Gas: Definition, Law, Formula, Equation, Examples, Questions

Edited By Shivani Poonia | Updated on Jul 02, 2025 07:59 PM IST

Matter has no fixed shape or volume. Like fluids but unlike solids, gases have no fixed shape and take the volume of the container. This expansion takes place because gas molecules are far apart and moving in a random manner. This behavior is described by the kinetic theory of gases, which says that the gas molecules are constantly moving, with continuous collisions between themselves and with the walls of the container.

This Story also Contains

The Gaseous State
Characteristics of Gas
Some Solved Examples
Summary

Gas: Definition, Law, Formula, Equation, Examples, Questions

The Gaseous State

Gases and their properties play an important role in our daily lives. Our atmosphere consists Of a Mixture Of gases like dioxygen, dinitrogen, carbon dioxide, water vapors, etc. These gases shield us from harmful radiation. Life is supported by the dioxygen in the air that we breathe. Plants need carbon dioxide for photosynthesis.
There are in total eleven elements in the periodic table that exist as gases under normal conditions.

The composition of gases is always from non-metal eg. O₂, N₂, He₂, Cl etc.

Following are the few physical properties of the gaseous state :

(i) The volume and shape of gases are not fixed. These assume the volume and shape of the container.

(ii) The thermal energy of gases >> molecular attraction.

(iii) Gases have infinite expansibility and high compressibility.

(iv) Gases exert pressure equally in all directions

(v) Gases have a much lower density than solids and liquids due to negligible intermolecular forces.

vi) Gas mix evenly with other gases or their mixtures are homogeneous in composition.

Characteristics of Gas

There are certain parameters or measurable properties which are used to describe the characteristics of gases

Volume (V): The volume of the container is the volume of the gas sample as gases occupy the entire space available to them.
Pressure (P): Pressure Of the gas is the force exerted by the gas per unit area on the walls of the container in all directions.
$\begin{aligned} & \text { S.I unit }=\text { pascal }(\mathrm{Pa}) \\ & 1 \mathrm{~Pa}=1 \mathrm{Nm}^{-2} \\ & 1 \mathrm{~atm}=1.013 \times 10^5 \mathrm{~Pa} \\ & \text { Conversions } \\ & 1 \mathrm{bar}=10^5 \mathrm{~Pa}=0.987 \mathrm{~atm} \\ & 1 \mathrm{~atm}=760 \mathrm{~mm} \mathrm{Hg} \\ & 1 \mathrm{~atm}=760 \text { torr } \\ & 1 \mathrm{~atm}=1.013 \times 10^5 \mathrm{~Pa}\end{aligned}$
Temperature: It is the measure of hotness of the system and energy of the system.
$\begin{aligned} & \text { S.I unit }=\mathrm{m}^3 \\ & \text { C.G.S. unit }=\mathrm{cm}^3 \\ & \text { Commonly used unit }=\mathrm{L} \\ & 1 \mathrm{~L}=1000 \mathrm{~mL} \\ & 1 \mathrm{~mL}=10^{-3} \mathrm{~L} \\ & 1 \mathrm{~m}^3=10^3 \mathrm{dm}^3 \\ & 1 \mathrm{~m}^3=10^3 \mathrm{~L} \\ & 1 \mathrm{~m}^3=10^6 \mathrm{~cm}^3 \\ & 1 \mathrm{~m}^3=10^6 \mathrm{~mL}\end{aligned}$
$
\begin{aligned}
& \text { S.I unit }=\text { kelvin }(\mathrm{K}) \\
& \mathrm{K}={ }^o \mathrm{C}+273
\end{aligned}
$
${ }^{\circ} \mathrm{C} \rightarrow$ centigrade degree or Celsius degree

Mass: The mass of a gas can be determined by weighing the container in which the gas is enclosed and again weighing the container after removing the gas. The mass of the gas is related to the number of moles of the gas i.e.Moles of gas $(\mathrm{n})=\frac{\text { Mass in grams }}{\text { Molar mass }}=\frac{\mathrm{m}}{\mathrm{M}}$

Some Solved Examples

Example 1:
A gas occupies a volume of 500 mL at 27°C and 1 atm pressure. What will be its volume at 47°C and 1 atm pressure?

Solution:
Given:
- Initial volume (V₁) = 500 mL
- Initial temperature (T₁) = 27°C = 27 + 273 = 300 K
- Final temperature (T₂) = 47°C = 47 + 273 = 320 K
- Pressure remains constant at 1 atm

Using the formula: V₁/T₁ = V₂/T₂
V₂ = (V₁ × T₂) / T₁
V₂ = (500 mL × 320 K) / 300 K
V₂ = 533.33 mL

Therefore, the volume of the gas at 47°C and 1 atm pressure is 533.33 mL.

