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

Short answer

The gas behaves as an ideal gas due to close agreement of calculated and measured volumes.

Step-by-step solution

Analyze the Given Conditions Using the Ideal Gas Law

The ideal gas law is given as \( PV = nRT \). Here, \( P = 0.99 \text{ atm} \), \( V = 2.241 \text{ L} \), \( T = 273 \text{ K} \) (since \(0^{\circ} \mathrm{C}\) is 273 K), and \( R = 0.0821 \text{ L atm/mol K} \). We need to calculate \( n \), the number of moles of \( \text{SO}_2 \). To find moles, divide the given mass by the molar mass of \( \text{SO}_2 \) (64.07 g/mol).\[ n = \frac{6.4}{64.07} \approx 0.0998 \text{ moles} \]

Calculate the Predicted Volume with Ideal Gas Law

Using the ideal gas law equation, we calculate the predicted volume. Substitute the values into the equation:\[ V = \frac{nRT}{P} \]Substituting the known values:\[ V = \frac{(0.0998) \times (0.0821) \times 273}{0.99} \approx 2.239 \text{ L} \]

Compare the Measured Volume to the Predicted Volume

The measured volume of 2.241 L is very close to the predicted volume of 2.239 L. This finding suggests that the behavior of the gas is very close to ideal under the given conditions.

Key concepts

Real Gases

When we talk about gases, they essentially fall into two categories: ideal and real. Ideal gases are theoretical gases that strictly follow the Ideal Gas Law, whereas real gases are the substances we deal with in the real world. In theory, gases should behave ideally, meaning they don't have any intermolecular forces, and the molecules occupy no space of their own. However, all real gases deviate from ideal behavior at various conditions.

Many of these deviations become more noticeable at high pressures and low temperatures because intermolecular attractions are more significant under those conditions. At these extremes, the volume of the gaseous particles and the forces between them cannot be ignored, which makes it necessary to use a modified version of the gas laws to predict their behavior accurately.

In our case, the sulfur dioxide ( SO_2 ) gas behaves largely like an ideal gas under the experimental conditions provided. This close match with ideal behavior is evident because the calculated volume using the Ideal Gas Law is almost the same as the measured volume.

Intermolecular Forces

Intermolecular forces are the forces that hold molecules together. They're quite different from the forces within a molecule, like covalent or ionic bonding. There are several types of intermolecular forces, including:

• Dispersion Forces
• Dipole-Dipole Interactions
• Hydrogen Bonding

In gases, these forces are typically weak, which allows the gas molecules to drift far apart. However, as gases become denser (like under high pressure or low temperatures), these forces start to have a significant effect.

In the context of the given example, if the sulfur dioxide had significant intermolecular attractions or repulsions, we would see more noticeable deviations in volume predictions using the Ideal Gas Law. However, since the predicted and actual volumes are nearly the same, it implies that the intermolecular forces in SO_2 are either weak or cancel each other out effectively.

Molar Volume of Gas

The molar volume of a gas is the volume occupied by one mole of the gas at a given temperature and pressure. At standard temperature and pressure (STP), which is set at 0°C and 1 atm, one mole of an ideal gas occupies approximately 22.4 liters. This fixed relationship makes it easier to understand and predict how gases will behave under different conditions.

In our example, we calculated the number of moles of SO_2 to be approximately 0.0998 moles and found that the volume it occupied was very close to the one predicted using the Ideal Gas Law. This consistency indicates that under the given conditions, the SO_2 gas behaves almost ideally, reaffirming that its molar volume closely aligns with what would be expected from an ideal gas. Variances typically occur more drastically under non-standard conditions or with gases that experience strong intermolecular forces.