avagadro’s law 1.4.4 1.4.5. q – what can you tell me about gases?
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Let’s review KMT1. Gases are composed of very small
particles, either molecules or individual atoms.
2. The gas particles are tiny compared to the distances between them.
3. The collisions with the inside container walls are what comprise the pressure of the gas.
4. The gas particles are assumed to neither attract nor repel each other. They may collide with each other, but if they do the collisions are assumed to be elastic. No kinetic energy (KE) is lost, only transferred from one gas molecule to another.
KE per molecule = 1/2 mv2
(m=mass of the individual molecule)
5. The average kinetic energy of the gas is proportional to the Kelvin temperature.
• KE per mol = 3/2 RT or…• KE = 3/2 RTn
• A gas that obeys these five postulates is called an ideal gas.
History Lesson 1
Joseph Louis Gay-Lussac6 December 1778 – 9 May 1850
Studied chemical reactions between gases Found that volumes of gases always
reacted in simple whole number ratios like:1L of hydrogen reacts with 1L of chlorine to
make 2L of product or… 1 + 1 = 2
2L of hydrogen reacts with 1L of oxygen to make 2L of steam○ 2 + 1 = 2?
History Lesson 2
Lorenzo Romano Amedeo Carlo Bernadette Avogadro di Quaregna e Cerreto August 1776, -9 July 1856
He attempted to explain Gay-Lussac’s LawHow did he do that?
Avogadro’s LawEqual volumes of gases at the same T & P
contain the same number of molecules.V n
History Lesson 2
Later, this relationship between gas volumes and molecules was used to develop the idea of the mole and the number of particles in one mole was named in his honor.
602000000000000000000000 6.02 x 1023 particles (symbol = L or NA)
So now, when working stoichiometry problems you can use: Grams Moles Liters of a gas
Molar Volume of a gas At STP
Standard Temperature (273K or 0oC)& (Standard) Pressure (101.3 kPa or 1
atm) 1 mole of any gas takes up 22.4
dm3 of space. Q – Which postulate of KMT
explains why this is? A – 2nd
Molar Volume Sample Problem
At STP, how much volume would 25g of evaporated ethanol (C2H5OH) have?
25g/(24+5+16+1)g/mol=0.54mol 0.54mol x 22.4dm3/mol = 12 dm3
Vapor Pressure The vapor pressure is an indication of a
liquid's evaporation rate. It relates to the tendency of particles to escape from the liquid (or a solid). A substance with a high vapor pressure at normal temperatures is often referred to as volatile.
Q – What is the relationship between the temperature of a liquid and its vapor pressure?
Yet another gas law…• Dalton’s Law of Partial Pressures
• Ptotal = PA + PB + PC + …• Meaning that in a closed container, the total
pressure exerted by gasses on the container is equal to the sum of the pressures of each individual gas in the container.
Q – Where have you heard of Dalton before?
A – The Dalton Model of atomic theory. It was his study of gasses and partial pressures that lead him to his atomic theory.
The Mole Fraction
This is defined as the ratio of the number of moles of a given component in a mixture to the total number of moles in the mixture and is usually noted as X.In a mixture of gas a and gas b,
○ Xa= na / n total (moles of gas a / total gas moles) or
○ Xa = Pa / P total (partial pressure of gas a / total P)
Mole Fraction Problem The partial pressure of CH4(g) is 0.175
atm and that of O2(g) is 0.250 atm in a mixture of the two gasses. What is the mole fraction of each gas in the mixture?In a mixture of gas a and gas b,
○ XCH4 = PCH4 / P total = 0.175/(0.175+0.250)=0.412
○ XO2 = PO2 / P total = 0.250/(0.175+0.250)=0.588Q – What should the sum of mole fractions
be?A - 1
Class Problem 1 You fill a 2L soda bottle with CO.
Your plan is to release it into Carlson’s office. How many moles would that have if you bottled it at STP?
Class Problem 1 Answer You fill a 2L soda bottle with CO.
Your plan is to release it into Carlson’s office. How many moles would that have it you bottled it at STP?
A – You’re not a very nice person, put it in Mr. Lewis’ office instead.
2L/(22.4L/mol)=0.09mol
Class Problem 2 Calculate the mole fractions of
hydrogen and oxygen in a container that has 2 moles of oxygen and 1 mole of hydrogen.
Class Problem 2 Answer Calculate the mole fraction of
hydrogen in a container that has 2 moles of oxygen and 1 mole of hydrogen.
XH=1/(1+2)=0.3 XO=2/(1+2)=0.7 XH+XO=1
Class Problem 3 How many moles of argon are in
150 dm3 container at STP if the mole fraction of argon is 0.75?
Class Problem 3 Answer How many moles of argon are in
150 dm3 container at STP if the mole fraction of argon is 0.75?
150dm3/(22.4dm3/mol)=6.7mol total
6.7mol x (0.75mol Ar/total mol)=5.0 mol argon
Class Problem 4 How many dm3 of methane gas
could you react if you only had 24 L of oxygen at the same temperature and pressure? How many moles would that be at STP? How many grams?
Class Problem 4 Answer How many dm3 of methane gas could
you react if you only had 24 L of oxygen at the same temperature and pressure? How many moles would that be at STP? How many grams?
CH4 + 2O2 CO2 + 2H2O 24L/2 = 12 L CH4 used 12L/22.4 = 0.53 mol 0.53 mol x 16 = 8.5 g
Class Problem 5 A metal tank contains three gases:
oxygen, helium, and nitrogen. If the partial pressures of the three gases in the tank are 35 atm of O2, 5 atm of N2, and 25 atm of He, what is the total pressure inside of the tank?
Class Problem 5 Answer A metal tank contains three gases:
oxygen, helium, and nitrogen. If the partial pressures of the three gases in the tank are 35 atm of O2, 5 atm of N2, and 25 atm of He, what is the total pressure inside of the tank?
65 atm
Class Problem 6 Blast furnaces give off many
unpleasant and unhealthy gases. If the total air pressure is 0.99 atm, the partial pressure of carbon dioxide is 0.05 atm, and the partial pressure of hydrogen sulfide is 0.02 atm, what is the partial pressure of the remaining air?
Class Problem 6 Answer Blast furnaces give off many
unpleasant and unhealthy gases. If the total air pressure is 0.99 atm, the partial pressure of carbon dioxide is 0.05 atm, and the partial pressure of hydrogen sulfide is 0.02 atm, what is the partial pressure of the remaining air?
0.92 atm
Class Problem 7 If the air from problem 2 contains
22% oxygen, what is the partial pressure of oxygen near a blast furnace?
Class Problem 7 answer If the air from problem 2 contains
22% oxygen, what is the partial pressure of oxygen near a blast furnace?
0.92 x 0.22 = 0.20 atm
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