General Chemistry Chapter 9 Gases PPT
Reactions involving Gas: In reactions involving reactants or products, we often specify the quantity of a gas in terms of its volume at a given temperature and pressure
- As we have seen, stoichiometry involves relationships between amounts in moles - For stoichiometric calculations involving gases, we can use the ideal gas law to determine the amounts in moles from the volumes, or to determine the volumes from the amounts in moles n= PV/RT V= nRT/P
Boyle's Law The pressure of a gas is inversely proportional to its volume. As P increases, V decreases by the same factor. P × V = constant P1 × V1 = P2 × V2
- Constant T and amount of gas. - Graph P vs. V is a curve. - Graph P vs. 1/V is a straight line.
The sum of the partial pressures of all the gases in the mixture equals the total pressure:
- Dalton's law of partial pressures - Gases behave independently Ptotal = Pa + Pb + Pc +..........
Charles' Law Equation
- Kelvin T = Celsius T + 273 - V = constant × T (if T is measured in kelvins) - V1/T1=V2/T2
We can calculate the partial pressure of a gas if
- we know what fraction of the mixture it composes and the total pressure, or - we know the number of moles of the gas in a container of known volume and temperature.
The pressure of a gas depends on several factors:
-Number of gas particles in a given volume -Volume of the container -Average speed of the gas particles -Units of P : atm, mmHg, torr, psi, kPa
Real Gases
A plot of PV/RT versus P for 1 mole of a gas shows the difference between real and ideal gases It reveals a curve that shows the PV/RT ratio for a real gas is generally lower than ideal for "low" pressures—meaning that the most important factor is the intermolecular attractions It reveals a curve that shows the PV/RT ratio for a real gas is generally higher than ideal for "high" pressures—meaning that the most important factor is the molecular volume
Boyle's Law
A principle that describes the relationship between the pressure and volume of a gas at constant temperature (as pressure increases, volume decreases)
Boyle's Law Equation
As P increases, V decreases by the same factor P × V = constant P1 × V1 = P2 × V2
Molecular interpretation of Boyle's Law
As the volume of a gas sample decreases, gas molecules collide with surrounding surfaces more frequently, resulting in greater pressure
The average kinetic energy of the gas particles is directly proportional to the Kelvin temperature
As you raise the temperature of the gas, the average speed of the particles increases. But not all the gas particles are moving at the same speed!
The Effect of the Finite Volume of Gas Particles
At low pressures, the molar volume of argon is nearly identical to that of an ideal gas But as the pressure increases, the molar volume of argon becomes greater than that of an ideal gas - At the higher pressures, the argon atoms themselves occupy a significant portion of the gas volume, making the actual volume greater than that predicted by the ideal gas law
The Effect of Intermolecular Attractions
At lower temperatures, the gas atoms spend more time interacting with each other and less time colliding with the walls, making the actual pressure less than that predicted by the ideal gas law
When the amount of gas in a sample increases at constant temperature and pressure, its volume increases in direct proportion because the greater number of gas particles fill more space. Which law is this?