Example 2:
A gas occupies a volume of 2 L at 27°C and 1 atm pressure. What will be its volume at 47°C and 0.5 atm pressure?

Solution:
Given:
- Initial volume (V₁) = 2 L
- Initial temperature (T₁) = 27°C = 27 + 273 = 300 K
- Final temperature (T₂) = 47°C = 47 + 273 = 320 K
- Initial pressure (P₁) = 1 atm
- Final pressure (P₂) = 0.5 atm

Using the formula: (V₁ × P₁) / T₁ = (V₂ × P₂) / T₂
V₂= (V₁ × P₁ × T₂) / (T₁× P₂)
V₂ = (2 L × 1 atm × 320 K) / (300 K × 0.5 atm)
V₂ = 4.27 L

Therefore, the volume of the gas at 47°C and 0.5 atm pressure is 4.27 L.

Example 3:
A gas occupies a volume of 1 L at 27°C and 1 atm pressure. How many moles of the gas are present?

Solution:
Given:
- Volume (V) = 1 L = 1000 mL
- Temperature (T) = 27°C = 27 + 273 = 300 K
- Pressure (P) = 1 atm

Using the ideal gas equation: PV = nRT
Where:
- R = 0.082057 L⋅atm⋅mol⁻¹⋅K⁻¹

n = (P × V) / (R × T)
n = (1 atm × 1000 mL) / (0.082057 L⋅atm⋅mol⁻¹⋅K⁻¹ × 300 K)
n = 40.82 mol

Therefore, there are 40.82 moles of the gas present.

Example 4:
A gas occupies a volume of 2 L at 27°C and 1 atm pressure. How many molecules of the gas are present?

Solution:
Given:
- Volume (V) = 2 L = 2000 mL
- Temperature (T) = 27°C = 27 + 273 = 300 K
- Pressure (P) = 1 atm

Using the ideal gas equation: PV = nRT
Where:
- R = 0.082057 L⋅atm⋅mol⁻¹⋅K⁻¹

n = (P × V) / (R × T)
n = (1 atm × 2000 mL) / (0.082057 L⋅atm⋅mol⁻¹⋅K⁻¹× 300 K)
n = 81.64 mol

1 mol = 6.022 × 10²³ molecules (Avogadro's number)

Number of molecules = n × 6.022 × 10²³
Number of molecules = 81.64 mol × 6.022 × 10²³molecules/mol
Number of molecules = 4.92 × 10²⁵ molecules

Therefore, there are approximately 4.92 × 10²⁵ molecules of the gas present.

Example 5:
A gas occupies a volume of 3 L at 27°C and 1 atm pressure. What will be its volume at 47°C and 2 atm pressure?

Solution:
Given:
- Initial volume (V₁) = 3 L
- Initial temperature (T₁) = 27°C = 27 + 273 = 300 K
- Final temperature (T₂) = 47°C = 47 + 273 = 320 K
- Initial pressure (P₁) = 1 atm
- Final pressure (P₂) = 2 atm

Using the formula: (V₁ × P₁) / T₁ = (V₂ × P₂) / T₂
V₂ = (V₁× P₁ × T₂) / (T₁ × P₂)
V₂ = (3 L × 1 atm × 320 K) / (300 K × 2 atm)
V₂ = 3.2 L

Therefore, the volume of the gas at 47°C and 2 atm pressure is 3.2 L.

Summary

Gas molecules travel very fast and far apart, which causes intermolecular forces to become negligible. These forces that keep them moving so fast, coupled with the spacing, give gases a very low density. Gases is that they are highly compressible. Whereas solids and liquids cannot so easily be compressed to exist in smaller volumes, this certainly is not the case for pressurized gases.

Frequently Asked Questions (FAQs)

1. What is a gas and how does it differ from other states of matter?

A gas is a state of matter characterized by particles with high kinetic energy that are far apart and move randomly. Unlike solids and liquids, gases have no fixed shape or volume and expand to fill their container. The particles in a gas have much more freedom of movement compared to those in liquids or solids.

2. Why do gases exert pressure on their containers?

Gases exert pressure because their particles are in constant, rapid motion. As these particles collide with the walls of their container, they transfer momentum, resulting in a force per unit area, which we perceive as pressure. The more frequent and forceful these collisions, the higher the pressure.

