Module 5: Chapter 15 - Ideal Gases Flashcards
What is the equation for pressure?
Pressure = force / area
What is standard atmospheric pressure?
101kPa
What are the units for pressure?
- Pascals (Pa)
- Nm⁻²
How does a gas exert a pressure on its container?
A gas consists of molecules in constant random motion. When a molecule collides with a surface, it undergoes a momentum change as it reverses direction. By Newton’s second and third laws the surface therefore experiences a force from the colliding molecule. The pressure exerted by the gas is equal to the total force exerted by the molecules on a unit area of the surface.
What are the 5 assumptons about ideal gases and kinetic theory?
- The gas contains a very large number of atoms or molecules moving in random directions with random speeds
- The atoms or molecules of the gas occupy a negligible volume compared with the volume of the gas
- The collisions of atoms or molecules with each other and the container walls are perfectly elastic - there is no loss in kinetic energy
- The time of collisions between the atoms or molecules is negligible compared to the time between the collisions
- Electrostatic forces between atoms or molecules are negligible except during collisions
What is Avogadro’s constant?
Avogadro’s constant, NA, is equal to the number of atoms in exactly 12g of the isotope carbon-12.
What is the numerical value of Avogadro’s constant?
6.02x10²³
What is the amount of substance?
The amount of substance is the quantity of a substance measured in moles, where 1 mole (mol) = NA (6.02x10²³) particles of a substance
What is the equation for the number of molecules in a substance?
N = n x NA
Number of molecules = number of moles x Avogadro’s constant
What is the molar mass, M, of a substance?
The molar mass, M, of a substance is equal to the mass of one mole of the substance.
What is the equation for the mass of a substance?
m = Mn
Mass = Molar Mass x number of moles
When does a gas behave like an ideal gas?
Real gases at relatively low pressures and well above their condensation temperature begave like an ideal gas. Therefore, air at room temperature and pressure is a good approximation to an ideal gas.
What is boyle’s law?
For a fixed mass of gas at a constant temperature:
pV = constant
Therefore, when a gas changes pressure while undergoing a volume change:
p₁V₁ = p₂V₂
p ∝ 1/V
What is an ideal gas?
A gas that obeys Boyle’s law at all pressures, it is a model of a gas that includes assumptions that simplify the behaviour of real gases
When do gases not behave like ideal gases?
- At very high temperatures
- When they are cooled near their condensation point
What is the ideal gas pressure law?
For a fixed mass of gas at a constant volume:
p/T = constant
Therefore, when a gas changes pressure while undergoing a temperature change:
p₁/T₁ = p₂/T₂
p ∝ T
What is absolute zero?
Absolute zero is the lowest possible temperature, an object has minimum internal energy at absolute zero
What is Charles’ law?
For a fixed mass of gas at a constant pressure:
V/T = constant
Therefore, when a gas changes pressure while undergoing a volume change:
V₁/T₁ = V₂/T₂
V ∝ T
What is the volume of a gas at 0K?
zero volume
What happens if you combine Boyles law, Charles’ law, and the ideal pressure law?
You produce the ideal gas equation
What is the ideal gas equation?
pV = nRT
Pressure x Volume = number of moles x Ideal (Molar) Gas Constant x Temperature
What is the Ideal/Molar gas constant?
8.31 J K⁻¹ mol⁻¹
What are the units for pressure in the ideal gas equation?
Pascals (Pa)
What are the units for number of moles in the ideal gas equation?
mol
What are the units for temperature in the ideal gas equation?
Kelvin
What are the units for volume in the ideal gas equation?
metres cubed (m³)
How was the ideal gas equation derived?
By combining Boyles law, Charles’ law, and the ideal pressure law
What is the numerical value for the boltzmann constant?
1.38x10⁻²³ J K⁻¹
What is the ideal gas equation using the boltzmann constant?
pV = NkT
Pressure x Volume = number of molecules x Boltzmann Constant x Temperature
What is the boltzmann constant?
k = R/NA
Boltzmann constant = ideal (molar) gas constant / Avogadro’s constant
How can the ideal gas equation using the boltzmann constant be derived?
pV = nRT
pV = (N/NA) RT
pV = (R/NA) NT
pV = NkT
Boltzmann constant, k = R/NA
What is the kinetic theory of gases?
The kinetic theory of gases states that a gas consists of point molecules moving about in random motion
How does the kinetic theory explain how gas pressure changes with volume?
If the volume of the container is decreased:
* There will be a greater number of molecules gitting the inside of the container per second
* A greater force will be exerted
* Pressure will increase
How does the kinetic theory explain how gas pressure changes with temperature?
If the termperature of a container is increased:
* Molecules will be moving at greater speeds
* More molecules will be hitting the inside of the container per second and they will each exert a greater force
* A greater overall force will be exerted
* Pressure will increase
What is the molecular speed variation?
The molecules inside an ideal gas have a continuous spread of speeds. The speed of an individual molecule may change when it collides with another gas molecule but the distribution of speeds remain the same provided the gas temperature does not change
What is the effect of temperature change on the molecular speed variation?
T2 > T1
What is teh equation for Root Mean Square speed, cᵣₘₛ?
What is the kinetic theory equation?
N = number of molecules, m = mass of each molecule, V = volume, p = pressure
Cᵣₘₛ² = root mean square velocity squared
Show that the kinetic theory equation can be written as:
What is the equation for the average translational kinetic energy of a molecule in a gas?
Derive the equation for the average translational kinetic energy of a molecule in a gas?
What is translational kinetic energy?
Kinetic energy due to linear motion
What is Root Mean Square speed, cᵣₘₛ?
The square root of the mean square speed (of all the particles in a gas)
What is the maxwell-boltzmann distribution?
The distribution of the speeds of particles in a gas
What is the relationship between mean kinetic energy and temperature of a particle?
Direct proportion
What can be said about the kinetic energy and r.m.s speeds of different particles in a gas at a constant temperature?
- At a given temperature, each particle in the gas will have the same average kinetic energy regardless of their differences in masses.
- However, due to their differences in masses, they must have difference r.m.s speeds in order to have a constant kinetic energy
What is the internal energy of an ideal gas?
The internal energy of a gas is the sum of the kinetic and potential energies of the particles inside the gas. However, one of the assumptions of an ideal gas states that the electrostatic forces between particles is negligible except during collisions, therefore there is no electrical potential energy in an ideal gas. Therefore, all the internal energy in an ideal gas is in the form of the kinetic energy of the particles
What is the internal energy of a non-ideal gas?
The internal energy of a gas is the sum of the kinetic and potential energies of the particles inside the gas
What is “Nm” in this equation?
The mass of the entire gas (the mass of each individual molecule combined)
2740 ms⁻¹
483 ms⁻¹
Calculate the difference in r.m.s velocity of an Oxygen molecule and a Carbon Dioxide molecule at 0°C:
TOUGH QUESTION
~70ms⁻¹
