Problem 7 - 43 Years JEE ADVANCED (1978-2020) + JEE MAIN Chapterwise & Topicwise Solved Papers Chemistry

Question

An unknown chlorohydrocarbon has \(3.55 \%\) of chlorine. If each molecule of the hydrocarbon has one chlorine atom only, chlorine atoms present in \(1 \mathrm{~g}\) of chlorohydrocarbon are: (Atomic wt. of \(\mathrm{Cl}=35.5 \mathrm{u}\); Avogadro constant \(=6.023 \times 10^{23} \mathrm{~mol}^{-1}\) (a) \(6.023 \times 10^{9}\) (b) \(6.023 \times 10^{23}\) (c) \(6.023 \times 10^{21}\) (d) \(6.023 \times 10^{20}\)

Step-by-Step Solution

Answer

(d) \(6.023 \times 10^{20}\)

Step 1: Calculate Mass of Chlorine in 1 g Sample

The question states that chlorine makes up 3.55% of the chlorohydrocarbon. Therefore, the mass of chlorine in a 1 g sample is calculated as follows:\[\text{Mass of Chlorine} = \frac{3.55}{100} \times 1 \text{ g} = 0.0355 \text{ g}\]

Step 2: Convert Mass of Chlorine to Moles

To find the number of moles of chlorine, we use the formula:\[\text{Moles of } \text{Cl} = \frac{\text{Mass of } \text{Cl}}{\text{Atomic Weight of } \text{Cl}}\]Substitute the values:\[\text{Moles of } \text{Cl} = \frac{0.0355 \text{ g}}{35.5 \text{ g/mol}} = 0.001 \, \text{mol}\]

Step 3: Calculate Number of Chlorine Atoms

Using Avogadro's constant, we can find the number of atoms in the 0.001 mol of chlorine:\[\text{Number of Cl atoms} = 0.001 \text{ mol} \times 6.023 \times 10^{23} \text{ atoms/mol}\]Calculate:\[\text{Number of Cl atoms} = 6.023 \times 10^{20} \text{ atoms}\]

Step 4: Conclusion: Choose the Correct Option

The number of chlorine atoms in 1 g of chlorohydrocarbon is \(6.023 \times 10^{20}\), which corresponds to option (d).

Key Concepts

Chlorohydrocarbon

Chlorohydrocarbon compounds are fascinating molecules that contain hydrogen, carbon, and chlorine atoms. They are a type of hydrocarbon where one or more hydrogen atoms have been replaced by chlorine. This replacement can dramatically alter the properties of the original hydrocarbon, such as its reactivity and physical characteristics.

Chlorohydrocarbons have important applications in everyday products and industrial processes. They are widely used in solvents, refrigerants, and the production of polyvinyl chloride (PVC). Understanding their structure and composition is crucial because of their widespread use and environmental impact.

• The term 'chlorohydrocarbon' emphasizes the presence of chlorine atoms within the carbon backbone of the molecule.
• In chemical structures, chlorine atoms are typically represented by the halo group (-Cl) attached to carbon atoms.

Avogadro's Constant

Avogadro's Constant is a fundamental concept in chemistry, often symbolized as \(6.023 \times 10^{23}\). It represents the number of particles, typically atoms or molecules, found in one mole of a substance. This constant is named after the 19th-century Italian scientist Amedeo Avogadro and is a cornerstone for calculations involving molar quantities.

Understanding Avogadro's Constant lets chemists easily convert between the macroscopic scale we can measure and the microscopic scale of atoms and molecules. By knowing that one mole of any substance contains this large number of particles, one can calculate the amount of atoms or molecules in a given sample with ease.

• It's crucial in determining the number of molecules in chemical reactions.
• Avogadro's Constant links the molecular scale with the gram scale used in laboratories.

Atomic Weight Calculation

Atomic weight calculation is essential for figuring out the amount of an element in a compound. The atomic weight (also known as atomic mass) is the average mass of atoms of an element, calculated using the relative abundance of isotopes in a naturally-occurring sample.

For example, the atomic weight of chlorine is approximately 35.5 u. This value accounts for the naturally mixed isotopes, primarily \(^{35}Cl\) and \(^{37}Cl\). In stoichiometric calculations, this atomic weight is vital for converting grams to moles, enabling the use of Avogadro's Constant to find the number of atoms.

• The atomic weight is listed on the periodic table and remains constant for each element.
• It is used to calculate moles (\text{moles} = \frac{\text{mass}}{\text{atomic weight}}).
• Knowing the atomic weight helps predict the quantities and behavior of atoms in reactions.