3. What is Boyle's Law and how does it relate to gas behavior?

Boyle's Law states that for a fixed amount of gas at constant temperature, the pressure and volume are inversely proportional. In other words, as the volume of a gas decreases, its pressure increases, and vice versa. This relationship is expressed as P₁V₁ = P₂V₂, where P is pressure and V is volume.

4. How does Charles's Law describe the relationship between temperature and volume of a gas?

Charles's Law states that for a fixed amount of gas at constant pressure, the volume is directly proportional to its absolute temperature. As the temperature of a gas increases, its volume increases proportionally, and vice versa. This relationship is expressed as V₁/T₁ = V₂/T₂, where V is volume and T is absolute temperature.

5. What is the significance of absolute zero in gas behavior?

Absolute zero (-273.15°C or 0 K) is the theoretical temperature at which all molecular motion ceases. It's significant in gas behavior because many gas laws use the Kelvin scale, which starts at absolute zero. This ensures that gas volume never becomes negative in calculations, as it would if we used Celsius or Fahrenheit scales.

6. What is the kinetic molecular theory of gases and how does it explain gas behavior?

The kinetic molecular theory of gases is a model that explains gas behavior based on the following assumptions: 1) Gas particles are in constant, random motion. 2) Gas particles have negligible volume. 3) Collisions between particles are elastic. 4) There are no attractive or repulsive forces between particles. This theory helps explain gas laws and properties like pressure, diffusion, and temperature effects.

7. What is the Ideal Gas Law and how does it combine Boyle's, Charles's, and Gay-Lussac's laws?

The Ideal Gas Law is an equation of state for a hypothetical ideal gas. It combines Boyle's, Charles's, and Gay-Lussac's laws into a single equation: PV = nRT, where P is pressure, V is volume, n is the number of moles of gas, R is the universal gas constant, and T is absolute temperature. This law relates all these variables for a fixed amount of gas.

8. Why do real gases deviate from ideal gas behavior?

Real gases deviate from ideal gas behavior because of two main factors: 1) The volume of gas particles, which is negligible in ideal gases but significant in real gases, especially at high pressures. 2) Intermolecular forces between gas particles, which are absent in ideal gases but present in real gases, especially at low temperatures and high pressures.

9. What is Dalton's Law of Partial Pressures and how is it applied?

Dalton's Law of Partial Pressures states that the total pressure exerted by a mixture of gases is equal to the sum of the partial pressures of each individual gas. Mathematically, P(total) = P₁ + P₂ + P₃ + ... This law is applied in various fields, including respiratory physiology and gas mixture calculations.

10. How does temperature affect the average kinetic energy of gas particles?

Temperature is directly proportional to the average kinetic energy of gas particles. As temperature increases, the average kinetic energy of the particles increases, causing them to move faster and collide more frequently and forcefully with their surroundings. This relationship is key to understanding many gas laws and behaviors.

11. How does gas solubility in liquids change with temperature and pressure?

Gas solubility in liquids generally decreases with increasing temperature (as kinetic energy of gas particles increases, allowing them to escape the liquid more easily) and increases with increasing pressure (as more gas is forced into the liquid). This relationship is described by Henry's Law, which states that the amount of dissolved gas is proportional to its partial pressure above the liquid. Understanding gas solubility is crucial in fields like environmental science and beverage production.

12. What is the significance of Boyle temperature in gas behavior?

The Boyle temperature is the temperature at which a real gas behaves most like an ideal gas over a range of pressures. At this temperature, the competing effects of molecular volume and intermolecular attractions roughly cancel out. Above the Boyle temperature, a gas generally has a compressibility factor greater than 1, while below it, the factor is less than 1. Understanding the Boyle temperature is crucial for accurately predicting gas behavior in various industrial and scientific applications.

13. How does the equipartition theorem relate to the heat capacity of gases?

The equipartition theorem states that energy is shared equally among all energetically accessible degrees of freedom of a system. For an ideal monatomic gas, this leads to a molar heat capacity at constant volume (Cv) of 3/2R, where R is the gas constant. For diatomic gases, rotational degrees of freedom add to this, typically resulting in Cv = 5/2R at room temperature. This theorem is fundamental in understanding the heat capacities of gases and their temperature dependence.

14. How does Gay-Lussac's Law relate pressure and temperature of a gas?

Gay-Lussac's Law states that for a fixed amount of gas at constant volume, the pressure is directly proportional to its absolute temperature. As the temperature increases, the pressure increases proportionally, and vice versa. This relationship is expressed as P₁/T₁ = P₂/T₂, where P is pressure and T is absolute temperature.

