Properties of Gases Flashcards
How do you calculate the mean, square mean, and mode of a maxwell-boltzmann graph?
Integrate the equation given from 0 to infinity (usually with scale factor so speeds), multiplied by v for mean, and v squared for square mean
Its easier to integrate with alpha first, then substitute the values for alpha
Differentiate and equate to 0 for the turning point point for the mode
What are gases?
One of the three states of matters, which expand to fill its container unless subject to an external force
What are the two types of properties gases possess with an example?
Intensive: constant throughout a system in equilibrium regardless of size e.g temperature, pressure
Extensive: dependent on the size of the system
e.g KE, entropy
How do you calculate the mean nearest neighbour distance between particles?
Volume/N of particles in volume
Cube root this for the distance
e.g for a gas under standard conditions, (24/1000) / Avagadro’s
Cube root
How has the ideal gas equation been derived? When is it valid?
From 4 laws:
- Boyle’s: pV=constant
- Charles’: volume proportional to temp
- : pressure proportional to temp
- : volume proportional to moles
pV=nRT
Exhibited at low densities, when the gas molecules are far enough apart that they can be considered to not interact with each other
How can you estimate the mass of the atmosphere?
Imagine a 1m² column of atmosphere, at sea level so p=10⁵ Pa
p=F/a
so force= 10⁵ N
f=ma
assuming a=10
Mass of 1m² =10⁴ kg
Surface area= 4πr², of earth r=6400km
multiply by 10⁴ kg
How can the differential equation for gas pressure at different heights be derived?
How can the pressure of a liquid be calculated and why is this valid?
How can the pressure of a gas at different heights be calculated from the differential equation?
Remember M is in g/mol in periodic table, but needs to be Kg/mol for the equation
What is the compressibility factor? When do deviations for the ideal gas law occur and why?
Z= pv/ nRT
Should be 1 for ideal
If >1 repulsive interactions, or impossibility of two molecules overlapping, high temps and light gases
If <1 attractive forces, usually larger compounds, low temps, high pressures
Arising from intermolecular forces, and attractive/repulsive dependent on potential graph curve
Starting from the model of pressure in a box, how has the relation being temperature and average kinetic energy been derived?
What are the equations linking pressure and mean square speed? And average kinetic energy?
How can the relationship between average kinetic energy and temperature be proven from a thermodynamic viewpoint?
What is the principle of equipartition theorem?
Each quadratic degree of freedom contributes 1/2KbT (if per molecule) of 1/2 RT (per mol) to the internal energy (U)
i.e Each x,y,z or the rotation/translations a molecule can have will contribute 1/2KbT to U
How can the heat capacities for monatomic, diatomic, and polyatomic molecules?
Cv= derivative of U
Cp= Cv + R
What are the conditions of the function required to represent the Maxwell-Boltzmann distribution?
The velocity x, y, and z components are independent and equally distributed
i.e p(x,y,z) = p(x)p(y)p(z)
And so changing one component has no impact on the others
The velocity distribution is spherical, as the gas has the same properties in x,y,z directions
v2= vx2+vy2+vz2
How can N1 and alpha be found with the M-B distribution?
How do the 1d and 3d M-B graphs differ? And can you convert these velocities to speeds?
3d is the cube of 1d
Many velocities have the same speed, and so by multiplying by 4πv² the graph is transformed
Assumes all velocities lie on sphere with radius v
What happens to the speeds of the M-B distribution at high and low velocities? What experimental evidence support the distribution?
Small v, 4πv² dominates, quadratic in nature with a turning point
At larger v, the exponential decay term dominates
Beam through rotating sphere with a slit, time to detect and intensities plotted
Or time for particles to fall under gravity
How do you find the root square mean of the M-B distribution? Why does the mean, mode and rms differ?
Use equipartition
so KbT=m ms(x)
ms(x) = KbT/m
Mean>mode as positively skewed
rms>mean as the average difference in the mean and point > 0
How can you derive the equation for effusion?
and M-B= 2x infinity to 0 as left and right for mean speed
What is Graham’s law of effusion?
The effusion rate is inversely proportional to the square root of the relative molecular masses
How do you derive the rate of collision of a gas?
How do you derive the equation for mean free path?
How do you calculate the rate constants for homogeneous collisions?How do you calculate the rate constants for heterogeneous collisions?
