Grade 11 chemistry-Review Package
States of matter
Matter can exist in at least 3 phases (there are many more than three, but we are not concerned with that at the moment): Solid, liquid or gas. If we were to describe the states of matter in terms of what is happening to the molecules, we would end up with the following:
SOLID LIQUID GAS
Solid: In the solid state, the molecules are tightly packed and move very little.
Type of molecular movement: vibration
A solid has a specific volume and a specific shape
Liquid: In a liquid, the molecules are less tightly packed and have more freedom of movement
Type of molecular movement: vibration and rotation
A liquid has a specific volume, but not a specific shape
Gas: In a gas, the molecules have a lot of movement, and spread out to fill the container they are in
Type of molecular movement: vibration, rotation, and translation
A gas has a no specific volume or specific shape. It spreads out to fill the container it is in.
Phase changes
Matter can undergo phase changes when energy (in the form of heat) is added or removed from the system. You can think of water: Ice, solid, melts to liquid when heated, and evaporates to vapor when heated further. Conversely, water vapor condenses when cooled to become liquid which then freezes to ice upon further cooling.
When energy is added to the system, the molecules become excited and they gain more movement. When energy is removed (cooling), the molecules slow down their movement until they reach the solid state and merely vibrate.
In this chapter, we are concentrating on the gas phase. But why should we care?
Gases are very important to our daily lives, from the air we breathe to their technological applications, to the safety in our environment. In order to be able to answer questions on these important issues, one must understand how molecules in this phase behave. To that end, we will consider the kinetic molecular theory of gases.
The kinetic molecular theory of gases
The word KINETIC derived from the Greek word kineos meaning movement, motion. So what we are talking about is the movement of gas molecules. By understanding how they behave, we can explain many observations as you will see later on.
There are six postulates (principles) to this theory:
1. Gases are made of molecules (duh! but needs to be said)
2. The distances between the gas molecules are much greater than the dimensions of the molecules themselves. In other words, we can consider them to be points/dots and not worry about their masses, which are negligible compared to the distances between them.
3. Gas molecules are in perpetual motion and can displace themselves in any direction.
4. Kinetic energy is proportional to temperature: the higher the temperature, the more kinetic energy the molecules have, the more they move. On the other hand, the lower the temperature, the less kinetic energyà less molecular movement.
5. Gas molecules collide with each other and with the containers that they are in.
6. These collisions are perfectly elastic, meaning that molecules which have collided with each other move off with the same amount of energy, nothing is lost, no molecules slow down.
Some vocabulary relating to gases….
Expansion: this occurs when a gas moves outwards, it is the result of an increase in the space between the gas molecules.
Compression: This is when the distance between the gas molecules is decreased.
Diffusion: This is when a gas is released and begins to mix with another gas. For example, when ammonia gas (a very strong smelling gas) is released, after a short time, everyone in the room could smell it; this is the time it takes for the gas to mix with the surrounding air.
Effusion: occurs when a gas escapes through a small hole.
Pressure
Pressure is defined as the force applied per unit area. Since force is measured in Newtons (N) and area, in m2, the SI unit for pressure is N/m2.
1 N/m2 = 1 Pascal or P
The atmosphere exerts pressure on everything around us. The pressure of the atmosphere is 101325Pa. Pressure can be measured in many different units:
Atmospheric pressure: 1 atm = 760mm Hg (millimeter mercury)
= 760 Torr (in honor of Torricelli)
= 101 325 Pa
= 101.325 KPa
Note: atm stands for atmosphere so 1atm is 1 atmosphere of pressure.
Although the stories were awesomely cool, and thoroughly researched (yeah right), you are not responsible for the history on how atmospheric pressure was discovered.
If you think of pressure in terms of the kinetic molecular theory, the pressure exerted by a gas is due to the molecules of the gas colliding with the sides of the contained. Compress the gas and you end up forcing more of these types of collisions, causing an increase in pressure, as shown below:
In second case, when weights are added to the moveable lid of the container, the gas molecules are moved closer together and the chances of them hitting the side of the container increase which results in the higher pressure.
When looking at gases, we can describe them in terms of some of their properties. Namely:
Pressure (P)
Volume occupied by the gas (V)
Temperature (T)
Quantity of molecules, number of moles (n)
It is useful to describe a gas in terms of these 4 characteristics.
Several scientists made some interesting discoveries about these 4 characteristics with respect to how they relate to one another. They are known as the Gas Laws. We will look at these laws individually, and how they relate to one another in the combined gas law.
Ideal gas
What is an ideal gas? This is a gas that can be described by the kinetic molecular theory. Although real gases do not all behave this way, they can simulate ideal gases at high temperatures and pressure. Also, knowing how ideal gases behave, corrections for molecular attractions can be made to predict the behavior of real gases. The gas laws for this course relate to ideal gases only.
Temperature:
There are many different scales of temperature. You are familiar with the Celsius (˚C) scale. In science, we often use the Kelvin scale. It came about for more mathematical reasons, which were elegantly explained in class. However, for your purposes, all you need to concern yourself with is that any time you use temperature for the gas laws, make sure that it is expressed in degrees Kelvin (K).
To convert from one to the other:
TK = T˚C + 273
STP (Standard Temperature and Pressure)
Often when talking about gases, they are analyzed at STP. That means that the gas is at 0˚C and 1 atm pressure.
1. Boyle’s Law (AKA Boyle-Marriotte Law)
Statement: In a closed system at constant temperature, where the number of molecules remains constant, the pressure and volume of a gas are inversely proportional, meaning as one gets bigger, the other gets smaller.
