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An ideal gas is a theoretical gas comprised of a number of randomly moving point particles that do not interact with one another.
- The ideal gas concept is valuable because it obeys the ideal gas law, which is a simplified equation of state, and is susceptible to statistical mechanics analysis.
- Many real gases behave qualitatively like ideal gases under various temperature and pressure conditions, with the gas molecules (or atoms for monatomic gases) performing the role of the ideal particles.
- Many gases, including nitrogen, oxygen, hydrogen, noble gases, heavier gases like carbon dioxide, and mixes like air, can be regarded as ideal gases within tolerable tolerances throughout a wide parameter range based on standard temperature and pressure.
Pressure is defined as the force applied perpendicular to an object's surface per unit area across which that force is distributed.
The formula for finding the pressure of an ideal gas is given by
P = 1/3 ρv2
Where
- ρ is the density of the gas and
- v is the mean square speed of the gas.
The pressure of an ideal gas can also be calculated from the ideal gas equation
PV = nRT
Where
- P is the pressure of the gas
- V is the volume of the gas
- n is the number of moles
- R is the gas constant
- T is the temperature
Very Short Answers Questions [1 Mark Questions]
Ques. Which are laws that are incorporated in the ideal gas equation?
Ans. The ideal gas equation is a combination of fundamental laws such as Boyle's law, Gay-Lussac's law, Charle's law, and Avogadro's law.
Ques. What are the three types of ideal gases?
Ans. The three types of ideal gases are
- The Classical or Maxwell-Boltzmann ideal gas
- The ideal quantum Fermi gas comprises fermions
- The ideal quantum Bose gas, composed of Bosons
Ques. What is the formula for finding the pressure of an ideal gas?
Ans. The formula for finding the pressure of an ideal gas is given by
P = 1/3 ρv2
Where ρ is the density of the gas and v is the mean square speed of the gas.
The pressure of an ideal gas can also be calculated from the ideal gas equation
PV = nRT
Ques. Give some ideal gas examples.
Ans. Several gases, including hydrogen, oxygen, nitrogen, noble gases, carbon dioxide, and various air mixes, can be called ideal gases within certain tolerances around basic pressure and temperature.
Ques. The _________ is also called the molar gas constant or ideal gas constant.
- Kelvin Plancks Constant
- Universal Gas Constant
- Force Constant
- Boltzmann Constant
Ans. The correct answer is b. Universal Gas Constant
Explanation: The molar gas constant, ideal gas constant, and universal gas constant are all names for the gas constant.
Short Answers Questions [2 Marks Questions]
Ques. What is meant by an ideal gas?
Ans. An ideal gas is a hypothetical gas composed of multiple arbitrarily moving point particles that are unaffected by interparticle interactions. Boyle and Charles established these laws known as Boyle's law and Charles' law, respectively. The ideal gas concept is useful because it obeys the ideal gas laws, has a fundamental equation of state, and is receptive to examination under statistical mechanics.
Ques. What is meant by pressure?
Ans. The force exerted perpendicular to the surface of a body per unit area (the region where force is applied) is defined as pressure. Gauge pressure is a type of pressure that is measured in relation to normal atmospheric pressure. Pressure is expressed in a variety of units. Few of the units are formed by dividing a force unit by an area unit. The pascal (Pa) is the SI unit of pressure (Newton per square meter or N/m2).
Ques. Explain the ideal gas equation.
Ans. The ideal gas law, often known as the ideal gas equation, is the state equation for a hypothetical ideal gas. It is an acceptable approximation of the behavior of various gases under many situations, however, it has many drawbacks. The ideal gas law can be written in an empirical form as
PV = nRT
Ques. What are the ideal gas law units?
Ans. The unit of pressure should be in atmospheres (atm) when temperature T in kelvin (K), and volume in litres (L) for the gas constant R = 0.082 L.atm/K.mol.
For the gas constant R = 8.31 J/K mol, pressure P should be expressed in pascals(Pa) if temperature T in kelvin K, and volume in liters L.
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Long Answers Questions [3 Marks Questions]
Ques. What are the ideal gas laws?
