Question

In the formation of carbon monoxide, \(\mathrm{CO},\) it is found that \(2.445 \mathrm{~g}\) of carbon combine with \(3.257 \mathrm{~g}\) of oxygen. What is the atomic mass of oxygen if the atomic mass of carbon is 12.01 amu?

Short answer

The atomic mass of oxygen is approximately 15.99 amu.

Step-by-step solution

Understand the Information Given

The question provides us with the masses of carbon and oxygen that combine to form carbon monoxide (\(\text{CO}\)). We are also given the atomic mass of carbon, which is 12.01 amu. We need to find the atomic mass of oxygen.

Use the Law of Conservation of Mass

According to the stoichiometry of \(\mathrm{CO}\), the molar ratio of carbon to oxygen is 1:1. This means that the ratio of the mass of carbon to the mass of oxygen in the compound depends on their atomic masses.

Calculate the Moles of Carbon

Calculate the moles of carbon using the formula: \(\text{moles of carbon} = \frac{\text{mass of carbon}}{\text{atomic mass of carbon}}\). Substitute the given values: \(\frac{2.445\,\mathrm{g}}{12.01\,\mathrm{amu/g}}\approx 0.2037\,\text{moles of carbon}\).

Calculate the Moles of Oxygen

Since carbon and oxygen combine in a 1:1 mole ratio for carbon monoxide, the moles of oxygen will be equal to the moles of carbon: \(0.2037\,\text{moles of oxygen}\).

Determine the Atomic Mass of Oxygen

Using the moles and the given mass of oxygen, calculate the atomic mass of oxygen: \(\text{atomic mass of oxygen} = \frac{\text{mass of oxygen}}{\text{moles of oxygen}}\). Thus, \(\frac{3.257\,\mathrm{g}}{0.2037\,\text{moles}}\approx 15.98\,\mathrm{amu/g}\), which rounds to 15.99 amu.

Key concepts

Atomic Mass

Atomic mass, also known as atomic weight, is the average mass of an atom of an element, usually expressed in atomic mass units (amu). It represents the mass of one mole of atoms of an element. For example, carbon's atomic mass is 12.01 amu. This means that one mole of carbon atoms weighs 12.01 grams. The atomic mass helps us compare the mass of different atoms.
Measured in amu, atomic mass is a crucial tool in stoichiometry - it allows chemists to convert between moles, mass, and number of particles. It serves as a bridge between the mass of a substance and the amount of particles it contains.
To find the atomic mass of an element in a compound, like oxygen in CO, we use the mass of the element's portion in the compound and the mole concept.

Carbon Monoxide

Carbon monoxide (CO) is a compound made of one carbon atom and one oxygen atom. The chemical formula CO tells us there is a 1:1 ratio of carbon to oxygen in this molecule.
Carbon monoxide is a simple molecule but plays a significant role in understanding stoichiometry. In forming CO from its elements:

• 2.445 grams of carbon combine with 3.257 grams of oxygen.
• This reaction exemplifies the law of multiple proportions, which states that elements can combine in different ratios to form different compounds.

Due to CO's simplicity, it is often used in exercises to demonstrate basic stoichiometric calculations, such as relating mass to mole ratios.

Law of Conservation of Mass

The Law of Conservation of Mass states that in a chemical reaction, mass is neither created nor destroyed. Instead, it remains constant. This principle is foundational in stoichiometry, as it implies that the mass of reactants must equal the mass of products in a reaction.
In the formation of carbon monoxide from carbon and oxygen:

• The mass of carbon (2.445 g) and the mass of oxygen (3.257 g) sum up to yield the total mass of CO formed.
• This supports the law, where combined elements in known amounts perfectly result in the final compound.

Maintaining mass balance is crucial in chemical reactions and helps chemists predict the amount of product formed from given reactants.

Mole Concept

The mole concept is a fundamental principle in chemistry used to quantify and relate amounts of substances. One mole of any substance contains Avogadro’s number of entities, approximately 6.022 x 10^23. This concept allows us to convert between atoms, molecules, and grams.
In the given problem:

• The calculation of moles involved dividing the mass of carbon by its atomic mass, providing the moles of carbon used in the reaction.
• The same number of moles directly translates to oxygen because of the 1:1 mole ratio stipulated by CO's formula.

Understanding moles helps chemists determine proportions in chemical reactions and predict how much product or reactant is needed or produced, making it a powerful tool in predicting the course of reactions.