# Avagadro’s Law 1.4.4 1.4.5. Q – What can you tell me about gases?

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Q – What can you tell me about gases?

Let’s review KMT 1. 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 mv 2 (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-Lussac 6 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 Law How did he do that?  Avogadro’s Law Equal 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 10 23 particles (symbol = L or N A )  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 0 o C) & (Standard) Pressure (101.3 kPa or 1 atm)  1 mole of any gas takes up 22.4 dm 3 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 (C 2 H 5 OH) have?  25g/(24+5+16+1)g/mol=0.54mol  0.54mol x 22.4dm 3 /mol = 12 dm 3

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 P total = P A + P B + P C + … 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, ○ X a = n a / n total (moles of gas a / total gas moles) or ○ X a = P a / P total (partial pressure of gas a / total P)

Mole Fraction Problem  The partial pressure of CH 4 (g) is 0.175 atm and that of O 2 (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, ○ X CH4 = P CH4 / P total = 0.175/(0.175+0.250)=0.412 ○ X O2 = P O2 / P total = 0.250/(0.175+0.250)=0.588 Q – 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.  X H =1/(1+2)=0.3  X O =2/(1+2)=0.7  X H +X O =1

Class Problem 3  How many moles of argon are in 150 dm 3 container at STP if the mole fraction of argon is 0.75?

Class Problem 3 Answer  How many moles of argon are in 150 dm 3 container at STP if the mole fraction of argon is 0.75?  150dm 3 /(22.4dm 3 /mol)=6.7mol total  6.7mol x (0.75mol Ar/total mol)= 5.0 mol argon

Class Problem 4  How many dm 3 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 dm 3 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?  CH 4 + 2O 2  CO 2 + 2H 2 O  24L/2 = 12 L CH 4 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