Question

Which of the following statements is(are) true? a. A balanced equation relates the numbers of molecules of reactants and products (or numbers of moles of reactants and products). b. To convert between moles of reactants and moles of products, we use mole ratios derived from the balanced equation. c. Often reactants are not mixed in stoichiometric quantities (they do not "run out" at the same time). In that case, we must use the limiting reactant to calculate the amounts of products formed. d. When a chemical reaction occurs, it must follow the law of conservation of mass.

Short answer

All four statements (a, b, c, and d) are true. A balanced equation relates the numbers of molecules or moles of reactants and products, mole ratios are used to convert between moles of reactants and products, limiting reactants must be considered when reactants are not mixed in stoichiometric quantities, and chemical reactions must follow the law of conservation of mass.

Step-by-step solution

Statement a:

A balanced equation relates the numbers of molecules of reactants and products (or numbers of moles of reactants and products). This statement is true. A balanced chemical equation shows the proportions of reactants and products in a chemical reaction. The coefficients in a balanced equation represent the numbers of moles of each substance, which in turn represent the number of molecules of each substance (since one mole contains Avogadro's number of particles).

Statement b:

To convert between moles of reactants and moles of products, we use mole ratios derived from the balanced equation. This statement is also true. Mole ratios are derived from the coefficients in a balanced chemical equation and are used to convert between moles of different substances in the reaction. These ratios tell us how many moles of one substance are needed or produced for every mole of another substance in the reaction.

Statement c:

Often reactants are not mixed in stoichiometric quantities (they do not "run out" at the same time). In that case, we must use the limiting reactant to calculate the amounts of products formed. This statement is true as well. When reactants do not have the exact stoichiometric proportions, one of them is going to run out before the others, limiting the amount of product that can be formed. To calculate the amounts of products formed in such a case, we must first identify the limiting reactant and use its amount to calculate the amounts of products formed.

Statement d:

When a chemical reaction occurs, it must follow the law of conservation of mass. This statement is true. The law of conservation of mass states that the total mass of reactants in a chemical reaction is always equal to the total mass of products formed. This means that the atoms of each element in the reactants must be accounted for in the products without any loss or gain of mass. This principle is the basis for balancing chemical equations. In conclusion, all four statements (a, b, c, and d) are true.

Key concepts

Balanced Chemical Equation

At the heart of stoichiometry lies the balanced chemical equation. This equation represents the roadmap to a chemical reaction. Imagine baking a cake, where the recipe provides specific quantities of ingredients to mix; a balanced chemical equation does the same but for chemical reactions. It aligns with the law of conservation of mass, ensuring that the atoms of each element are conserved from reactants to products.

The coefficients in these equations are pivotal—they reveal the proportion of molecules or moles of each substance that participate in the reaction. For example, in the equation \( 2H_2 + O_2 \rightarrow 2H_2O \), we interpret the coefficients as ratios: for every 2 moles of hydrogen (\( H_2 \) gas), 1 mole of oxygen (\( O_2 \) gas) is required to produce 2 moles of water (\( H_2O \) liquid). This accurate ratio maintains balance and makes sure the scales of reaction don't tip — it's chemical equality at its finest.

Mole Ratio

Building on from a balanced equation, the mole ratio is like the currency exchange rate in the world of chemistry. It allows us to convert between moles of different substances involved in a chemical reaction. Just as you would exchange dollars for euros based on the current rate, mole ratios help chemists convert between reactants and products.

These ratios are derived from the coefficients in the balanced chemical equation; hence, understanding the equation is essential for correct conversions. For instance, in the combustion of propane described by the equation \( C_3H_8 + 5O_2 \rightarrow 3CO_2 + 4H_2O \), the mole ratio between \( C_3H_8 \) and \( CO_2 \) is \(1:3\). This signifies that each mole of propane burned should yield three moles of carbon dioxide, given there is enough oxygen. It's like a molecular choreography, where each participant knows its count for the performance.

Limiting Reactant

Chemical reactions are a bit like a buffet where certain dishes are more popular than others. The limiting reactant in a chemical reaction is similar to the first dish that runs out at a buffet. It's the substance that limits the extent of the reaction and ultimately determines how much product can be formed.

Identifying the limiting reactant is crucial when the reactants are not mixed in their perfect stoichiometric ratios. Just as if you run out of flour while baking a large batch of cookies, no matter how much of the other ingredients you have, you can't produce more cookies. In chemical terms, once the limiting reactant is consumed, the reaction stops. For a real-life application, consider a reaction between nitrogen and hydrogen to form ammonia: \( N_2 + 3H_2 \rightarrow 2NH_3 \). If you start with 10 moles of hydrogen and only 3 moles of nitrogen, nitrogen will be your limiting reactant because it will run out first.

Law of Conservation of Mass

The law of conservation of mass is a scientific pinning that holds the universe's matter accounted for, just like a meticulous inventory of a store's stock. This law asserts that mass is neither created nor destroyed in a chemical reaction; rather, the mass of the reactants must equal the mass of the products. It's a matter of universal bookkeeping.

When we balance chemical equations, we are honoring this law. For example, if you observe the simple formation of water from hydrogen and oxygen, no hydrogen or oxygen atoms are lost or gained in the process. They simply rearrange to form water molecules. This principle is not just important for academic chemistry; it has practical applications. For example, when designing a chemical process in an industrial plant, engineers must ensure that the mass entering and exiting the process is balanced to prevent the accumulation of unreacted materials or waste products.