Lastly, in “What are the 5 gas laws in physics? Important Gas Laws in Thermodynamics”, all the basic laws have been discussed. These laws include Boyle’s Law, Charles’s Law, Gay-Lussac’s Law, and Avogadro’s Law. Now, we shall discuss the Ideal Gas Law and its extension, the Combined Gas Law.
Table of Contents
Introduction
In the study of gases, the ideal gas law and the combined gas law are closely related concepts.
The ideal gas law is characterised by the equation PV = nRT and describes the behaviour of an ideal gas under specific conditions. The ideal gas law deals with a single set of conditions such as pressure (P), volume (V), amount of substance (n), and temperature (T) of a gas through the gas constant (R).
Conversely, the combined gas law is characterised by the equation (P1V1) / T1 = (P2V2) / T2 and combines 3 fundamental laws: Boyle’s Law, Charles’s Law, and Gay–Lussac’s Law. The combined gas law deals with the two sets of conditions, where subscript 1 refers to the initial condition and subscript 2 refers to the final condition
By understanding these laws, scientists and engineers forecast the behaviour of gases and design efficient thermodynamic processes or systems.
What Are the 5 Gas Laws in Physics?
The 5 gas laws serve as a guiding path in scientific and industrial applications. They not only enhance our understanding of how gases behave under different conditions but also provide valuable insights into the relationship between different properties of gases. These laws comprise:
- Boyle’s Law
- Charles’s Law
- Avogadro Law
- Gay–Lussac’s Law
- Ideal Gas Law
The Ideal Gas Law
The Ideal Gas Law is a theoretical model to study the behaviour of real gases under certain conditions. The equation of the ideal gas law, PV = nRT, defines the behaviour of an ideal gas for given conditions such as pressure, volume, temperature, and quantity (the number of moles).
Important Characteristics of Ideal Gas
Ideal gases are characterised by several assumptions:
- The molecules of an ideal gas are regarded as point particles with negligible volume.
- The molecules of an ideal gas do not interact with each other except for elastic collisions.
The equation of the ideal gas law is developed based on these assumptions.
Mathematical Formulation and Its Interpretation
The equation of ideal gas law is obtained by relating the pressure (P), volume (V), temperature (T), and number of moles (n) of an ideal gas, as given in Boyle’s Law, Charles’s Law, and Avogadro’s Law.
According to Boyle’s Law,
PV = constant
According to Charles’s Law,
V/T = constant
According to Avogadro’s Law,
V/n = constant
By combining these laws into a single equation, we get:
PV/nT = constant
PV/nT = R
PV = nRT
Here, R is the constant of proportionality, called the gas constant. The gas constant R is also known as the ideal gas constant or general gas constant. The value of R is the same for all ideal gases.
The Ideal Gas Law in Terms of Density and Molar Mass
The equation of the ideal gas law PV = nRT can also be written in terms of the density and molar mass of the gas. Since the number of moles is the ratio of the mass of the gas (m) in the cylinder to the molar mass of the gas (M),.
n = m/M
Now, the ideal gas equation can be written as:
PV = (m/M) RT
Rearranging the parameters involved:
PM = (m/V) RT
Since the ratio of mass to volume is called density (ρ),
PM = (ρ) RT
PM = ρRT
Significance of the Gas Constant (R) and Its Units
The value of the gas constant R is influenced by the units of pressure, volume, and temperature. It provides a conversion factor and allows us to convert between different units of pressure, volume, temperature, and moles.
The most commonly used values of the gas constant (R) are:
R = 0.0821 (atm L)/(mol K)
R = 8.314 J/(mol K)
R = 8.314 (kPa dm3)/(mol K)
R = 62.3637 (mmHg L)/(mol K)
R = 1.987 cal/(mol K)
Significance of the Ideal Gas Law
The ideal gas law functions as a benchmark that assists us in understanding behaviour of gases in different situations. With this law, we can anticipate things like pressure, volume, temperature, and the amount of gas in a thermodynamic system.
Even though it does not match the real-world applications perfectly, in schools and universities, students learn about this law, since it is the basis for many other topics in science and engineering and is employed in different fields, including chemistry, physics, etc.
Comparison between Ideal Gases and Real Gases
Real gases deviate from ideal gas behaviour under particular conditions. Even though the ideal gas law offers a valuable estimate of gas behaviour, it does not consider the complexities that cause real gas characteristics at high pressures and low temperatures.
Why are real gases important?
Understanding real gases is crucial for accurately visualising and describing gas behaviour in practical applications. Even though ideal gases provide a ballpark figure under many conditions, real gases must still be considered when dealing with extreme pressures, temperatures, or cases where intermolecular forces become significant.
