Question

Which of the following is not truc? (1) The "b" parameter in Van der Waal's equation is related to the intermolecular forces. (2) The actual pressure of gas is always less than the pressure calculated from the ideal gas equation. (3) Temperature is a measure of the average kinetic energy. (4) The total pressure of the mixture of gases at constant temperature is equal to the sum of their individual partial pressures.

Short answer

(1) is not true: The 'b' parameter is related to the volume occupied by gas molecules, not intermolecular forces.

Step-by-step solution

- Understand Van der Waal's Equation

Van der Waal's equation for real gases is: \[\bigg( P + \frac{a}{V^2} \bigg) (V - b) = RT \] Here, 'a' is related to the intermolecular forces, and 'b' is related to the volume occupied by gas molecules. Thus, 'b' is not related to intermolecular forces.

- Compare Ideal and Real Gas Pressures

The pressure of a real gas is often less than the pressure predicted by the ideal gas law because real gases experience intermolecular attractions, which reduce the impact of the gas molecules on the container walls.

- Check Temperature and Kinetic Energy Relationship

Temperature is indeed a measure of the average kinetic energy of the molecules in a substance. Higher temperatures mean higher average kinetic energy.

- Examine Dalton's Law of Partial Pressures

According to Dalton's Law, the total pressure of a gas mixture is the sum of the partial pressures of each individual gas assuming ideal behavior. This is true for gases at a constant temperature.

- Identify the False Statement

By examining the above steps, we see that the only incorrect statement is (1). The 'b' parameter in Van der Waal's equation is not related to intermolecular forces; it is related to the volume occupied by the gas molecules.

Key concepts

Intermolecular Forces

Intermolecular forces are the forces that act between molecules and affect the physical properties of substances. These forces differ from chemical bonds, which hold the atoms within a molecule together. Intermolecular forces are weaker than chemical bonds.

There are several types of intermolecular forces:

• London Dispersion Forces: These are the weakest intermolecular forces and occur due to temporary fluctuations in electron distribution within molecules or atoms.
• Dipole-Dipole Interactions: These occur between molecules that have permanent dipoles; that is, they have regions with slight positive and negative charges.
• Hydrogen Bonds: These are a special type of dipole-dipole interaction that occurs specifically when hydrogen is directly bonded to a highly electronegative atom like oxygen, nitrogen, or fluorine.

The Van der Waals equation corrects the Ideal Gas Law to account for intermolecular forces (parameter 'a') and the finite size of molecules (parameter 'b'). It helps better represent real gas behavior.

Ideal Gas Law

The Ideal Gas Law is a fundamental equation in chemistry that shows the relationship between pressure (P), volume (V), temperature (T), and the number of moles (n) of a gas: \[ PV = nRT \] Where R is the universal gas constant.

This equation assumes ideal gas behavior, where interactions between gas molecules are negligible, and the volume of the gas molecules themselves is not considered. However, real gases deviate from this ideal behavior under high pressure and low temperature due to intermolecular forces and molecular volume.

The Van der Waals equation modifies the Ideal Gas Law to account for these real-world factors.

Kinetic Energy

Kinetic energy is the energy of motion, and in the context of gases, it refers to the energy possessed by gas molecules due to their motion.

The kinetic theory of gases states that the temperature of a gas is a measure of the average kinetic energy of its molecules. This relation can be mathematically expressed as: \[ KE_{\text{avg}} = \frac{3}{2} k_B T \] where \text{k_B} is Boltzmann's constant.

As the temperature increases, the average kinetic energy of the gas molecules also increases, leading to more energetic collisions and higher pressure if the volume is kept constant. This direct relationship between temperature and kinetic energy is crucial in understanding gas behavior.

Dalton's Law of Partial Pressures

Dalton's Law of Partial Pressures states that in a mixture of gases, each gas exerts a pressure independently of the others. The total pressure of the mixture is the sum of the partial pressures of each individual gas. Mathematically, this can be expressed as: \[ P_{\text{total}} = P_1 + P_2 + ... + P_n \]

Each partial pressure is the pressure that the individual gas would exert if it occupied the entire volume alone. This law holds true for ideal gases and provides a simple way to calculate the total pressure in gas mixtures.

Understanding Dalton's Law is crucial when dealing with gas mixtures in various practical and theoretical applications, such as calculating the behavior of air in the atmosphere or gases in chemical reactions.