Question

How many moles of \(\mathrm{Bi}\) atoms are needed to combine with \(1.58 \mathrm{~mol}\) of \(\mathrm{O}\) atoms to make \(\mathrm{Bi}_{2} \mathrm{O}_{3}\) ?

Short answer

1.0533 mol of \(\mathrm{Bi}\) atoms are needed to combine with 1.58 mol of \(\mathrm{O}\) atoms.

Step-by-step solution

Write down the chemical reaction

Understand the chemical formula of bismuth(III) oxide, which is \(\mathrm{Bi}_2\mathrm{O}_3\).

Determine the mole ratio

From the chemical reaction \(\mathrm{Bi}_2\mathrm{O}_3\), we can see that 2 moles of \(\mathrm{Bi}\) combine with 3 moles of \(\mathrm{O}\). The mole ratio of \(\mathrm{Bi}\) to \(\mathrm{O}\) is 2:3.

Calculate the moles of \(\mathrm{Bi}\)

Set up the proportion based on the mole ratio. If 3 moles of \(\mathrm{O}\) require 2 moles of \(\mathrm{Bi}\), then \(1.58 \mathrm{~mol}\) of \(\mathrm{O}\) will require \(\frac{2}{3} \times 1.58 \mathrm{~mol}\) of \(\mathrm{Bi}\).

Solve for the number of moles of \(\mathrm{Bi}\)

Perform the calculation to find the moles of \(\mathrm{Bi}\): \(\frac{2}{3} \times 1.58 \mathrm{~mol} = 1.0533 \mathrm{~mol}\) of \(\mathrm{Bi}\) are needed (rounded to four significant figures).

Key concepts

Understanding Chemical Reactions

When studying chemistry, one of the key concepts is the chemical reaction, a process where substances, known as reactants, are transformed into different substances called products. This transformation occurs as atoms are rearranged in a precise pattern that follows the law of conservation of mass, meaning nothing is lost or created in the process, just changed.

To properly understand a chemical reaction, it's vital to comprehend chemical equations that symbolize the reaction. For example, in the case of forming bismuth(III) oxide ( Bi_{2}O_{3}), the equation would showcase the reactant atoms of bismuth ( Bi) and oxygen ( O) rearranging to form the product molecules. The equation not only tells you what reacts and what is produced but also the proportions in which the substances react and are produced - this is essential when calculating how much of each reactant is needed to create a certain amount of product.

The Role of Mole Ratio in Stoichiometry

The mole ratio is crucial for solving stoichiometry problems. This ratio comes directly from the coefficients of a balanced chemical equation, indicating the proportion of moles of each reactant and product involved in the reaction. In the context of this exercise, where we are forming bismuth(III) oxide ( Bi_{2}O_{3}), the balanced chemical equation tells us that two moles of bismuth ( Bi) react with three moles of oxygen ( O) atoms.

Understanding this 2:3 mole ratio allows us to calculate the precise amount of bismuth that must react with a given quantity of oxygen. It's similar to following a recipe - if a recipe states that you need two eggs for every three cups of flour, and you only have one and a half cups of flour, you would need to determine how many eggs you require based on that fixed ratio. Similarly, with mole ratios, knowing the amount of one reactant lets you calculate the necessary amount of the other reactant or the yield of the product.

Calculating Molar Mass

The molar mass is another cornerstone concept in stoichiometry, representing the mass of one mole of a substance, typically expressed in grams per mole ( g/mol). It's akin to the 'molecular weight' of a compound and calculates by summing the atomic masses of all atoms present in a molecule.

For example, to calculate the molar mass of water ( H_2O), one would add the molar masses of hydrogen and oxygen based on their quantities in a molecule of water. This concept becomes especially important when dealing with the physical quantities of substances in a reaction. Instead of counting individual atoms or molecules which is impractical, chemists use the molar mass to relate a chemical's mass to its amount in moles, thereby establishing a tangible connection to the molecular scale.

The knowledge of molar mass is instrumental when converting grams to moles or vice versa, which is a fundamental step in solving many stoichiometry problems, including determining how much of a reactant is needed or what amount of product will be produced in a reaction.