Flashcards in Gases Deck (35)
Definition of a gas?
A fluid that expands to fill its container, gases are highly mobile and flow from regions of higher pressure to lower pressure, gases mix easily with other gases
At constant temperature the volume of a fixed amount of gas is reduced in proportion as the pressure increases ie if the pressure is double the volume of gas occupied is halved
P is proportional to 1/V
The volume is inversely proportional to pressure and vice versa
V is proportional to 1/P
At constant temperature the volume of a fixed amount of gas increase linearly with rising temperature, for a fixed amount of gas at constant pressure the linear relationship can be expressed as V is proportional to T, the volume of a fixed amount of gas at a constant pressure is proportional to the absolute temperature, if the absolute temperature doubles the volume occupied by the gas double
Equal volumes of gases at constant temperature and pressure contain equal numbers of molecules, for an amount of gas n at lower temperature and pressure this is equivalent to saying V is proportional to n, the volume depends only on the number of moles and not the nature of the gas
A gas whose properties exactly obey the ideal gas law is called an ideal gas, the ideal gas equation links all of the properties required to define the state of a gas and so is also called an equation of state, for many gases around atmospheric pressure and temperature the ideal gas equation describes their behaviour reasonable well and gases are usually assumed to behave ideally unless they are at high pressures or very low temperature
Units of pressure?
Pascal Pa 1Nm-2
Bar 1 x 10^5 Pa
Torr 1mmHg = 133.32Pa
Standard atmosphere atm 1.013 bar = 101325Pa = 760 Torr
Standard ambient temperature and pressure?
298.15 K or 25 degrees C
Why can two gases easily mix?
There is plenty of space between the molecules in a gas this means that when gases mix together the molecules can easily intermingle
What is the pressure of two gases mixing together - Daltons law?
Given the larger distances between them the molecules do not interact so each gas in the mixture exerts the same pressure as if it were the only substance in the container, therefore the total pressure is simply the sum of the two individual pressures this is daltons law the total pressure exerted by a mixture of gases is the sum of the partial pressure of each individual gas
What is the partial pressure?
Pressure that would be exerted if the gas were alone in the container
Equation for daltons law?
Total = pA + pB + pC
What is the mole fraction use for?
To describe the proportion of each component in a mixture the mole fraction of the component is used given by:
Xa = number of moles A/ total number of mole present
Units and components of mole fractions?
Note that the sum of the mole fractions for all the components in a mixture is 1, note also that the mole fraction has no units
For an ideal gas mole fraction and partial pressure?
For an ideal gas at constant V and T pA is proportional to nA so for a component A in a mixture of gases: Pa/Ptotal = nA/ntotal = Xa
and the partial pressure of gas A is given by:
pA = XaPtotal
this means you can work out the partial pressures in a mixture of gases if you know the molar composition of the mixture and the total pressure
What is the kinetic model of gases?
Gas consists of molecules that are in constant random motion in all directions throughout the container
The molecules collide with each other and walls of the container, the steady pressure exerted by the gas in the container walls is explained interns of the collisions of the gas molecules with the walls, kinetic energy of a molecules with mass m and speed s is equal to EKE = 1/2ms^2 thus a molecules with a higher mass has greater kinetic energy than one with a lower mass moving at the same speed, alternatively for two molecules of the same mass the one moving faster has higher kinetic energy, the mean kinetic energy of the molecules in a gas is directly proportional to the absolute temperature so the molecules most faster when the gas is hotter
Assumptions in the kinetic model?
The gas molecules have negligible size compound with the container they are treated as point masses
Collisions between the molecules and the container walls are elastic so that here is no energy loss or gain on collision
The molecules do not interact with each other
The size of the molecules is very much smaller than the total volume occupied by the gas
What is wrong with the assumption that the molecules do not interact with each other?
Most molecules do interact however these interactions are significant only when the molecules are very close together at the relatively large intermolecular distances in a gas the assumption of negligible interactions is quite reasonable
What is pressure a result of?
Defined as force per unit area, in a gas the force is equal to the rate of change of momentum of molecules when they collide with the container walls, pressure is exerted as a result of molecules colliding with the walls of the container, the pressure depends on how many molecules hit the walls of the container per second and the force they exert on the wall when they hit it which depends on how fast they are moving
Maxwell Boltzmann distribution?
Maximum value on the curve represents the most probable value of the speed that is the one that occurs most often
What is the Maxwell Boltzmann distribution affected by?
The molar mass of the gas and its temperature, for a gas with high molar mass there is a narrow spread of speeds distributed around a relatively low speed, gases with lower molar masses have a significant fraction of their molecule move with speeds close to this most probably value, at high temperatures there is a much broader range of speeds
The process by which gas molecules pass through a small hole eg a pore in a membrane
Rate of effusion?
At a given temperature and gas pressure the rate of effusion is the number of molecules passing's through the hole per second is inversely proportional to the square root of the molar mass (1/M^1/2), this is known as Grahams law
Gases with different molar masses will therefore effuse at different rates a gas with a low molar mass effuses faster than a gas with a higher molar mass
Rate of diffusion?
Depends on the movement of molecules, diffusion occurs when two or more gases come into contact and mix, there are large spaces between the molecules so they can easily mix, the only impediment to mixing is the collisions between the molecules and this means that mixing does not occur instantaneously but takes some time, the time taken for gases to mix depends on the speed of the molecules and on the frequency of intermediate collisions, it thus depends on the temperature, molar masses, and the pressure of the gas, the higher the pressure the more frequent the collisions
What is the collision frequency?
The mean number of collisions that a molecules undergoes per second, the number of collisions that a molecules will undergo in 1 seconds depend on the distance that it moves and the number of gas molecules per unit volume, in a give time period a molecule will collide with any other molecules whose centre lies within a cylinder with cross sectional area
How will a gas move?
It is characteristic of gases that their molecules move a large distance between collisions compared with their size this is very different from the situation in solids and liquids
Gas molecules undergo a huge number of collisions the molecules move in all directions at random and undergo many changes in direction, this is the origin of the random motion of dust or other particles suspended in gas known as Brownian motion, the dust particles have no intrinsic motion but they move and change dimension under the constant random bombardment of gas molecules
Why do gases diffuse slowly?
Under normal pressures gas molecules undergo many more collisions with each other than they do with the walls of the container this means that despite the molecules moving with high speed, gases diffuse quite slowly because they have a long way to travel on their random route
What does the med free path depend on?
Conditions, the mean free path decreases at higher pressure, at a pressure of 1 atm the molecule travels twice the distance, this is because there are more molecules in a given volume at high pressure, at low pressure the mean free path is several metres
Why is the assumption that the size of the molecule is negligible not correct?
It is a good approximation when there are large distances between the molecules compared with their sizes, in other words at low pressures. At high pressure the size of the molecule matters because they occupy a significant proportion of the volume so there is less space available to move around it