10.3 Additional Gas laws Flashcards
Daltons Law of Partial Pressures
* Total pressure when you’ve got multiple gases inside a container is the sum of the partial pressures of individual gases
* Basically this means that each gas is responsible for a part of the pressure within the container
* It turns out the only thing that really matters is how much of taht gas you have relative to everything else
mole fraction = fraction of the total moles that a particular gas is reposnsible for.
Most gas is made up of mostly empty space. Doesnt matter how big or small the individual gas molecules are, the majority will always be empty space
Every gas has a chance to contribute equally to the pressure, just dpendent upon how much you have.
* meaning that if you have = amounts of 2 different gases they would contribute equally to the total overall pressure.
EX: 10 moles N2, 8 Moles O2, 2 Moles CO2
* So that means that 1/2 the partial pressure is coming from the 10 moles of N2
* O2 is responsible for 8/20 of the total moles, so its responsible for 40% of the total pressure
* CO2 = 10% of the total pressure
So the reason the individual molecule size seems to be irrevent is because theres so much empty space between molecules anyways, that the tiny difference is negligible
below is showing you the equation for how to calculate individual partial pressures within a sample
STP = standard temperature and pressure
* T = 273K
* P = 1ATM
* so these are the norms in STP
1 mol of a gas, at STP, thats behaving ideally, will have a volume of 22.4L
* memorize this
PV = nRT
* V = NRT/P
* if you plug in 1 mole for n, the gas constant, the 273K at STP and the 1ATM, you will get 22.4L
EX: We have 48.6g of Mg, reacting w/ excess HCl (thats your key that Mg is the limiting reagent), reacts to completion, what volume gas at STP is produced.
* so were trying to caculate a volume of H2 produced, meaning we’ll have to figure out the # of mols of gas produced first.
* so we would do the mol:mol ratio, and instead of converting it to g, or something we’ve done in the past, were going to use our conversion factor that 1mol = 22.4L (volume)
* Remember, it must be at STP to utilize 22.4L for volume
Density = mass/volume
For ideal gas we describe density as preesure* molar mass / RT
* so this is still = to m/v which is density
What is the density of helium gas at a pressure of 2.0atm and a temperature of 273k
density is an intensive property, meaning size of sample doesnt matter
* so we can essentially just choose sample sizes when it comes to calculating density becaue the density will be the same either way.
assumed 1 mol
Graham’s Law of Effusion
* Effusion = when a gas escapes through a narrow slit or hole.
We have a balloon below that has = #’s of O2 and H2 in it.
Graham’s law gives us rates of effusion
* The rate of how fast 1 gas effuses compared to the rate at which the other gas effuses
The average kinetic E of a gas is dependent only on its temperature.
And as long as these 2 gases have been in the balloon the same amount of time, they will be at the same temperature.
* meaning they’ll have the same average kinetic energy
KE avg O2 = KE avg H2
* however, having the same KE doesnt actually mean they’re moving at the same speed
* they have different masses and velocity (KE = 1/2mv^2, meaning thye won’t have the same velocoity
* Think putting an engine of a car and putting it in a car, vs a semi truck, the velocity is going to be different (the both have the same amount of E, just one of them is bigger)
* so they have the same KE, but O2 is way larger, so its on average going to be moving much slower
* So on aevrage they have the same kinetic E, just not the same average velocity.
* as a result of the H2 molecules moving faster, they’re going to move out of the balloon faster.
can take the velocities and subsitute them for the rates of effusion (because one will leak out more quickly)
r = ratio of effusion (bigger one on top, H is ontop because it moves out quicker so will be more big)
so we dont know the rate of effusion for O or for H, we just know the ratio of them comapred to eachother. and H escapes 4 times faster
remember, density is something where size doesnt matter. meaning we can just pick mole amounts for these elements.
Im going to pick 1 mol
So the reason we can change n to m / M
* m = mass of same (its in grams)
* M = molar mass (g/mol) is because that grams/mol is essentially the same thing as dividing by 1 (its the molar mass) its essentially just to change the unit, but we don’t have to apply it to the other side because its just like dividing by 1, so it doesnt cahnge anything but the units
The goal in this equation is to isolate mass/volume because thats the equation for density.
so doing it this way we don’t actaully need the mass when we just plug into this equation
really whichever one had the highest molar mass has the highest density.
Thats the derivation
yeah that was a mess but the finish line is in sight
Im going to show both good ways to solve this
the trick is knowing even though they’re different gases they all contribute the same amount to the total pressure
*.I think this is because theres so much space between individual molecules, that the weight of the molecules is negligible, thereby they all contribute the same partial pressure amount (because its the space between them that does it?)
