Problem 57 - A Complete Resource Book in Chemistry for JEE Main

Question

\(6.4 \mathrm{~g} \mathrm{SO}_{2}\) at \(0^{\circ} \mathrm{C}\) and \(0.99 \mathrm{~atm}\) pressure occupies a volume of \(2.241 \mathrm{~L}\). Predict which of the following is correct? (a) the gas is ideal (b) the gas is real with intermolecular attraction (c) the gas is real without intermolecular repulsion (d) the gas is real with intermolecular repulsion greater than intermolecular attraction

Step-by-Step Solution

Answer

Option (b): The gas is real with intermolecular attraction.

Step 1: Use the Ideal Gas Law

To predict if sulfur dioxide (\(\mathrm{SO}_2\)) is behaving as an ideal gas, we'll use the Ideal Gas Law: \(PV = nRT\). Our aim is to calculate the number of moles \(n\) and check if \(PV\) matches \(nRT\). Given: \(P = 0.99\) atm, \(V = 2.241\) L, \(T = 273\) K (since \(0^\circ\mathrm{C} = 273\) K). The universal gas constant \(R\) is \(0.0821\) L atm K\(^{-1}\) mol\(^{-1}\).

Step 2: Calculate the Number of Moles

First, calculate the molar mass of \(\mathrm{SO}_2\). Sulfur (S) has a molar mass of approximately 32.07 g/mol, and oxygen (O) is about 16.00 g/mol. Thus, \(\mathrm{SO}_2 = 32.07 + 2 \times 16.00 = 64.07\, \text{g/mol}\).Now, calculate \(n\):\[n = \frac{6.4\, \text{g}}{64.07\, \text{g/mol}} \approx 0.0999\, \text{mol}.\]

Step 3: Verify Using Ideal Gas Law

Substitute the values into the Ideal Gas Law equation:\[PV = nRT \Rightarrow 0.99\, \text{atm} \times 2.241\, \text{L} = 0.0999\, \text{mol} \times 0.0821\, \mathrm{L\ atm\ K^{-1}\ mol^{-1}} \times 273\, \text{K}\]Calculate both sides:\[PV = 2.21979\, \text{L}\, \text{atm} \quad \text{and} \quad nRT \approx 2.22696\, \text{L}\, \text{atm}.\]

Step 4: Interpret the Results

The calculations are close, but not exact, indicating a slight deviation from ideal behavior. The observed pressure-volume product (\(PV\)) is slightly less than predicted by \(nRT\), suggesting slight intermolecular attraction (as it causes a decrease in pressure compared to the ideal case). Hence, \(\mathrm{SO}_2\) exhibits real gas behavior with intermolecular attractions.

Key Concepts

Real Gases

In our everyday observations, many gases don't behave exactly as the Ideal Gas Law predicts. These gases are referred to as real gases. While the Ideal Gas Law is a helpful tool, it doesn't account for certain realities of gas particles, such as their volumes and the forces between them. This is especially true at high pressures and low temperatures where gases deviate significantly from ideal behavior.
Real gases consider:

• Finite volume of gas particles: Unlike ideal particles, real gas particles do occupy some space.
• Intermolecular forces: Real gases experience attractions or repulsions among the particles that ideal gases do not.

When using the Ideal Gas Law, the minor deviations that occur are typically due to these factors. In our exercise, \( \mathrm{SO}_2 \) was shown to have a pressure-volume product slightly less than expected, hinting at real gas behavior due to intermolecular attractions.

Intermolecular Forces

Intermolecular forces (IMFs) are forces that mediate interaction between molecules, including attraction or repulsion. These forces are particularly significant in understanding the behavior of real gases. In gases, they can be weak due to the large distances between particles, but still affect gas behavior.

• Dipole-Dipole Interactions: Occur between polar molecules. \( \mathrm{SO}_2 \), for example, is polar, leading to dipole-dipole attractions.
• London Dispersion Forces: These are weaker and occur even in nonpolar molecules due to temporary dipoles.
• Hydrogen bonding: A strong type of dipole interaction, though less common in gaseous states.

The slightly reduced pressure observed in \( \mathrm{SO}_2 \)'s behavior indicates that intermolecular attractions, likely dipole-dipole interactions, are present and influencing the gas particles to pull closer, reducing the space they occupy.

Gas Behavior

Understanding gas behavior involves assessing how gases respond under various conditions. The Ideal Gas Law provides a simplified model, which assumes no volume or attractions among molecules. However, real gases deviate due to intermolecular forces and particle volumes.
Factors influencing gas behavior:

• Temperature and Pressure: Real gases come closer to ideal gas behavior at low pressures and high temperatures, where particles are farther apart with less influence on each other.
• Type of Gas: Non-polar gases or those with weak intermolecular forces tend to behave more ideally.
• Volume: In compressed states, the finite size of particles becomes significant, altering expected outcomes.

In the specific case of \( \mathrm{SO}_2 \), its behavior was predominantly due to slight dipole attractions, leading to a decreased measured pressure as the molecules were drawn closer together than in an ideal scenario.