Question

Describe how a mole ratio is correctly expressed when it is used to solve a stoichiometric problem.

Short answer

A mole ratio is correctly expressed when it is used to solve a stoichiometric problem by following these steps: 1. Write the balanced chemical equation. 2. Identify the mole ratio of interest. 3. Extract the mole ratio from the balanced equation as a fraction. 4. Set up the stoichiometric problem using the mole ratio to convert the given number of moles of one substance to the moles of another substance. 5. Solve the stoichiometric problem by plugging in the values for the moles of the given substance and the mole ratio, and calculate the moles of the unknown substance. For example, if the balanced equation is \(2A + 3B \rightarrow 4C\) and we need the mole ratio of A:B, the mole ratio would be \(\frac{2}{3}\). To determine the moles of A needed to react with 9 moles of B, the calculation would be: \(\text{Moles of A} = 9\,moles\,B \times \frac{2\,moles\,A}{3\,moles\,B} = 6\,moles\,A\).

Step-by-step solution

Write the balanced chemical equation

The balanced chemical equation is necessary to determine the mole ratios of the substances involved in the reaction. Make sure that the number of atoms for each element on the reactant side is equal to the number of atoms for the same element on the product side.

Identify the mole ratio of interest

Identify the substances you are working with to establish the mole ratio needed. For example, if the problem is asking how many moles of substance A are required to react with a given number of moles of substance B, the mole ratio of A:B will be needed.

Extract the mole ratio from the balanced equation

Once you have the balanced equation, look at the coefficients in front of the substances you are working with. The coefficients represent the number of moles of each substance involved in the reaction. Write down the mole ratio expressed as a fraction. For example, if the balanced equation is: \(2A + 3B \rightarrow 4C\) And we need the mole ratio of A:B, it would be: \(Mole\,ratio\,of\,A:B = \frac{2}{3}\)

Set up the stoichiometric problem

You'll now use the mole ratio to convert the given number of moles of one substance to the moles of another substance. For example, if you have 9 moles of substance B, you can use the mole ratio to find out how many moles of substance A are needed: \(\text{Moles of A} = \text{Moles of B} \times \frac{\text{Moles of A}}{\text{Moles of B}}\)

Solve the stoichiometric problem

Plug in the values for the moles of the given substance and the mole ratio, then calculate the moles of the unknown substance. Continuing the example: \(\text{Moles of A} = 9\,moles\,B \times \frac{2\,moles\,A}{3\,moles\,B}\) \(\text{Moles of A} = 9 \times \frac{2}{3}\) \(\text{Moles of A} = 6\) From the stoichiometric calculation, 6 moles of substance A are needed to react with 9 moles of substance B.

Key concepts

Mole Ratio

Mole ratio is a crucial element of stoichiometry, helping you understand the quantitative relationships between reactants and products in a chemical reaction. When you have a balanced chemical equation, the mole ratio allows you to identify how many moles of one substance are needed to react with a certain number of moles of another substance. For example, if a balanced equation shows that 2 moles of hydrogen react with 1 mole of oxygen to produce water, the mole ratio is 2:1.
This ratio provides a straightforward way to convert between the amounts of different reactants or products in a chemical reaction. It acts like a conversion factor that lets you switch from moles of one substance to moles of another, ultimately aiding in solving stoichiometric problems.

Balanced Chemical Equation

A balanced chemical equation is fundamental in stoichiometry as it ensures the law of conservation of mass is upheld. In a balanced equation, the number of atoms for each element is the same on both sides of the reaction. This is important because chemical reactions do not create or destroy atoms, only rearrange them.
To balance a chemical equation, you adjust the coefficients, the numbers used to multiply the molecules or formula units, without altering the chemical formulas of the reactants or products. For example, in the reaction between hydrogen and oxygen to produce water:

• The unbalanced equation:
  • H₂ + O₂ → H₂O
• The balanced equation:
  • 2H₂ + O₂ → 2H₂O

This shows that 2 molecules of hydrogen react with 1 molecule of oxygen to produce 2 molecules of water, maintaining the same number of hydrogen and oxygen atoms on both sides of the equation.

Stoichiometric Problem

A stoichiometric problem involves calculating the amounts of reactants or products using the relationships given by a balanced chemical equation. The mole ratio, derived from the coefficients in the balanced equation, is instrumental in solving these problems.
For instance, if you are asked to determine how many moles of a product can be produced from a certain amount of reactant, you'll start with the balanced equation to find the relevant mole ratio. Using this ratio, you can set up a proportion and solve for the unknown quantity. This process involves:

• Identifying the known quantities (given moles of a reactant or product).
• Identifying the required quantity (moles of another reactant or product).
• Using the mole ratio as a conversion factor to perform the necessary calculations.

The efficiency and accuracy of solving stoichiometric problems depends on a correctly balanced equation and accurately identified mole ratios.

Chemical Reaction Coefficients

Chemical reaction coefficients are numbers placed before the compounds in a chemical equation to indicate the number of moles of each substance involved. They are crucial for balancing chemical equations and establishing the mole ratios. These coefficients ensure the law of conservation of mass is followed, with the same number of each type of atom on both sides of the equation.
For example, in the equation 2H₂ + O₂ → 2H₂O, the coefficients are 2, 1, and 2, corresponding to H₂, O₂, and H₂O respectively. These numbers help you understand:

• The proportionate amounts of reactants and products.
• The quantitative relationships necessary for solving stoichiometric problems.
• The mole ratio between substances, allowing conversions from one substance to another.

Without these coefficients, you wouldn't be able to perform stoichiometric calculations or predict the outcomes of chemical reactions accurately.