Graphically:
V V
P 1/P
Equation: PV= constant
or
P1V1=P2V2
Kinetic molecular theory explanation: When the volume is decreased, the number of collisions between gas molecules is increased leading to an increase in pressure. On the other hand, when increasing the volume, there are less chances for molecules to collide with each other or with the container and therefore there is less pressure.
Example:
2L of gas at 0.5atm pressure is compressed to 1.2L. What is the new pressure?
V1=2L
P1=0.5atm
V2=1.2L
P2=?
P1V1=P2V2à V2=P1V1/P2
= (1atm)(2L)/(1.2L)
= 1.67atm
Does this make sense? Yes, because if the volume was decreased, we expect the pressure to increase, which is what we found.
Caution! Be sure that both volumes and pressures are in the same units!!!
2. Charles’ Law
Statement: In a closed system at constant pressure, where the number of molecules remains constant, the temperature and volume of a gas are directly proportional, meaning if one is increased, the other will increase by the same factor.
Graphically:
V
T (K)
Equation: V/T= constant
or
V1/T1=V2/T2
Kinetic molecular theory explanation: If the temperature of a gas is increased, the gas molecules gain energy and increase their movement. This, in turns, increases the movement of the gas molecules causing them to translate more and therefore the gas will expand. Conversely, if a gas is cooled, the molecules slow down and the intermolecular distances decrease, leading to a decrease in volume.
Example:
Find the volume of a gas at 32°C., if at 18°C the gas occupied a volume of 152 mL.
V1=152 ml
T1=18 °C = 291 K
V2=?
T2=32°C = 305 K
V1/T1=V2/T2 à V2=V1T2/T1
= (152ml)(305 K)/(291)
= 159 ml
Does this make sense? Yes, because if the temperature is increased, we expect the gas to expand, which would give an increase in volume.
Caution! Temperature must always be in KELVIN!!
3. Gay-Lussac’s Law
Statement: In a closed system at constant volume, where the number of molecules remains constant, the temperature and pressure of a gas are directly proportional, meaning if one is increased, the other will increase by the same factor.
Graphically:
P
T (K)
Equation: P/T= constant
or
P1/T1=P2/T2
Kinetic molecular theory explanation: If the temperature of a gas is increased, the gas molecules gain energy and increase their movement, causing an increase in the likelihood of intermolecular collisions as well as collisions with the container holding the gas. These increases in collisions result in increases in the pressure of the gas.
Example:
A cylinder contains a gas which has a pressure of 125kPa at a temperature of 200 K. Find the temperature of the gas which has a pressure of 100 kPa.
P1=125 kPa
T1=200K
T2=?
P2=100kPa
P1/T1=P2/T2 à T2=P2T1/P1
= (100kPa)(200 K)/(125kPa)
= 160K
Does this make sense? Yes, because the temperature is decreased, from 200K to 160K, then we expect the pressure to decrease as well.
Caution! Temperature must always be in KELVIN!!
Avogadro’s hypothesis
Cool guy, heck, they named the mole after him!
Anyhoo… he observed the following:
“Equal volumes of gases measured at the same temperature and pressure contain an equal number of moles”. (I am paraphrasing, he said it in Italian!)
So, basically, if P, V, and T are constant, then n is the same (makes sense when you already know about the combined gas law…think about it).
So if I have a balloon filled with oxygen (O2) and another, identical one filled with Helium (He), at the same temperature and pressure and volume, then: moles O2= moles He.
Of course, this can also be expressed as: V1/n1 = V2/n2
About the mole….did you know that 1 mole of gas at STP occupies 22.4L? And it doesn’t even matter what type of gas it is!
At STP, 1 mole NH3(g) or 1 mole CO2(g) or 1 mole Ne(g) all have a volume of 22.4L.
Stoichiometry is the gas phase:
During a gaseous reaction, meaning that all reactants and products are in the gas phase, there is a relationship between the volumes of the reactants and the volumes of the products, as shown below.
Given:
2H2(g) + O2(g) à 2H2O(g)
If you start with 40ml H2, you will need 20ml O2 and get 40ml H2O.
The combined gas law
Putting it all together, we have already seen that:
V T (means proportional to)
V 1/P
V n
So, V T x 1/P x n
To relate volume and T,P, n with an equal sign, you need a constant.
This constant, called the Ideal Gas Constant, is denoted by R, where
R= 8.31 L·KPa/K·mol
or
R=0.082 L·atm/K·mol
Or
R = 62.36 L·mmHg/K·mol (try to figure this one out on your own)
Using the above constant, we get
PV = nRT
Where pressure is in the same units found in the gas constant used, temperature is in Kelvin, n is in moles, and V is in liters.
And now, knowing any 3 of the 4 characteristics of a gas, using the combined gas law, you can find the missing value.
Of course, because R is a constant that means that:
PV/nT=constant
And so: P1V1/n1T1= P2V2/n2T2
You can actually use the above to derive any of the gas laws. For example, Boyle’s law, which states that if you keep the temperature and number of moles constant, P and T are inversely proportional. Well, n1=n2, and T1=T2, when you cross multiply, they will cancel out, leaving you with P1V1=P2V2.
Example: What is the volume occupied by 4mol of methane gas at 18°C and 1.4atm pressure?
n=4mol PV=nRTà V = nRT/P
T=18°C = 291K = (4 mol)( 0.082 L·atm/K·mol)(291K)/(1.4atm)
P=1.40 atm = 68L
V=?
Make sure when using the formula that all your units cancel out, otherwise, you made a mistake!!
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