Avogadro's Law
Gas Laws Explained - Avogadro's Law
Avogadro's law states that the volume of a gas is directly proportional to the number of gas molecules Increasing the number of gas molecules causes more of them to hit the wall at the same time. To keep the pressure constant, the volume must then increase
Real Gas Behavior
Because real molecules take up space, the molar volume of a real gas is larger than predicted by the ideal gas law at high pressures
The Nature of Pressure
Because the gas particles are constantly moving, they strike the sides of the container with a force The result of many particles in a gas sample exerting forces on the surfaces around them is a constant pressure P= F/A
Gas Laws Explained - Boyle's Law
Boyle's law states that the volume of a gas is inversely proportional to the pressure - Decreasing the volume forces the molecules into a smaller space More molecules will collide with the container at any one instant, increasing the pressure
P total is the total pressure and Pa, Pb, Pc, . . . are the partial pressures of the components. This relationship is known as
Dalton's law of partial pressures Ptotal= Pa + Pb + Pc+....... = na RT/V + nb RT/V + nc RT/V +...... = (na + nb + nc +........) RT/V = (ntotal) RT/V
Gas Laws Explained - Dalton's Law
Dalton's law: The total pressure of a gas mixture is the sum of the partial pressures According to kinetic molecular theory, the particles have negligible size, and they do not interact - Particles of different masses have the same average kinetic energy at a given temperature Because the average kinetic energy is the same, the total pressure of the collisions is the same
Density of a Gas at STP equation
Density = molar mass/ molar volume
Example of Mixture of Gas
Dry air, for example, is a mixture containing nitrogen, oxygen, argon, carbon dioxide, and a few other gases in trace amounts
Charles's Law - Molecular View
If we move a balloon from an ice water bath to a boiling water bath, its volume expands as the gas particles within the balloon move faster (due to the increased temperature) and collectively occupy more space
Charles's Law As temperature increases volume
Increases
Robert Boyle and Robert Hooke used a _______ to measure the volume of a sample of gas at different pressures
J-tube
A low concentration of gas particles results in _________ pressure. A high concentration of gas particles results in _______ pressure.
Low; high
Many gas samples are not pure but are
Mixtures of gases
Molar Mass of a Gas Equation
Molar Mass (M) = mass (m) / moles (n)
Molar mass of a gas
One of the methods chemists use to determine the molar mass of an unknown substance is to heat a weighed sample until it becomes a gas; measure the temperature, pressure, and volume; and then use the ideal gas law
Boyle's Law Example A woman has an initial lung volume of 2.75 L, which is filled with air at an atmospheric pressure of 1.02 atm. If her lung volume increases to 3.25 L (without her inhaling any additional air), what is the new pressure in her lungs?
P1V1 = P2V2 P2 = V1/V2 P1 2.75L/3.25L 102atm =0.863 atm
Formula for Pressure
P=F/A *Force/Area
Mole fraction Example: For gases, the mole fraction of a component is equivalent to its percent by volume divided by 100%. Nitrogen has a 78% composition of air; find its partial pressure.
PN2 = 0.78 x 1.00 atm = 0.78 atm Ptotal = PN2 + PO2 + PAr Ptotal= 0.78 atm + 0.21 atm + 0.01 atm = 1.00 atm
Ideal Gas Law Equation
PV=nRT *V= RnT/P
Mole fraction equation
Pa / Ptotal = na / ntotal Pa = na/ntotal Ptotal =XaPtotal *Pa=XaPtotal
Mole Fraction The ratio of the partial pressure a single gas contributes and total pressure is equal to the mole fraction
Pa / Ptotal = na(RT/V) / ntotal (RT/V) = na/ntotal *Xa= na/ntotal
Dalton's Law of Partial Pressures: For a multicomponent gas mixture, we calculate the partial pressure of each component from the ideal gas law and the number of moles of that component (nn) as follows:
Pa= na RT/V , Pb= nb RT/V, Pc=nc RT/V
Gases are composed of?
Particles that are moving around very fast in their container(s)
We can calculate partial pressure from the ideal gas law by assuming that each gas component acts independently
Pn= nn RT/V
Collisions with surfaces create
Pressure
Dalton's Law of Partial Pressures: The sum of the partial pressures of the components in a gas mixture equals the total pressure:
Ptotal= Pa+Pb+Pc+........
Ideal Gas Law By combining the gas laws, we can write a general equation
R is called the gas constant. The value of R depends on the units of P and V. - We will use PV=nRT and convert P to atm and V to liters The other gas laws are found in the ideal gas law if two variables are kept constant
Real Gases - Why is it the "Ideal" gas law?
