Problem 79 - Chemistry Matter and Change

Question

Why must an equation be balanced before using it to determine the volumes of gases involved in a reaction?

Step-by-Step Solution

Answer

An equation must be balanced before using it to determine the volumes of gases involved in a reaction because it ensures the conservation of mass, as dictated by the law of conservation of mass. Balancing an equation provides the correct mole ratios which can be converted into volume ratios based on Avogadro's Law. This allows us to accurately calculate the volumes of gases, both reactants and products, involved in a reaction. If the equation is not balanced, the calculated volumes will be incorrect, leading to errors in experimental results and calculations.

Step 1: Law of Conservation of Mass

According to the law of conservation of mass, the total mass of the reactants is equal to the total mass of the products in a chemical reaction. Balancing an equation ensures that the number of atoms for each element remains the same in the reactants and the products, thus expressing this law.

Step 2: Stoichiometry

Stoichiometry refers to the calculation of the relative quantities of reactants and products in chemical reactions based on the balanced equation. It allows us to determine the required amount or volume of reactants and the possible amount or volume of products formed in a reaction.

Step 3: Application of Balanced Equations in Gas Reactions

In gaseous reactions at constant temperature and pressure, the mole ratios of gases can be converted into volume ratios due to Avogadro's Law, which states that equal volumes of different gases at the same temperature and pressure contain the same number of particles (atoms or molecules). The balanced equation provides the required information to calculate the volumes of gases involved in a reaction.

Step 4: Importance of Balancing Equations

Balancing an equation is necessary for determining the volumes of gases involved in a reaction because it gives the mole ratios, which can be converted into volume ratios. If the equation is not balanced, the calculated volumes will be incorrect, leading to errors in experimental results and calculations.

Step 5: Example

Consider the following unbalanced reaction: \(N_{2} + H_{2} \rightarrow NH_{3}\). If we use the unbalanced equation, it incorrectly states that 1 mole of nitrogen reacts with 1 mole of hydrogen to produce 1 mole of ammonia. This would confuse our calculations for the volumes of gases involved. If we balance the equation, we get the balanced equation: \(N_{2} + 3H_{2} \rightarrow 2NH_{3}\), which correctly states that 1 mole of nitrogen reacts with 3 moles of hydrogen to produce 2 moles of ammonia. Now we can correctly determine the volumes of gases involved in the reaction, respecting the law of conservation of mass and Avogadro's Law.

Key Concepts

Conservation of Mass

In any chemical reaction, the principle of the conservation of mass dictates that matter is neither created nor destroyed. This means that the total mass of the reactants must equal the total mass of the products. For this reason, it is crucial to balance chemical equations. By ensuring the number of atoms for each element remains the same on both sides of the equation, we uphold the law of conservation of mass. For example, if you are reacting hydrogen with oxygen to form water, you must have an equal number of hydrogen and oxygen atoms in both the reactants and products. This helps us accurately predict the outcome of the reaction.

Stoichiometry

Stoichiometry is a key concept in chemistry that involves calculating the relative quantities of reactants and products in chemical reactions. It relies on balanced chemical equations to provide the initial measurements to determine needed or produced quantities. When you have a balanced equation, stoichiometry lets you understand how much of each reactant is necessary or how much product will be formed.

• Helps in determining the exact amounts of substances needed.
• Based on the principle of mole ratios from the balanced equation.
• Ensures accurate predictions of the reaction progress.

Without a balanced equation, stoichiometric calculations can lead to incorrect results, undermining experimental accuracy.

Avogadro's Law

Avogadro's Law is a fundamental principle that states equal volumes of gases, at the same temperature and pressure, contain an equal number of particles. This concept is particularly useful when dealing with gaseous reactions. It allows the use of mole ratios from balanced chemical equations to predict volume ratios of gases involved in a reaction. Thus, a balanced equation becomes a tool in calculating gas volumes by ensuring that mole ratios directly translate to volume ratios. This understanding is key to solving problems related to gas-related reactions efficiently and accurately.

Mole Ratios

Mole ratios, derived from the coefficients in a balanced chemical equation, are crucial in determining the relationship between reactants and products. These ratios tell us how many moles of one substance react with a given amount of another substance. In gas reactions, due to Avogadro's Law, these mole ratios can also be interpreted as volume ratios. This simplifies calculations in gas reactions because you can directly use the balanced equation to determine the necessary volumes of gases required or produced. For instance, in the balanced equation for forming ammonia, the mole ratio of nitrogen to hydrogen to ammonia is 1:3:2, meaning one mole of nitrogen reacts with three moles of hydrogen to yield two moles of ammonia.