Problem 28 - A Complete Resource Book in Chemistry for JEE Main

Question

The molecular weight of \(\mathrm{O}_{2}\) and \(\mathrm{SO}_{2}\) are 32 and 64 respectively. At \(15^{\circ} \mathrm{C}\) and \(150 \mathrm{~mm} \mathrm{Hg}\) pres sure, one litre of \(\mathrm{O}_{2}\) contains 'N' molecules. The number of molecules in two litres of \(\mathrm{SO}_{2}\) unde the same conditions of temperature and pressure will be (a) \(\mathrm{N}\) (b) \(\frac{\mathrm{N}}{5}\) (c) \(4 \mathrm{~N}\) (d) \(2 \mathrm{~N}\)

Step-by-Step Solution

Answer

The number of molecules in two liters of \(\mathrm{SO}_2\) is \(2N\).

Step 1: Understanding the Problem

We need to find the number of molecules in two liters of \(\mathrm{SO}_2\) under the same conditions of temperature and pressure as one liter of \(\mathrm{O}_2\). We know that one liter of \(\mathrm{O}_2\) under these conditions contains \(N\) molecules.

Step 2: Applying Avogadro's Law

According to Avogadro’s Law, equal volumes of gases, at the same temperature and pressure, contain equal numbers of molecules. Therefore, one liter of \(\mathrm{SO}_2\) will also contain \(N\) molecules under the same conditions.

Step 3: Calculating Molecules in Two Liters of SO2

Since one liter of \(\mathrm{SO}_2\) contains \(N\) molecules, two liters will contain double the number of molecules. Therefore, two liters of \(\mathrm{SO}_2\) will contain \(2N\) molecules.

Step 4: Conclusion

Based on the calculations, the number of molecules in two liters of \(\mathrm{SO}_2\) is \(2N\). Hence, the correct answer is option (d) \(2N\).

Key Concepts

Molecular Weight

Molecular weight, often referred to as molecular mass, is a fundamental concept in understanding the mass of a molecule. It is defined as the sum of the atomic masses of all atoms in a molecule. The molecular weight of a substance is usually expressed in atomic mass units (amu). This measurement helps chemists determine how much of a substance is needed for a reaction.

For example, the molecular weight of oxygen (\(\mathrm{O}_{2}\)) is 32 amu, because oxygen has an atomic mass of approximately 16 amu, and there are two oxygen atoms in an \(\mathrm{O}_{2}\) molecule. Similarly, the molecular weight of sulfur dioxide (\(\mathrm{SO}_{2}\)) is 64 amu due to the sum of one sulfur atom (approximately 32 amu) and two oxygen atoms (each around 16 amu).

• Knowing the molecular weight enables calculation of the number of molecules in a given mass of a substance.
• This value is also crucial in stoichiometry, where it aids in the conversion of grams to moles.

Understanding molecular weight is essential for molecular calculations and helps provide insights into the properties and behaviors of gases.

Molecular Calculation

Molecular calculation involves determining the number of molecules in a given sample by understanding the ideal gas equation and Avogadro’s number. These calculations are eloquently tied to molecular weight and the understanding of moles. A mole is a standard quantity in chemistry that represents \(6.022 \times 10^{23}\) entities (Avogadro's Number) of a substance.

To find the number of molecules in a volume of gas under specific conditions, the steps are straightforward:

• First, determine the volume of gas and calculate the number of molecules it contains using Avogadro's Law.
• Given the same temperature and pressure, any other gas occupying the same volume will have the same number of molecules.
• Scaling these measurements allows you to calculate the molecule count for different volumes under the same conditions.

Thus, understanding molecular calculation is directly connected to core principles like Avogadro's Law and molecular weight, fortifying one's understanding of chemistry.

Gas Laws

Gas laws describe the behaviors of gases and how they interact under various conditions of temperature, pressure, and volume. These laws, which include Boyle's Law, Charles's Law, and Avogadro's Law, among others, are critical in predicting how gases will behave.

Avogadro's Law, which played a key role in the discussed problem, states that equal volumes of gases, at the same temperature and pressure, contain the same number of molecules. This principle allows for simple calculations of molecular quantities across different gases, as showcased when determining the number of molecules in \(\mathrm{SO}_{2}\) as compared to \(\mathrm{O}_{2}\).

• Boyle's Law states that the pressure of a gas is inversely proportional to its volume when temperature is kept constant.
• Charles's Law indicates that the volume of a gas is directly proportional to its temperature, provided pressure remains unchanged.

Understanding these gas laws empowers students to analyze various gaseous reactions and phenomena, providing a solid foundation for more complex chemical studies.