Real gases often do not behave like ideal gases at high pressure or low temperature Ideal gas laws assume 1. no attractions between gas molecules 2. gas molecules do not take up space Based on the kinetic molecular theory At low temperatures and high pressures these assumptions are not valid
Kinetic Molecular Theory and the Ideal of Gas Law
The kinetic molecular theory is a quantitative model that implies PV = nRT The pressure on a wall of a container occupied by particles in constant motion is the total force on the wall (due to the collisions) divided by the area of the wall
Mole Fraction
The partial pressure of a component in a gaseous mixture is its mole fraction multiplied by the total pressure
Ideal Gas Law
The relationships that we have discussed so far can be combined into a single law that encompasses all of them
Molar Volume
The volume occupied by one mole of a substance is its molar volume at STP (T =273 K or 0 °C and P = 1atm)
Charles Law: Temperature and Volume The volume of a fixed amount of gas at a constant pressure increases linearly with increasing temperature in kelvins:
The volume of a gas increases with increasing temperature
Mixtures of Gas
Therefore, in certain applications, the mixture can be thought of as one gas - Even though air is a mixture, we can measure the pressure, volume, and temperature of air as if it were a pure substance - We can calculate the total moles of molecules in an air sample, knowing P, V, and T, even though they are different molecules
What happens to the particles in gases?
These particles move in straight lines until they collide with either the container wall or another particle, and then they bounce off
Kinetic Molecular Theory The collision of one particle with another (or with the walls of its container) is completely elastic
This means that when two particles collide, they may exchange energy, but there is no overall loss of energy - Any kinetic energy lost by one particle is completely gained by the other
Manometers are
U-shaped tubes partially filled with a liquid that are connected to the gas sample on one side and open to the air on the other
Charles's Law Example A sample of gas has a volume of 2.80 L at an unknown temperature. When the sample is submerged in ice water at T = 0.00 ºC, its volume decreases to 2.57 L. What was its initial temperature (in K and in ºC)?
V1/T1=V2/T2 T1=V1/V2(T2) Before you substitute the numerical values to calculate T1, convert the temperature to kelvins (K). Remember, gas law problems must always be worked with Kelvin temperatures. T2(K) = 0.00 + 273.15 = 273.15 K Substitute T2 and the other given quantities to calculate T1. > 2.80L /2.57L (273.15K) =297.6 K Calculate T1 in ºC by subtracting 273.15 from the value in kelvins. T1(ºC) = 297.6 - 273.15 = 24 ºC
Avogadro's Law Equation
V=kn * Constant times n * Constant P & T
Molar Volume example:
V=nRT/P = 1.00 mol x 0.08206 L•atm/ mol•K x 273 K = 22.4 L
Avogandro's Law: Volume and Amount (Moles)
Volume is directly proportional to the number of gas molecules - V = constant × n - Constant P and T - More gas molecules = larger volume Equal volumes of gases contain equal numbers of molecules - The gas doesn't matter.
In Kinetic Molecular Theory, What happens to the gas particles?
When the moving gas particles hit another gas particle or the container, they do not stick, but they bounce off and continue moving in another direction There is a lot of empty space between the gas particles compared to the size of the particles
A snapshot of these particles in a gas will reveal that there is
a lot of empty space in the container
Charles's Law If the lines are extrapolated back to a volume of "0," they all show the same temperature, −273.15 °C = 0 K, called
absolute zero
Charles's Law The extrapolated lines cannot be measured experimentally because
all gases condense into liquids before -273.15 °C is reached
In Kinetic Molecular Theory, The particles of a gas (either atoms or molecules) ___________ and the attraction between particles is __________
are constantly moving; negligible
Avogadro's Law
as amount of gas increases, volume increases
Collecting Gases Gases are often collected by having them displace water from a container The problem is that,
because water evaporates, there is also water vapor in the collected gas
In the Kinetic Molecular Theory, a gas is modeled as a
collection of particles (either molecules or atoms, depending on the gas) in constant motion
A __________ is established between the pressures of the atmosphere and the gas.