15. How does Graham's Law of Diffusion relate to gas particle movement?

Graham's Law of Diffusion states that the rate of diffusion or effusion of a gas is inversely proportional to the square root of its molecular mass. This means lighter gases diffuse or effuse faster than heavier gases. The law is expressed as: Rate₁/Rate₂ = √(M₂/M₁), where M is the molecular mass of the gases.

16. What is meant by the term "standard temperature and pressure" (STP) in gas calculations?

Standard Temperature and Pressure (STP) refers to specific conditions used as a reference point in many gas calculations. The internationally accepted values for STP are 0°C (273.15 K) for temperature and 1 atmosphere (101.325 kPa) for pressure. These conditions allow for consistent comparisons of gas properties across different experiments and calculations.

17. How does the concept of mean free path relate to gas particle behavior?

Mean free path is the average distance a gas particle travels between collisions with other particles. It's inversely proportional to the density of the gas and the size of the particles. In less dense gases or those with smaller particles, the mean free path is longer. This concept is important in understanding gas diffusion, viscosity, and heat conduction.

18. What is the significance of Avogadro's Law in understanding gas behavior?

Avogadro's Law states that equal volumes of gases at the same temperature and pressure contain the same number of molecules, regardless of their chemical nature. This law is crucial for understanding the relationship between the volume of a gas and the number of particles it contains, and it forms the basis for the concept of the mole in chemistry.

19. How do real gases behave differently at high pressures compared to ideal gases?

At high pressures, real gases deviate significantly from ideal gas behavior. The volume occupied by the gas particles themselves becomes significant, and intermolecular forces play a larger role. This leads to a higher pressure than predicted by the ideal gas law. The gas becomes less compressible, and its behavior can be better described by more complex equations of state, such as the van der Waals equation.

20. What is the van der Waals equation and how does it improve upon the ideal gas law?

The van der Waals equation is an improvement on the ideal gas law that accounts for the behavior of real gases. It introduces two correction factors: one for the volume of the gas particles (a) and another for the attractive forces between particles (b). The equation is (P + an²/V²)(V - nb) = nRT, where n is the number of moles and R is the gas constant. This equation provides a more accurate description of real gas behavior, especially at high pressures and low temperatures.

21. How does the concept of compressibility factor (Z) help in understanding real gas behavior?

The compressibility factor (Z) is a measure of how much a real gas deviates from ideal gas behavior. It's defined as Z = PV/nRT, where PV/nRT is the ratio of the actual volume of a real gas to the volume predicted by the ideal gas law. For an ideal gas, Z = 1. Values of Z < 1 indicate that the gas is more compressible than an ideal gas, while Z > 1 indicates less compressibility. The compressibility factor varies with pressure and temperature, helping to quantify real gas behavior.

22. What is the significance of critical temperature and pressure for a gas?

The critical temperature is the temperature above which a gas cannot be liquefied by pressure alone. The critical pressure is the pressure required to liquefy a gas at its critical temperature. Together, these define the critical point of a substance. Above the critical point, the distinction between liquid and gas phases disappears, forming a supercritical fluid. Understanding critical points is crucial in industrial processes, such as supercritical fluid extraction.

23. How does the Maxwell-Boltzmann distribution describe the speeds of gas particles?

The Maxwell-Boltzmann distribution describes the range of speeds of particles in a gas at a given temperature. It shows that not all particles have the same speed; instead, there's a distribution of speeds. The distribution is asymmetric, with a long tail towards higher speeds. As temperature increases, the peak of the distribution shifts to higher speeds, and the distribution broadens, reflecting the increase in average kinetic energy of the particles.

24. What is Brownian motion and how does it relate to gas particle behavior?

Brownian motion is the random, erratic movement of particles suspended in a fluid (liquid or gas), caused by collisions with the fast-moving atoms or molecules in the fluid. In gases, this motion is a direct result of the constant, random movement of gas particles. Brownian motion provides evidence for the kinetic theory of gases and helps explain phenomena like diffusion and the equal distribution of gas particles throughout a container.

25. How does the effusion rate of a gas depend on its molecular mass?

The effusion rate of a gas is inversely proportional to the square root of its molecular mass, as described by Graham's Law. Lighter gases effuse (escape through a tiny hole) faster than heavier gases. This relationship is expressed mathematically as: Rate₁/Rate₂ = √(M₂/M₁), where Rate is the effusion rate and M is the molecular mass. This principle is used in processes like isotope separation.

26. What is the difference between diffusion and effusion in gases?

Diffusion is the movement of gas particles from an area of high concentration to an area of low concentration, resulting in the gradual mixing of gases. Effusion, on the other hand, is the process by which gas particles escape through a tiny hole in their container. While both processes are governed by Graham's Law, diffusion occurs within a gas or between gases, while effusion involves gas escaping from a container.