Compression Factor (Z)
The ratio of the observed pressure (Pobserved) to the ideal pressure (Pideal), estimated by the ideal gas law, of a gas is called the compression factor.
Compression Factor (Z) = Pobserverd/Pideal
The compression factor is a dimensionless quantity and is used to quantify deviations from ideal behaviour. For the case where,
- Z>1: The gas behaves less ideally than predicted by the ideal gas law. This typically takes place at high pressures or low temperatures, where intermolecular forces and molecular volume become significant.
- Z<1: The gas behaves more ideally than predicted by the ideal gas law. This is less common and typically takes place where intermolecular forces and molecular volume are insignificant.
The compression factor helps understand how actual gases behave under different circumstances since it offers a numerical representation of the degree of divergence from ideal behaviour.
Factors Leading to Deviations from Ideal Gas Behaviour
Real gases may demonstrate deviations from their ideal character due to the following reasons:
Deviations due to intermolecular forces
In ideal gases, molecules are assumed to not interact with each other except during collisions. However, this is not the case at high pressure and low temperature, as real gases experience attractive intermolecular forces such as van der Waals forces, dipole-dipole interactions, and hydrogen bonding in such situations.
Deviations due to Finite Particle Volume
The volume that gas particles occupy in a container increases significantly at high pressures and low temperatures. Consequently, the finite volume of gas particles results in less space in the container for particle mobility, and thus, the gas shows deviation from the ideal gas assumption of negligible volume.
Mathematical Formulation (The Van der Waals Equation)
To understand how gases behave in real scenarios, the Van der Waals equation is the best tool that provides a more accurate explanation of real gas behaviour by incorporating correction factors for intermolecular forces and finite particle volume. The equation is expressed as:
(P + an2/V2) × (V – nb) = nRT
Here,
- P: Pressure
- V: Volume
- n: Amount of gas in moles
- T: Temperature in Kelvin
- R: Gas constant
- a: Van der Waals constant related to intermolecular forces
- b: Van der Waals constant related to finite particle volume
Intermolecular Forces Correction
The term an2/V2 takes into consideration the attractive forces between gas molecules, correcting for the deviation from ideal behaviour caused by intermolecular attractions.
Finite Particle Volume Correction
The term nb takes into consideration the volume occupied by the gas particles, compensating for the finite size of the gas molecules.
Significance of Real Gas Law
Real gases provide us with an understanding of the behaviour of gases and the factors that contribute to deviations from ideal gas behaviour. It is important to know about these variations, as they play an important role in various scientific and engineering applications.
The introduction of the correction factors in the Van der Waals equation provides a more accurate picture of real gas behaviour, particularly under extreme conditions where deviations from ideal behaviour are significant.
The Combined Gas Law
The combined gas law is a blend of Boyle’s Law, Charles’s Law, and Gay-Lussac’s Law into a single equation that describes the link between the pressure (P), volume (V), and temperature (T) of a gas when the number of moles (n) remains constant.
The equation of combined gas law permits us to calculate the variation in the behaviour of a gas under changing conditions by relating its pressure, volume, and temperature.
Mathematical Formulation and Its Interpretation
For a given amount of an ideal gas that has a pressure (P), volume (V), and temperature (T), the equation of the combined gas law can be deduced like this:
According to Boyle’s Law,
PV = constant
According to Charles’s Law,
V/T = constant
According to Gay-Lussac’s Law,
P/T = constant
By combining these laws, we can derive the combined gas law equation:
(PV) / T = constant
If the gas in a system is undergoing a thermal change from state 1 to state 2, this law can be expressed as:
(P1 V1) / T1 = (P2 V2) / T2
Significance of Combined Gas Law
The combined gas law is a good tool to solve problems involving changes in the pressure, volume, and temperature of a gas while keeping the amount of the substance constant.
This law is a versatile tool and is widely used in chemistry, physics, engineering, and other fields.
Application of the Combined Gas Law
The combined gas law comes in handy in cases where one or more of the variables (P, V, and T) are altered while keeping the number of moles constant. It allows an individual to determine unknown initial or final conditions in such scenarios.
In a nutshell, the Combined Gas Law is a useful tool for solving problems involving gas behaviour under changing conditions, making it invaluable for both theoretical analysis and practical applications.
Problem-Solving Exercises: The Combined Gas Law
Example 1: A sample of gas has an initial volume of 2.0 L, a pressure of 1.0 atm, and a temperature of 300 K. If the temperature is increased to 350 K while keeping the pressure constant, what is the final volume of the gas?
