Problem 131 - A Complete Resource Book in Chemistry for JEE Main

Question

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

Step-by-Step Solution

Answer

(a) 10 g molecules

Step 1: Understand the Problem

To find the number of gram molecules of oxygen in \(6.02 \times 10^{24}\) CO molecules, we must first understand that one molecule of CO contains one atom of oxygen. Thus, the number of gram molecules of oxygen is directly related to the number of CO molecules.

Step 2: Use Avogadro's Number

Avogadro's number, \(6.022 \times 10^{23}\), represents the number of molecules in one mole of a substance. To find moles of CO, divide the number of CO molecules by Avogadro's number: \[\text{Moles of CO} = \frac{6.02 \times 10^{24}}{6.022 \times 10^{23}}.\]

Step 3: Perform the Calculation

Calculate the moles of CO by dividing the numbers:\[\text{Moles of CO} \approx \frac{6.02}{6.022} \times 10^{24-23} = 10 \text{ moles}.\]

Step 4: Relate Moles to Gram Molecules

Since each mole of CO corresponds to one mole of oxygen (because there is one oxygen atom per CO molecule), the number of gram molecules of oxygen is the same as the number of moles of CO.

Key Concepts

Avogadro's Number

Avogadro's Number is a fundamental constant in chemistry used to express the amount of substance. The number is defined as the number of atoms, ions, or molecules in one mole of a substance, which is approximately \(6.022 \times 10^{23}\). This large number helps chemists convert between the atomic scale and the macroscopic scale. When we say one mole of a substance, it means it contains exactly \(6.022 \times 10^{23}\) entities, whether they are atoms or molecules.

• This concept allows chemists to count particles by weighing, as one mole of a substance has a mass equal to its relative molecular mass expressed in grams.
• For example, one mole of carbon-12 atoms weighs exactly 12 grams, and this equivalence allows for easy laboratory calculations.

Understanding Avogadro's Number is crucial for performing stoichiometric calculations, which integrate this constant to relate the quantities of reactants and products in a chemical reaction.

Gram Molecules

In the context of chemistry, a "gram molecule" refers to the molar mass of a substance expressed in grams. This term is synonymous with "mole" today, yet remains a useful concept when discussing molecules and molecular weight.
When we talk about the number of gram molecules, we're essentially discussing how many moles of a specific molecular entity we have. For instance:

• If you determine the molar mass of a compound like carbon monoxide (CO), you simply add the atomic masses of carbon (approximately 12 g/mol) and oxygen (16 g/mol) to find a molar mass of 28 g/mol.
• When you have a sample of 28 grams of CO, you have one gram molecule or one mole of CO molecules, which contains Avogadro's Number of molecules.

The concept of gram molecules becomes highly significant in determining proportions and measurements in chemical reactions, ensuring accurate and reliable results.

Stoichiometry

Stoichiometry is the branch of chemistry that deals with the quantitative relationships of the elements and compounds in chemical reactions. It involves calculations based on the balanced equations that show how many moles of reactants are required to produce a certain number of moles of products.
Understanding the stoichiometric relationships allows us to:

• Predict the amount of products formed from a given amount of reactants.
• Determine the limiting reactant, which is the reactant that will be completely used up first, thus limiting the amount of products formed.
• Manage resources efficiently in industrial chemical processes by knowing exact amounts necessary for reactions.

In our exercise, stoichiometry was used to calculate the moles of CO molecules from the given quantity using Avogadro's Number. This helps in figuring out that we have an equivalent number of moles of oxygen atoms, which in turn gives us the number of gram molecules of oxygen, illuminating the numerical relationships that underscore all chemical reactions.