Question

What is meant by the term mole ratio? Give an example of a mole ratio, and explain how it is used in solving a stoichiometry problem.

Short answer

Mole ratio is a numerical comparison of moles of one substance to another substance in a balanced chemical equation, used for stoichiometric calculations. For example, in the equation \(2 H_2 + O_2 \rightarrow 2 H_2O\), the mole ratios are 2 moles of H2 to 1 mole of O2, 2 moles of H2 to 2 moles of H2O, and 1 mole of O2 to 2 moles of H2O. To solve a stoichiometry problem using mole ratios, find the mole ratio from the balanced equation, convert given moles using the mole ratio, and solve for the unknown moles. In our example, 4 moles of H2 reacting with excess O2 would produce 4 moles of H2O.

Step-by-step solution

Definition of Mole Ratio

Mole ratio is a numerical comparison of moles of one substance to another substance in a balanced chemical equation. It is used to convert from moles of one substance to moles of another substance and form a basis for stoichiometric calculations in a chemical reaction.

Example of Mole Ratio

Consider the following balanced chemical equation: \(2 H_2 + O_2 \rightarrow 2 H_2O\) The mole ratios in this equation are: - 2 moles of hydrogen (H2) to 1 mole of oxygen (O2) - 2 moles of hydrogen (H2) to 2 moles of water (H2O) - 1 mole of oxygen (O2) to 2 moles of water (H2O)

Use of Mole Ratio in Solving a Stoichiometry Problem

To demonstrate the use of mole ratios in a stoichiometry problem, let's consider the above balanced chemical equation and find the amount of water formed (in moles) when 4 moles of hydrogen (H2) react with an excess of oxygen (O2). Step 1: Identify the Given Information We are given that 4 moles of hydrogen (H2) react, and we need to find the moles of water (H2O) formed. Step 2: Determine Mole Ratio from Balanced Equation From the balanced equation above, we have a mole ratio \[2 H_{2} : 2 H_{2}O\] Step 3: Convert Given Moles Using Mole Ratio To convert 4 moles of hydrogen (H2) to moles of water (H2O): \(\frac{moles\ of\ H_{2}O}{moles\ of\ H_{2}} = \frac{2}{2}\) Step 4: Solve for Unknown Moles Now, we will solve for moles of water (H2O): \[\frac{moles\ of\ H_{2}O}{4\ moles\ of\ H_{2}} = \frac{2}{2}\] So, \[moles\ of\ H_{2}O = 4\ moles\ of\ H_{2}\] Thus, when 4 moles of hydrogen react, 4 moles of water are formed using the mole ratio concept in stoichiometry.

Key concepts

Understanding Stoichiometry

Stoichiometry is a fundamental concept in chemistry that involves the quantitative relationships between the reactants and products in a chemical reaction. It hinges on the conservation of mass, where the mass of reactants used and products formed are equal. This is because in a chemical reaction, atoms are neither created nor destroyed; they are simply rearranged.

Stoichiometry uses the mole as a basic unit to measure the amount of a substance. Since molecules are extremely small and numerous, it is impractical to count each molecule individually. Instead, chemists use the mole, which is approximately equal to \(6.022 \times 10^{23}\) entities—Avogadro's number. Stoichiometry allows us to predict the amounts of products formed in a reaction or the amounts of reactants needed to form a certain amount of product. To do this accurately, a balanced chemical equation is essential as it provides the mole ratios of the reactants and products needed to perform these calculations.

The Role of a Balanced Chemical Equation

The balanced chemical equation is the 'recipe' for a chemical reaction. It tells us exactly what and how much we need of each substance to create a desired product. Balancing an equation is crucial because it reflects the law of conservation of mass—you must have the same number of each type of atom on both sides of the reaction.

A balanced chemical equation also reveals the mole ratio of reactants and products. Since a mole of any substance contains the same number of entities (Avogadro's number), these ratios allow us to convert between moles of different substances accurately. For instance, the balanced equation \(2 H_2 + O_2 \rightarrow 2 H_2O\) indicates that 2 moles of hydrogen gas react with 1 mole of oxygen gas to produce 2 moles of water. This is an intrinsic part of stoichiometry and a key in understanding how different quantities of reactants can produce a certain amount of product.

Applying Stoichiometric Calculations

Stoichiometric calculations are the mathematical aspect of stoichiometry employed to solve problems related to chemical reactions. Utilizing mole ratios derived from balanced chemical equations, these calculations allow us to convert moles of one substance to moles of another. To perform stoichiometric calculations:

• First, start with a balanced chemical equation to obtain the mole ratios between reactants and products.
• Then, determine what information is given and what is required—whether it’s the amount of reactant needed or the amount of product that will be formed.
• Use the mole ratio to set up conversion factors and apply dimensional analysis to solve for the unknown quantity.

For example, using the mole ratio from our earlier balanced equation (2 moles of \(H_2\) for 2 moles of \(H_2O\)), we can calculate that reacting 4 moles of \(H_2\) will produce 4 moles of \(H_2O\). These calculations are the cornerstone of quantitative analysis in chemistry, making it possible to scale reactions up or down and to predict yields, which is essential in industrial applications and research.