Solution: Assuming the given sample of gas is ideal:
Initial Volume: V1 = 2 L
Initial Pressure: P1 = 1 atm
Initial Temperature: T2 = 300 K
Final Temperature: T2 = 350 K
Final Pressure: P2 = 1 atm
Final Volume: V2 = ?
Using the combined gas law:
(P1 V1) / T1 = (P2 V2) / T2
(1 atm × 2 L) / (300 K) = (1 atm × V2) / (350 K)
V2 = 2.33 L
Example 2: A sample of gas occupies a volume of 10 dm3 at 1.2 atm in a cylinder with a moveable piston. At a temperature of 35℃, the volume is increased by one-eight of the original volume. What is the final pressure of the gas, assuming that the process is isothermal?
Solution: Assuming the given sample of gas is ideal:
Initial Volume: V1 = 10 dm3
Initial Temperature: T1 = 35 °C = 308 K
Initial Pressure: P1 = 1.2 atm
Final Temperature: T2 = 35 °C = 308 K
Final Volume: V2 = V1 + V1/8 = 11.22 dm3
Final Pressure: P2 = ?
Using the combined gas law:
(P1 V1) / T1 = (P2 V2) / T2
(1.2 atm × 10 dm3) / 308 K = (P2 atm × 11.22 dm3) / (308 K)
P2 = 1.07 atm
Conclusion
The study of 5 gas laws in physics, including Boyle’s Law, Charles’s Law, Avogadro Law, Gay-Lussac’s Law, and the Ideal Gas Law, provides a comprehensive framework for understanding the relationships between pressure, volume, temperature, and quantity of gases, both individually and collectively.
The Ideal Gas Law describes the behaviour of an ideal gas under particular conditions of pressure, volume, temperature, and quantity (number of moles) of a substance.
On the other hand, the Combined Gas Law deals with the changes in pressure, volume, and temperature of a gas while keeping the number of moles constant.
The comprehension of these laws and their applications enables scientists and engineers to predict and control behaviour of gas in different systems and processes in fields such as chemistry, physics, engineering, and environmental science. Some systems and processes are listed here:
- Internal Combustion Engines
- Refrigeration and Air Conditioning Systems
- Chemical Processing Plants
- Environmental Monitoring and Control Systems
- Gas Storage and Transportation Systems
Overall, gas laws serve as foundational principles in thermodynamics, offering insights into the behaviour of gases and enabling innovations across various scientific and engineering disciplines.
Through continual exploration and application of these laws, we can further boost our understanding and utilisation of gases in practical contexts.
Frequently Asked Questions (FAQs)
In what scenarios is the ideal gas law preferred over more complex equations like the Van der Waals equation?
The Ideal Gas Law is preferred for low pressures and high temperatures, or when simplicity and ease of calculation are prioritised. On the other hand, complex equations like the Van der Waals equation are used in cases where gases diverge significantly from ideal behaviour, such as at high pressures or low temperatures.
How does the concept of molar volume relate to the Ideal Gas Law?
The volume that one mole of a gas occupies in a container at a given temperature and pressure is known as its molar volume. According to the Ideal Gas Law, one mole of any ideal gas has a volume of 22.4 litters at standard temperature and pressure (STP).
How does the Ideal Gas Law explain the effect of temperature on gas behaviour, and relate it to the average kinetic energy of gas molecules?
The Ideal Gas Law considers temperature as the main factor affecting gas behaviour. According to this law, for an increase in temperature, there is an increase in the average kinetic energy of gas molecules.
This relationship is described by the kinetic molecular theory of gases, which defines temperature as being directly proportional to the average kinetic energy of gas molecules.
How is the ideal gas law equation derived?
The ideal gas law equation is derived by combining Boyle’s Law, Charles’s Law, and Avogadro’s Law into a single equation. This law relates the pressure, volume, temperature, and quantity of an ideal gas.
What is the significance of the gas constant (R) in the ideal gas law?
The gas constant allows for the conversion between different units of pressure, volume, temperature, and moles, serving as a fundamental constant in gas behaviour analysis.
How does the Van der Waals equation account for deviations from ideal gas behaviour?
The Van der Waals equation includes correction factors for intermolecular forces and finite particle volume, providing a more accurate description of real gas behaviour.
What is the compression factor (Z) and how is it used in gas behaviour analysis?
The compression factor quantifies deviations from ideal gas behaviour and provides insights into the extent of these deviations under different conditions.
Can you explain the mathematical formulation of the combined gas law?
The combined gas law equation relates pressure, volume, and temperature for a given amount of gas, derived from combining Boyle’s Law, Charles’s Law, and Gay-Lussac’s Law.