competition
Density of a Gas at STP example: For example, the densities of helium and nitrogen gas at STP are as follows:
dHe = 4.00g/mol /22.4L/mol = 0.179g/L dN2 = 28.02g/mol / 22.4L/mol = 1.25g/L
The process of a collection of molecules spreading out from high concentration to low concentration is called
diffusion
The process by which a collection of molecules escapes through a small hole into a vacuum is called
effusion
Avogadro's Law (quizlet)
equal volumes of gases at the same temperature and pressure contain equal numbers of molecules
Properties of Gases
expansion, fluidity, low density, compressibility, diffusion and effusion
Ideal Gas Laws allows us to
find one of the variables if we know the other three
Pressure exerted by a gas is dependent on the number of
gas particles in a given volume
Pressure decreases with
increasing altitude
The number of gas particles in a given volume decreases with
increasing altitude
The four properties of gas are
interrelated—when one changes, it affects the others
Robert Boyle and Robert Hooke trapped a sample of air in the J-tube and added mercury to increase the pressure on the gas They observed an __________ between volume and pressure
inverse relationship Hence, an increase in one causes a decrease in the other
What is Gas Pressure?
is the force exerted per unit area by gas molecules as they strike the surfaces around them
The simplest model for the behavior of gases is the
kinetic molecular theory
The fewer the gas particles, the ________ the force per unit area and the _________ the pressure
lower; lower
The pressure of a gas trapped in a container can be measured with an instrument called a
manometer
Reactions Involving Gases: •When gases are at STP, use 1 mol = 22.4 L. •The pressures here could also be partial pressures •The general conceptual plan for these kinds of calculations is as follows:
mass A ---> amount A (in moles) ---> amount B (in moles) ---> mass B P, V, T of gas A ---> amount of A (in moles) ---> amount B (in moles) ---> P, V, T of gas B
The number of moles of a component in a mixture divided by the total number of moles in the mixture is the _________
mole fraction
The pressure of a single gas in a mixture of gases is called its
partial pressure
The pressure due to any individual component in a gas mixture is its
partial pressure (Pn)
Simple Gas Laws: There are four basic properties of a gas:
pressure (P), volume (V), temperature (T), and amount in moles (n)
The rates of diffusion and effusion of a gas are both related to its
rms average velocity For gases at the same temperature, this means that the rate of gas movement is inversely proportional to the square root of its molar mass
Just as a ball exerts a force when it bounces against a wall, a gaseous atom or molecule exerts a force when it collides with a
surface
Pressure
the amount of force exerted per unit area of a surface
Gas pressure is a result of
the constant movement of the gas molecules and their collisions with the surfaces around them
The difference in the liquid levels is a measure of the difference in pressure between
the gas and the atmosphere
Avogadro's Law: The volume of a gas sample increases linearly with
the number of moles of gas in the sample.
The simple gas laws describe
the relationships between pairs of these properties
Collecting Gases The partial pressure of the water vapor, called the _________, depends only on the temperature - You can use a table to find out the partial pressure of the water vapor in the gas you collect - If you collect a gas sample with a total pressure of 758.2 mmHg* at 25 °C, the partial pressure of the water vapor will be 23.78 mmHg, so the partial pressure of the dry gas will be 734.4 mmHg
vapor pressure
Standard conditions when working with gases
•Because the volume of a gas varies with pressure and temperature, chemists have agreed on a set of conditions to report our measurements so that comparison is easy - We call these standard conditions - STP •Standard pressure = 1 atm • Standard temperature = 273 K = 0 °C
Density of a Gas at STP
•Density is the ratio of mass to volume. •Density of a gas is generally given in g/L. •The mass of 1 mole = molar mass. •The volume of 1 mole at STP = 22.4 L.
Properties of Gases
•Expand to completely fill their container •Take the shape of their container •Low density, much less than solid or liquid state •Compressible •Mixtures of gases are always homogeneous fluids.
Molar Volume at STP
•Solving the ideal gas equation for the volume of 1 mol of gas at STP gives 22.4 L - 6.022 × 1023 molecules of gas - Notice that the identity of the gas is immaterial. •We call the volume of 1 mole of gas at STP the molar volume. - It is important to recognize that one mole measurements of different gases have different masses, even though they have the same volume.
