Chapter 20 - Gases Flashcards
What does Boyle’s law state?
- For a fixed mass of gas at a constant temperature:
PV = constant
where p = gas pressure and v = volume
Why would you have to wait a few seconds to measure
the new volume in Boyle’s law experiment?
Work has been done on the gas, which increases temperature. We want to have constant temperature, so wait for thermal equilibrium to be reached
What does Charles law state?
V/T = constant
For a fixed mass of gas at constant pressure
How do you calculate the work done to keep the pressure constant when there is a change to the volume of a gas?
Work done = p x change in v
What is an isobaric change?
Any change at constant pressure
What does the pressure law state?
P/T = constant
for fixed mass of gas at constant volume
What is brownian motion?
Random movement (range of speeds in no preferred direction) of particles due to being bombarded unevenly and randomly by individual molecules
What experiment shows Brownian motion? (not required practical)
Observing smoke particles with a microscope when a beam of light is directed through
What is avogadro constant? Give the value
N(A) - Number of atoms in exactly 12g of carbon isotope C-12.
- 6.023x10^23
How many molecules of a substance is in 1 mole?
6.023 x 10^23
What is an ideal gas?
Gas that obeys Boyle’s law
Give the ideal gas equation
Pv = nRT
What is the value for the Boltzmann constant (K)?
1.38 x 10^-23 JK^-1
Whats the equation for boltzmann constant (K)?
K = R/Na
Give the ideal gas equations, including boltzmann constant
Pv = NkT N = number of particles
What is the root mean square speed?
Crms = (C1^2 +C2^2 +…+CN^2/N) ^1/2
What is the kinetic theory equation?
Pv = 1/3 Nm(Crms)^2
What are some assumptions that have to be made about an ideal gas to derive the kinetic theory equation?
- ) The molecules are point molecules - volume of each molecules is negligible compared with the volume of the gas.
- ) Do not attract each other.
- ) Move in continual random motion
- ) Elastic collisions
- ) Collisions with container surface much shorter duration than the time between impacts. Collision time negligible
- ) Newton’s laws apply
- ) Negligible intermolecular forces
- ) Molecules are identical
- ) Large number of particles
Derive the kinetic theory equation
C1^2 = u1^2 + v1^2 +w1^2 (perpendicular components of velocity)
distance to opposite face and back = 2lx
time between successive impacts = 2lx/u1
force = change in p/t
= -2mu1/2lx/u1 = -mu1^2/lx
P = mu1^2/lxlylz. lylz = area, so: mu1^2/v
P = mu1^2/v +mu2^2/v + mu3^2/v + ….+ muN^2/v
= m/v( u1^2 + u2^2 + u3^2+…+ uN^2) = Nmu*^2/v where u* is mean u and = u1^2 + u2^2+…. +uN^2/N
P = Nm/3v(u*^2+v*^2+w*^2)
Crms^2 = u*^2+v*^2+w*^2, therefore p = Nm/3v Crms^2 or Pv = 1/3NmCrms^2
What is the internal energy equal to an ideal gas?
Kinetic energy
What is the equation for the mean kinetic energy of a molecule of an ideal gas?
3/2kT
= 1/2m(Crms^2)
= 3RT/2Na
how do you work out the internal energy of n moles of an ideal gas?
3/2 nRT
What is thermal equilibrium?
When 2 bodies are the same temperature so there’s no net flow of thermal energy between them.
What happens when hot gas is mixed with cool gas - eventually reaching thermal equilibrium?
(Kinetic) energy exchanged in molecular collisions until average kinetic energy of all molecules is the same
Whats the equation for total kinetic energy in one mole of an ideal gas?
3/2RT (as k = R/Na)
When the temperature of an ideal gas in a sealed container falls, what happens to the pressure of the gas?
Decreases as frequency of collsions decreases, so rate of change of momentum decreases.
Or using PV = nRT: if T decreases then as V, n and R are constants, P must decrease
How is pressure exerted by a gas on the walls of a container?
Gas molecules move in random motion and when the collide with the walls they exert a force on the wall and the wall exerts an equal one back (Newton’s 3rd law). The molecules momentum changes and therefore creates pressure.
Use kinetic theory of gases to explain why: pressure exerted by an ideal gas increases when it is heated at constant volume
Collision frequency (with wall) increases and rate of momentum change per collision increases. Greater force because more momentum change per seeond, meaning greater pressure
