the reaction.
For instance, in the equation \(4 \text{P}(s) + 5 \text{O}_{2}(g) \rightarrow 2 \text{P}_{2} \text{O}_{5}(s)\), the molar ratios are:

• 4 moles of \(\text{P}\) to 5 moles of \(\text{O}_{2}\)
• 4 moles of \(\text{P}\) to 2 moles of \(\text{P}_{2} \text{O}_{5}\)
• 5 moles of \(\text{O}_{2}\) to 2 moles of \(\text{P}_{2} \text{O}_{5}\)

Molar ratios are essential for converting between moles of different substances in a reaction.
For example, if you know you have 8 moles of \(\text{P}\), you can use the molar ratio (4 moles of \(\text{P}\) : 5 moles of \(\text{O}_{2}\)) to find that you need 10 moles of \(\text{O}_{2}\). Molar ratios can also help determine the limiting reactant and calculate theoretical yields.

Chemical Reactions

Chemical reactions involve the breaking and forming of chemical bonds, resulting in the transformation of reactants into products. Each type of reaction has its own characteristics and behavior.
Main types of chemical reactions include:

• Combination reactions: Two or more substances combine to form a single product. Example: \(2 \text{H}_{2}(g) + \text{O}_{2}(g) \rightarrow 2 \text{H}_{2}\text{O}(l)\).
• Decomposition reactions: A single substance breaks down into two or more products. Example: \(\text{2HgO}(s) \rightarrow 2 \text{Hg}(l) + \text{O}_{2}(g)\).
• Displacement reactions: One element replaces another in a compound. Example: \(\text{Zn}(s) + \text{2HCl}(aq) \rightarrow \text{ZnCl}_{2}(aq) + \text{H}_{2}(g)\).
• Double displacement reactions: Ions in two compounds switch places. Example: \(\text{AgNO}_{3}(aq) + \text{NaCl}(aq) \rightarrow \text{AgCl}(s) + \text{NaNO}_{3}(aq)\).

Recognizing the type of reaction helps in predicting products and balancing the equations.