Question

From the values in Table $5.3$ for the van der Waals constant $a$ for the gases ${\mathrm{H}}_2,{\mathrm{CO}}_2,{\mathrm{N}}_2$, and ${\mathrm{CH}}_4$, predict which of these gas molecules show the strongest intermolecular attractions.

Short answer

CO₂ exhibits the strongest intermolecular attractions among the given gases, as it has the highest van der Waals constant 'a' with a value of $3.59$ L²·atm/mol².

Step-by-step solution

List the given values of van der Waals constant 'a'

According to the data provided in Table 5.3, we have the following values for the van der Waals constant 'a': - H₂: a = $2.74\times {10}^{-2}$ L²·atm/mol² - CO₂: a = $3.59$ L²·atm/mol² - N₂: a = $1.36$ L²·atm/mol² - CH₄: a = $2.38$ L²·atm/mol²

Compare the values of 'a' for each gas

In order to predict which of these gases exhibits the strongest intermolecular attractions, we need to identify the gas with the highest value of 'a'. Upon comparing the values from Step 1, we can see that CO₂ has the highest value: - H₂: a = $2.74\times {10}^{-2}$ L²·atm/mol² - CO₂: a = $3.59$ L²·atm/mol² (highest value) - N₂: a = $1.36$ L²·atm/mol² - CH₄: a = $2.38$ L²·atm/mol²

Conclude which gas has the strongest intermolecular attractions

Since CO₂ has the highest van der Waals constant 'a', it is the gas that shows the strongest intermolecular attractions among the given gases.

Key concepts

Intermolecular Attractions

Intermolecular attractions are the forces that act between stable molecules or between atoms and ions that are in close proximity. There are several types of intermolecular forces, including dipole-dipole interactions, hydrogen bonding, and London dispersion forces.

Understanding these forces is crucial as they explain many physical properties of substances, such as boiling points, melting points, and solubilities. For example, water has a relatively high boiling point for a small molecule due to strong hydrogen bonds between the water molecules. In contrast, methane (CH₄) has a lower boiling point because its molecules are held together by weaker London dispersion forces.

When dealing with gases, as in the given exercise, these intermolecular attractions can influence how these gases behave, especially under high pressure or low temperature. The ability of gas molecules to attract each other also affects how they deviate from the ideal behavior predicted by the Ideal Gas Law, leading to real-world observations being described by the van der Waals equation.

van der Waals Constants

The van der Waals constants 'a' and 'b' are empirical parameters that appear in the van der Waals equation, an equation of state for real gases that accounts for the non-ideal behavior of gases. The constant 'a' corrects for the attractive forces between gas molecules, while 'b' adjusts for the volume occupied by the gas molecules themselves.

The 'a' constant is specifically related to the strength of the intermolecular attractions in a gas. A higher value of 'a' indicates stronger attractive forces between the molecules. In the context of the exercise, CO₂ with the highest 'a' value is predicted to show the strongest intermolecular attractions among the listed gases. This is because the more significant the attractive force, the more the gas molecules tend to pull each other closer, affecting the pressure and volume relationships described by the van der Waals equation.

Gas Properties

Gas properties include characteristics such as pressure, volume, temperature, and the amount of gas (usually represented by moles). The Ideal Gas Law, given by the equation PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the gas constant, and T is temperature, describes the state of an ideal gas. However, real gases deviate from this ideal behavior due to intermolecular forces and the finite volume of gas molecules.

The properties of real gases are better described by the van der Waals equation, which considers these non-ideal interactions. As seen in the exercise, by comparing van der Waals constants, we can infer the relative strength of intermolecular attractions in different gases, which in turn can inform us about the gas's behavior. This is particularly important in practical applications like industrial gas storage, where understanding the properties of a gas under non-ideal conditions ensures safety and efficiency.