Chem 7 Chapter 5 - KimikaPostulate 1: Particle Volume Postulate 2: Particle Motion Postulate 3: Particle Collisions What are the implications of these statements? Gases are point particles

Gases Chapter 5

Matter exists commonly in three physical states:

Among the three, we focus on gases first. What differentiates gases from the other states?

1. Gas volume changes greatly with pressure.

2. Gas volume changes greatly with temperature.

3. Gases have relatively low viscosity.

4. Most gases have relatively low densities under normal conditions.

5. Gases are miscible.

We usually measure the presence or absence of a gas using pressure.

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Pressure(P) =ForceArea


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Pressure(P) =ForceArea


TRY THIS:

A geochemist heats a limestone (CaCO3) sample and collects the CO2 released in an evacuated flask. The CO2 pressure is 291.4 mmHg. Calculate the CO2 pressure in torrs, atmospheres, and kilopascals.

Some observations and experiments were made about gases. Robert Boyle showed that at constant temperature, the volume occupied by a fixed amount of gas is inversely proportional to the applied (external) pressure.

Robert Boyle showed that at constant temperature, the volume occupied by a fixed amount of gas is inversely proportional to the applied (external) pressure.

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V∝ 1P

V =constantP

PV = constantP1V1 = P2V2

In Boyle’s experiment, Temperature and amount of gas (moles) is constant

Jacques Charles and Joseph Louis Gay-Lusaac showed that At constant pressure, the volume of a fixed amount of gas is directly proportional to its absolute (Kelvin) temperature.

Jacques Charles and Joseph Louis Gay-Lusaac showed that At constant pressure, the volume of a fixed amount of gas is directly proportional to its absolute (Kelvin) temperature.

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V∝TV = constant * TVT

= constant

V1T1= V2T2

In Charles’ experiment, pressure and amount of gas (moles) is constant

Guillaume Amonton showed that At constant volume, the pressure exerted by a fixed amount of gas is directly proportional to its absolute temperature.

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P∝TP = constant * TPT

= constant

P1T1= P2T2

In Amonton’s experiment, volume and amount of gas (moles) is constant

If we combine all the Gas laws together:

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P∝ TV

P = constant * TV

PVT

= constant

P1V1T1

= P2V2T2

In this combination, amount of gas is constant.

BUT what if amount of gas is not constant?

Avogadro showed that at fixed temperature and pressure, equal volumes of any ideal gas contain equal numbers of particles (moles)

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V∝nV = constant *nVn

= constant

V1n1= V2n2

Following Avogadro’s law, at standard conditions of temperature and pressure (STP), same amount of gases (moles) occupy the same amount of space (volume)

Using all our data from the different laws, we can derive:

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V∝ nTP

V = constant * nTP

PVnT

= constant = R = 0.0821L *atmmol*K

P1V1n1T1

= P2V2n2T2

Ideal gas law constant/ Universal gas law constant

Using all our data from the different laws, we can derive:

THE IDEAL GAS LAW

PV = nRT

R = PV

nT =

1 atm x 22.414 L

1 mol x 273.15 K =

0.0821 atm•L

mol•K R is the universal gas constant

3 significant figures

From the ideal gas law, one can derive the other gas laws by Boyle, Charles, Amonton and Avogadro

Let’s try to solve some problems:

1. Boyle’s apprentice finds that the air trapped in a J tube occupies 24.8 cm3 at 1.12 atm. By adding mercury to the tube, he increases the pressure on the trapped air to 2.64 atm. Assuming constant temperature, what is the new volume of air (in L)?

2. A steel tank used for fuel delivery is fitted with a safety valve that opens if the internal pressure exceeds 1.00 x 103 torr. It is filled with methane at 23oC and 0.991 atm and placed in boiling water at exactly 100oC. Will the safety valve open?

3. A scale model of a blimp rises when it is filled with helium to a volume of 55.0 dm3. When 1.10 mol of He is added to the blimp, the volume is 26.2 dm3. How many more grams of He must be added to make it rise? Assume constant T and P.

4. A steel tank has a volume of 438 L and is filled with 0.885 kg of O2. Calculate the pressure of O2 at 21oC.

Let’s try to solve some problems:

The piston-cylinders depicted below contain a gaseous reaction carried out at constant pressure. Before the reaction, the temperature is 150 K; when it is complete, the temperature is 300 K.

Which of the following balanced equations describes the reaction?

(1) A2(g) + B2(g) 2AB(g) (2) 2AB(g) + B2(g) 2AB2(g)

(4) 2AB2(g) A2(g) + 2B2(g) (3) A(g) + B2(g) AB2(g)

Other parameters may be derived from the ideal gas equation (like gas density or MW of a gas):

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Density(ρ) =mV

n =mMW

PV = nRT

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PV = mMW

RT

P*MW =mVRT

P*MW = ρRT

ρ =P *MWRT

What if we have mixtures of gases?

