Problem 21 - 43 Years JEE ADVANCED (1978-2020) + JEE MAIN Chapterwise & Topicwise Solved Papers Chemistry

Question

The largest number of molecules is in \([1979]\) (a) \(36 \mathrm{~g}\) of water (b) \(28 \mathrm{~g}\) of carbon monoxide (c) \(46 \mathrm{~g}\) of ethyl alcohol (d) \(54 \mathrm{~g}\) of nitrogen pentoxide

Step-by-Step Solution

Answer

36 g of water contains the largest number of molecules.

Step 1: Calculate Moles of Water

First, we calculate the moles of water (H₂O). Water has a molar mass of 18 g/mol. The mass given is 36 g. Use the formula for moles: \[ \text{moles} = \frac{\text{mass}}{\text{molar mass}} = \frac{36}{18} \text{mol} = 2 \text{mol} \]

Step 2: Calculate Moles of Carbon Monoxide

Carbon monoxide (CO) has a molar mass of 28 g/mol. Given mass is 28 g. Use the moles formula:\[ \text{moles} = \frac{28}{28} \text{mol} = 1 \text{mol} \]

Step 3: Calculate Moles of Ethyl Alcohol

Ethyl alcohol (C₂H₅OH) has a molar mass of approximately 46 g/mol. Given mass is 46 g. Use the moles formula:\[ \text{moles} = \frac{46}{46} \text{mol} = 1 \text{mol} \]

Step 4: Calculate Moles of Nitrogen Pentoxide

Nitrogen pentoxide (N₂O₅) has a molar mass of 108 g/mol. The given mass is 54 g. Use the moles formula:\[ \text{moles} = \frac{54}{108} \text{mol} = 0.5 \text{mol} \]

Step 5: Determine Largest Number of Molecules

The number of molecules is directly proportional to the number of moles. We calculated: - Water: 2 mol - Carbon Monoxide: 1 mol - Ethyl Alcohol: 1 mol - Nitrogen Pentoxide: 0.5 mol Water, with 2 moles, contains the largest number of molecules.

Key Concepts

The Mole Concept

The mole is an essential concept in chemistry that helps in determining amounts of substances involved in chemical reactions. A "mole" is the SI unit that measures the quantity of substance. This concept revolves around the number known as Avogadro's number, which is approximately \(6.022 \times 10^{23}\). This represents the number of atoms, molecules, or particles in one mole of a substance.

Using the mole concept allows chemists to count and compare substances. This becomes particularly useful in stoichiometry for balancing chemical equations and calculating reactants and products. In the problem, calculating the moles of water, carbon monoxide, ethyl alcohol, and nitrogen pentoxide helps determine which has the most molecules by relating their mass to the number of moles.

• Moles = Mass / Molar Mass
• Avogadro's Number = \(6.022 \times 10^{23}\) particles/mol
• The greater the number of moles, the more molecules present.

By calculating moles, you can simplify complex conversions and understand quantities of chemical substances.

Understanding Molecular Mass

The molecular mass of a substance is the mass of a given molecule, expressed in atomic mass units (amu). It's an additive process, achieved by summing the atomic masses of all atoms in the molecule. Each element has its own atomic mass based on the atomic weight scale.

For example, water (H₂O) comprises two hydrogen atoms and one oxygen atom. With atomic masses of approximately 1 amu for hydrogen and 16 amu for oxygen, the molar mass of water is \(18\) g/mol.

• Water: \(2 \times 1 + 16 = 18\) g/mol
• Carbon Monoxide (CO): \(12 + 16 = 28\) g/mol
• Ethyl Alcohol (C₂H₅OH): \(2 \times 12 + 6 \times 1 + 16 = 46\) g/mol
• Nitrogen Pentoxide (N₂O₅): \(2 \times 14 + 5 \times 16 = 108\) g/mol

Accurate calculation of molecular mass facilitates balanced reactions, precise chemical measurements, and effective usage of stoichiometric equations.

Performing Chemical Calculations

Chemical calculations form the foundation of quantitative chemistry, allowing for predictions about the quantities of reactants and products. These calculations employ the relationships between mass, moles, and molecular mass to solve problems and conduct experiments efficiently.

For instance, when given a mass, we can find moles by dividing the mass by molecular mass. As shown in the original problem, these calculations help us discover the number of molecules in a given mass. Knowing which compound has the most moles helps us determine which one has the largest number of molecules. In stoichiometry, these calculations answer many queries regarding chemical reactions:

• Convert mass to moles and vice versa.
• Determine which substance has more molecules.
• Use mole ratio to predict product amounts.

Chemical calculations are not only crucial for solving classroom problems but also for real-world applications in fields such as pharmaceuticals, materials science, and food chemistry.