Question

The number of gram molecules of oxygen in \(6.02 \times\) \(10^{24} \mathrm{CO}\) molecule's' is: (a) \(10 \mathrm{~g}\) molecules (b) \(5 \mathrm{~g}\) molecules (c) \(1 \mathrm{~g}\) molecules (d) \(0.5 \mathrm{~g}\) molecules

Short answer

(a) 10 gram molecules

Step-by-step solution

Understand the Question

The problem asks us to find the number of gram molecules (or moles) of oxygen in a given number of carbon monoxide (CO) molecules. We should start by identifying what a gram molecule means, which is another term for a mole in this context.

Recall Avogadro's Number

Avogadro's number is the number of molecules in one mole of a substance. It is equal to \(6.02 \times 10^{23}\) molecules per mole.

Calculate Moles of CO

We are given \(6.02 \times 10^{24}\) molecules of CO. To convert this to moles, we divide by Avogadro's number: \[\text{moles of CO} = \frac{6.02 \times 10^{24}}{6.02 \times 10^{23}}.\]

Perform Division

Perform the division: \[\text{moles of CO} = 10.\] So, there are 10 moles of CO.

Relate CO to Oxygen Atoms

Each CO molecule contains exactly one oxygen atom. Hence, the number of moles of CO is equal to the number of moles of oxygen atoms.

Conclusion

Since we have 10 moles of CO and thus 10 moles of oxygen atoms, the number of gram molecules (moles) of oxygen is 10.

Key concepts

Gram Molecule

The concept of a gram molecule is closely related to the idea of a mole. A gram molecule essentially refers to the molecular weight of a substance expressed in grams. This weight is also known as the molar mass when discussing molecules. When you have a gram molecule of any substance, it means you have the same number of molecules as there are in 1 mole of that substance. This is an essential part of chemistry as it helps scientists measure and compare amounts of different substances.

For example, let's say you have carbon monoxide (CO). The gram molecule of CO refers to having the molecular weight of CO expressed in grams. Since the molecular weight of CO is approximately 28.01 g/mol, a gram molecule of CO would weigh 28.01 grams.

• "Gram molecule" involves the concept of moles.
• It references the molar mass expressed in grams.
• Provides a way to standardize measurements in chemical reactions.

Stoichiometry

Stoichiometry is the branch of chemistry that deals with the relationships between the quantities of reactants and products in chemical reactions. In simple terms, it helps us understand how much of one thing reacts with how much of another thing.

When the problem asks for the number of gram molecules of oxygen in a certain number of CO molecules, stoichiometry helps us find that relationship. Each molecule of carbon monoxide (CO) contains one atom of carbon and one atom of oxygen. Therefore, by understanding the stoichiometric relationship, we know that the number of moles of CO will tell us the number of moles of oxygen present.

Stoichiometry involves several key concepts:

• The law of conservation of mass, which states that mass is neither created nor destroyed in a chemical reaction.
• The balanced chemical equation, which shows the exact relationship between reactants and products.
• The mole ratio, derived from the coefficients of a balanced equation, which helps determine how much of each substance is used or formed in a reaction.

Avogadro's Number

Avogadro's number is a fundamental constant in chemistry, denoting the number of atoms, molecules, or other particles in one mole of a substance. This number is extremely large:\[6.02 \times 10^{23}\]This seemingly magical number allows scientists to convert between the microscopic world of atoms and molecules and the macroscopic world that we can measure and observe. When dealing with large numbers of small particles like atoms or molecules, this concept becomes extraordinarily useful.

For example, consider how we used Avogadro's number in the exercise to find the number of gram molecules of oxygen. Given the CO molecules totaled \(6.02 \times 10^{24}\), we used Avogadro's number to determine how many moles of CO that corresponded to:\[\text{moles of CO} = \frac{6.02 \times 10^{24}}{6.02 \times 10^{23}} = 10\]Avogadro's number enables us to connect the amount of substance at the molecular level to a quantity we can handle and measure in the lab or see on a balance.

Some key features of Avogadro's number include:

• Provides a link between the atomic scale and macroscopic quantities.
• Essential for calculations in stoichiometry.
• Helps in understanding and applying the mole concept in chemistry.