Ans. Ideal gas laws are the laws that deal with ideal gases. Boyle and Charles established these laws known as Boyle's law and Charles' law, respectively.
- Boyle's law states that the pressure of a given amount of gas at a constant temperature is inversely proportional to the volume of the gas.
- Charles' law states that for a given fixed gas mass at constant pressure, the volume of the gas is directly proportional to its temperature.
Ques. What is the kinetic theory of Ideal gas??
Ans. The following are the assumptions on which the kinetic theory of ideal gas is based
- Gas is composed of a huge number of particles that travel in non-uniform directions separated by a distance greater than the particle size.
- Gas molecules collide in a fully elastic collision.
- Heat is the transmission of kinetic energy between molecules.
- Gas particles have a negligible volume and are attracted by intermolecular forces.
Ques. What are the three factors that affect the pressure of an ideal gas?
Ans. The following are the factors that affect the pressure of an ideal gas
- Volume: The volume of a gas is inversely proportional to its pressure.
- Number of molecules in the gas: The number of molecules in a gas is directly proportional to the pressure of the gas. The more number of molecules in the gas more will be the pressure.
- Temperature: The temperature of a gas is directly proportional to its pressure. If the temperature of the gas is higher, the pressure of the gas will be higher.
Very Long Answers Questions [5 Marks Questions]
Ques. A sample of nitrogen occupies a volume of 350 cm3 at STP. Then, What is its volume at 550 K and 0.5 atm pressure?
Ans. STP stands for standard temperature and pressure. The standard temperature is 273 K and the standard pressure is 1 atmosphere (atm).
Given
- Initial pressure, P1 = 1 atm
- Initial temperature, T1 = 273 K
- Initial volume, V1 = 350 cm3
- Final pressure, P2 = 0.5 atm
- Final temperature, T2 = 550 K
Let V2 be the final volume, then from the ideal gas equation, we have
P1V1/T1 = P2V2/T2
⇒ V2 = (P1V1T2)/(T1P2)
On substituting the values, we get
V2 = (1 x 350 x 550)/(273 x 0.5)
⇒ V2 = 1410 cm3
Therefore, the sample of nitrogen occupies a volume of 1410 cm3 at 550 K and 0.5 atm pressure.
Ques. A sample of nitrogen gas is bubbled through liquid water at 25 ℃ and then collected in a volume of 750 cc. The total pressure of the gas which is saturated with water vapour, is found to be 740 mm at 25 ℃. The vapor pressure of water at this temperature is 24 mm. How many moles of nitrogen are in the sample?
Ans. Given
- The temperature of nitrogen gas and liquid water, T = 25 ℃ = 298 K
- Total volume, V = 750 cc = 750 x 10-3 L
- Total pressure, PT = 740 mm
- The pressure of water vapor, PW = 24 mm
The total pressure of the gas that is saturated with water vapour is equal to the sum of the pressure of the water vapor and pressure of nitrogen gas i.e.
PT = PW + PN
⇒ PN = PT - PW
⇒ PN = 740 - 24 = 716 mm of Hg = 0.94211 atm
Now from the ideal gas equation, we have
PV = nRT
Where
- P is the pressure of the gas
- V is the volume of the gas
- T is the temperature
- R is the Universal gas constant = 0. 0821 L atm K−1 mol−1
- n is the number of moles the gas
From the above equation, we get
n = PNV/RT
On substituting the values, the number of moles of nitrogen is given by
n = (0.94211 x 750 x 10-3)/(0. 0821 x 298)
⇒ n = 0.0288 moles
Ques. What are the limitations of an ideal gas?
Ans. The following are the limitations of the ideal gas
- Although the ideal gas does not exist in reality, the ideal gas equation is extremely helpful in understanding the behavior of gases during reactions.
- Gases with low density, low pressure, and high temperature behave roughly like Ideal Gases.
- The ideal gas law does not apply at low temperatures, high densities, or extremely high pressures because molecule size and intermolecular interactions are important.
- The ideal gas law does not apply to heavy gases (such as refrigerants) or gases with strong intermolecular forces (such as water vapor).
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