27. How does the concept of mean square speed relate to the temperature of a gas?

The mean square speed of gas particles is directly proportional to the absolute temperature of the gas. It's calculated as the root mean square (RMS) speed, which is the square root of the average of the squared speeds of all particles. The relationship is expressed as v(rms) = √(3RT/M), where R is the gas constant, T is absolute temperature, and M is molar mass. This concept links the microscopic motion of particles to the macroscopic property of temperature.

28. What is the significance of Joule-Thomson effect in gas behavior?

The Joule-Thomson effect describes the temperature change of a gas when it expands at constant enthalpy (adiabatic expansion). For most gases at room temperature, expansion causes cooling (positive Joule-Thomson coefficient). However, for hydrogen and helium at room temperature, expansion causes heating (negative Joule-Thomson coefficient). This effect is crucial in many industrial processes, including gas liquefaction and refrigeration.

29. What is Amagat's Law and how does it relate to gas mixtures?

Amagat's Law states that the volume of a gas mixture is equal to the sum of the volumes that each gas would occupy if it were alone at the temperature and pressure of the mixture. Mathematically, V(total) = V₁ + V₂ + V₃ + ... This law complements Dalton's Law of Partial Pressures and is useful in calculating the properties of gas mixtures, especially when dealing with volumes rather than pressures.

30. How does the concept of fugacity improve upon the ideal gas law for real gases?

Fugacity is a measure of the tendency of a substance to escape from a phase. For an ideal gas, fugacity equals pressure, but for real gases, it differs. The concept of fugacity allows thermodynamic equations developed for ideal gases to be applied to real gases by replacing pressure with fugacity. It accounts for the non-ideal behavior of real gases, especially at high pressures, and is crucial in chemical engineering and thermodynamics calculations.

31. What is the significance of the Linde technique in gas liquefaction?

The Linde technique is a method used to liquefy gases based on the Joule-Thomson effect. It involves compressing a gas, cooling it, and then allowing it to expand rapidly, which causes further cooling. This process is repeated until the gas liquefies. The technique is significant because it allows for the liquefaction of gases with low critical temperatures, such as nitrogen and oxygen, which is crucial for industrial gas separation and storage.

32. How does the concept of reduced variables help in understanding gas behavior across different substances?

Reduced variables are dimensionless quantities obtained by dividing actual variables (pressure, volume, temperature) by their critical values. For example, reduced temperature T(r) = T/T(c), where T(c) is the critical temperature. Using reduced variables allows for the comparison of gas behaviors across different substances. The principle of corresponding states suggests that all gases behave similarly when compared at the same reduced conditions, which is useful in predicting gas properties and behavior.

33. What is the virial equation of state and how does it improve upon the ideal gas law?

The virial equation of state is an improvement on the ideal gas law that accounts for non-ideal gas behavior. It's expressed as a power series in terms of 1/V or P: PV/nRT = 1 + B/V + C/V² + ..., where B, C, etc., are virial coefficients that depend on temperature and the specific gas. This equation provides a more accurate description of gas behavior over a wide range of conditions and can be truncated at different levels of accuracy as needed.

34. How does the speed of sound in a gas relate to its temperature and molecular mass?

The speed of sound in a gas is related to its temperature and molecular mass by the equation: v = √(γRT/M), where v is the speed of sound, γ is the ratio of specific heats (Cp/Cv), R is the gas constant, T is absolute temperature, and M is the molar mass of the gas. This relationship shows that sound travels faster in gases with higher temperatures or lower molecular masses, which is important in fields like acoustics and aerodynamics.

35. What is the significance of Avogadro's number in gas calculations?

Avogadro's number (approximately 6.022 × 10²³) represents the number of particles (atoms, molecules, or formula units) in one mole of a substance. In gas calculations, it's crucial for converting between the number of particles and the number of moles. It also helps in understanding the concept of the molar volume of a gas, which is the volume occupied by one mole of an ideal gas at STP (approximately 22.4 L).

36. How does the concept of mean free path change in a gas as pressure increases?

As pressure increases in a gas, the mean free path decreases. This is because higher pressure means more gas particles in the same volume, leading to more frequent collisions between particles. The relationship is inverse: mean free path is inversely proportional to pressure. This concept is important in understanding gas transport properties like diffusion and thermal conductivity, especially in applications like vacuum technology and plasma physics.

37. What is the significance of the Boltzmann distribution in gas behavior?

The Boltzmann distribution describes the probability of finding particles