Chapter 5: Problem 62
A gas that follows Boyle's law, Charles' law and Avogadro's law is called an ideal gas. Under what conditions a real gas behaves as ideal gas? (a) Under low pressure and temperature (b) Under high pressure and temperature (c) Under high pressure and low temperature (d) Under low pressure and high temperature
Short Answer
Expert verified
A real gas behaves as an ideal gas under low pressure and high temperature.
Step by step solution
01
Understanding Real and Ideal Gases
An ideal gas is a theoretical gas that perfectly follows all the gas laws (Boyle's, Charles', and Avogadro's law) without any deviations. Real gases, however, behave like ideal gases only under certain conditions, as they experience intermolecular forces and have molecular volumes that can't be ignored under certain conditions.
02
Recognizing Ideal Gas Behavior Conditions
Real gases behave most like ideal gases under conditions where the intermolecular forces are minimized and the size of the molecules compared to the space between them becomes negligible. This typically occurs under low pressure, where particles are far apart and have less interaction, and high temperature, where the increased kinetic energy of the particles overwhelms the intermolecular forces.
03
Evaluating the Given Options
By analyzing the given options, we can rule out the conditions that do not minimize intermolecular forces or make the size of the molecules negligible. High pressure would increase the interactions between particles (making them deviate from the ideal behavior), and low temperature would make it easier for intermolecular forces to influence the particles. Therefore, the correct condition is under low pressure and high temperature.
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Boyle's Law
Robert Boyle's discovery has been a foundation in understanding gas behavior. Boyle's law states that the pressure (\( P \) of a gas is inversely proportional to its volume (\( V \) when temperature and the amount of gas are held constant. In a simple mathematical relationship, Boyle's law is expressed as \( P \times V = \text{constant} \). This means that if you increase the pressure exerted on a gas, its volume decreases, provided the temperature doesn't change. Likewise, if you decrease the pressure, the volume increases. Boyle's law is particularly useful when dealing with changes in atmospheric pressure, like when scuba diving or flying.
When we consider this in terms of kinetic energy, we can see that as pressure increases, molecules are forced closer together, which can increase the frequency of collisions, affecting the gas's ability to behave ideally. However, at low pressures, as suggested in the ideal gas behavior, molecules are well-separated, collisions are less frequent, and the gas can thus conform to Boyle's law more accurately.
When we consider this in terms of kinetic energy, we can see that as pressure increases, molecules are forced closer together, which can increase the frequency of collisions, affecting the gas's ability to behave ideally. However, at low pressures, as suggested in the ideal gas behavior, molecules are well-separated, collisions are less frequent, and the gas can thus conform to Boyle's law more accurately.
Charles' Law
Charles' law, named after Jacques Charles, describes the relationship between temperature and volume within a gas at constant pressure. The law asserts that as the temperature of a gas increases, so does its volume. The formal relationship described by Charles' law is \( V \propto T \) or \( \frac{V_1}{T_1} = \frac{V_2}{T_2} \) when comparing two states of a gas where the pressure remains stable.
Imagine a balloon on a warm day, it expands as the gas particles inside it gain kinetic energy and push outwards more forcefully. Conversely, on a cold day, the balloon would contract as the particles lose energy and exert less pressure on the balloon's walls. Charles' law helps explain why a real gas under high temperature and constant pressure moves towards ideal gas behavior. The kinetic energy of the molecules is high enough to overcome the intermolecular forces, reducing their effect and allowing the gas to expand freely.
Imagine a balloon on a warm day, it expands as the gas particles inside it gain kinetic energy and push outwards more forcefully. Conversely, on a cold day, the balloon would contract as the particles lose energy and exert less pressure on the balloon's walls. Charles' law helps explain why a real gas under high temperature and constant pressure moves towards ideal gas behavior. The kinetic energy of the molecules is high enough to overcome the intermolecular forces, reducing their effect and allowing the gas to expand freely.
Avogadro's Law
Amedeo Avogadro proposed a principle that provides further insight into the nature of gases. Avogadro's law states that equal volumes of all gases, at the same temperature and pressure, contain the same number of molecules. It formalizes the direct proportionality between the volume (\( V \) of a gas and the number of moles (\( n \) of gas present, which means \( V \propto n \) or \( \frac{V_1}{n_1} = \frac{V_2}{n_2} \) when comparing two states.
Avogadro's law implies that the volume of a gas is determined by the number of gas particles it contains rather than the type of gas. This is a key component in understanding why gases at low pressures behave ideally, as increasing the amount of gas does not affect the pressure or temperature, allowing for consistent behavior reminiscent of an ideal gas where intermolecular forces are negligible.
Avogadro's law implies that the volume of a gas is determined by the number of gas particles it contains rather than the type of gas. This is a key component in understanding why gases at low pressures behave ideally, as increasing the amount of gas does not affect the pressure or temperature, allowing for consistent behavior reminiscent of an ideal gas where intermolecular forces are negligible.
Real Gases
Real gases are what we encounter in everyday life, as opposed to the theoretical ideal gases. The behavior of real gases deviates from the laws of ideal gases due to the particles' volume and the forces they exert on one another. Under certain conditions, mainly high pressures and low temperatures, these deviations become prominent because particles are closer together, leading to more significant intermolecular attractions and repulsions.
However, real gases can approximate ideal gas behavior under conditions of low pressure and high temperature. The increased kinetic energy at high temperatures allows particles to overcome attractions, and lower pressures mean the actual volume of the gas molecules is less significant compared to the space they occupy. Such conditions minimize the deviations caused by intermolecular forces and finite molecular volumes, allowing real gases to mimic ideal gas behavior more closely.
However, real gases can approximate ideal gas behavior under conditions of low pressure and high temperature. The increased kinetic energy at high temperatures allows particles to overcome attractions, and lower pressures mean the actual volume of the gas molecules is less significant compared to the space they occupy. Such conditions minimize the deviations caused by intermolecular forces and finite molecular volumes, allowing real gases to mimic ideal gas behavior more closely.
Intermolecular Forces
Intermolecular forces are the forces of attraction and repulsion between molecules. They play an essential role in the behavior of real gases and include dipole-dipole interactions, hydrogen bonding, and London dispersion forces. These forces can affect the physical properties of substances, such as boiling and melting points.
When it comes to gas behavior, intermolecular forces come into prominence at high pressures and low temperatures, where they cause deviations from ideal gas laws. The particles are close enough for these forces to become significant, disrupting the free movement of the gas molecules. This is why, to observe ideal gas behavior, it's crucial to have conditions that limit the strength of intermolecular forces by ensuring molecules are well separated and have enough kinetic energy to escape these forces.
When it comes to gas behavior, intermolecular forces come into prominence at high pressures and low temperatures, where they cause deviations from ideal gas laws. The particles are close enough for these forces to become significant, disrupting the free movement of the gas molecules. This is why, to observe ideal gas behavior, it's crucial to have conditions that limit the strength of intermolecular forces by ensuring molecules are well separated and have enough kinetic energy to escape these forces.
Kinetic Energy
Kinetic energy of gas particles is the energy due to their motion and is fundamentally related to temperature. The faster the gas particles move, the higher the temperature and kinetic energy. This energy is what allows gas particles to overcome intermolecular forces and move freely in space.
In the context of ideal gases, higher kinetic energy (at higher temperatures) means that the particles are moving rapidly enough to ignore their size and intermolecular attractions. As a consequence, at high temperatures, a gas is more likely to behave ideally. This is because kinetic energy provides the necessary mechanism for particles to move independently of one another, aligning with the concept of an ideal gas where interactions between particles are assumed to be non-existent.
In the context of ideal gases, higher kinetic energy (at higher temperatures) means that the particles are moving rapidly enough to ignore their size and intermolecular attractions. As a consequence, at high temperatures, a gas is more likely to behave ideally. This is because kinetic energy provides the necessary mechanism for particles to move independently of one another, aligning with the concept of an ideal gas where interactions between particles are assumed to be non-existent.