• Gases mix homogeneously in any proportions.

• Each gas in a mixture behaves as if it were the only gas present (assuming no chemical interactions).


Dalton’s law of Partial Pressures

Ptotal = P1 + P2 + P3 + ...

P1= χ1 x Ptotal where χ1 is the mole fraction

χ1 = n1

n1 + n2 + n3 +... =

n1

ntotal


In a study of O2 uptake by muscle at high altitude, a physiologist prepares an atmosphere consisting of 79 mol % N2, 17 mol % 16O2, and 4.0 mol % 18O2. (The isotope 18O will be measured to determine the O2 uptake.) The pressure of the mixture is 0.75 atm to simulate high altitude. Calculate the mole fraction and partial pressure of 18O2 in the mixture.


Gases can be collected over water.


Vapor pressure is the pressure due to water when there is a vacuum above a body of water.


Vapor pressure is the pressure due to water when there is a vacuum above a body of water.


So how do we compute for pressure?


Acetylene (C2H2), an important fuel in welding, is produced in the laboratory when calcium carbide (CaC2) reacts with water:

CaC2(s) + 2H2O(l) C2H2(g) + Ca(OH)2(aq)

For a sample of acetylene that is collected over water, total gas pressure (adjusted to barometric pressure) is 738 torr and the volume is 523 mL. At the temperature of the gas (23oC), the vapor pressure of water is 21 torr. How many grams of acetylene are collected?

Using the Ideal gas law, we can relate the moles of one gas to the moles of another gas in a chemical reaction, given P, V and T.

Copper reacts with oxygen impurities in the ethylene used to produce polyethylene. The copper is regenerated when hot H2 reduces the copper(II) oxide, forming the pure metal and H2O. What volume of H2 at 765 torr and 225oC is needed to reduce 35.5 g of copper(II) oxide?

The alkali metals [Group 1A(1)] react with the halogens [Group 7A(17)] to form ionic metal halides. What mass of potassium chloride forms when 5.25 L of chlorine gas at 0.950 atm and 293 K reacts with 17.0 g of potassium?

Why do gases behave the way they do?

Kinetic Molecular Theory (KMT) Chapter 5

Kinetic Molecular Theory states that for an IDEAL GAS:

Because the volume of an individual gas particle is so small compared to the volume of its container, the gas particles are considered to have mass, but no volume.

Gas particles are in constant, random, straight-line motion except when they collide with each other or with the container walls.

Collisions are elastic, which means that the colliding molecules exchange energy but do no lose any energy through friction. Therefore, the total kinetic energy (Ek) of the particles is constant.

Postulate 1: Particle Volume

Postulate 2: Particle Motion

Postulate 3: Particle Collisions

What are the implications of these statements?

Gases are point particles that are moving in a chaotic manner. When it hits other molecules (or the container walls) it exerts a force on it.. Giving rise to PRESSURE!

This shows how Boyle’s Law can be explained by KMT


We can also look at AVOGADRO’S Law in the same manner


Or Dalton’s Law of partial pressure


Since gases transfer energy as they move and collide, not all gases will have the same speed (Kinetic energy). Instead a collection of gas molecules will have a distribution of different speeds.. (Although you can get an AVERAGE KE, for a collection of gas molecules)

-oOo-

Changes in temperature gives the gas more energy of motion.

AVERAGE KE is proportional to Temp

Speed distribution changes, and average speed increases.


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KE =32* RNA

T

Where KE is the average kinetic energy of one gaseous particle!

R = universal gas constant in Joules per mol per K NA = Avogadro’s number

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KE =12mu2

From physics, we know that the KE of one particle (Ex. molecule or atom) is


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12mu2 =

32* RNA

T

m *NA * u2 = 3RT

Mass of one particle * avogadro’s number = Mass of one mole of particle (or molar mass)

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MW * u2 = 3RT

u =3RTMWHigher temperature, higher speed

Bigger molecules will move slower HOWEVER, KE is constant for a specific Temp no matter what the molecule is!


When energy increases, you have higher tendency to collide with the container… Increase in pressure felt by the container..

If the container cannot expand as in the case of steel containers, the pressure will just increase.

But if the container can expand as in the case of balloons, the pressure inside will equalize with the pressure outside resulting in increased volume

However, gases do not behave IDEALLY in all conditions

When one increases pressure (at a moderate level), gases will be too close to each other and attractive/repulsive forces is put into play. Collisions become inelastic! Pressure felt by the container MAY decrease.

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PVRT

=1For one mole of an ideal gas This happens when pressure is LOW


When one increases pressure (at an extreme level), gases will be too close to each other that volume of gas particle is not negligible to volume of container. Volume that can be occupied by gas decreases.

Furthermore, the path of gases are crowded.. More chances to collide into container. Thus, pressure felt by the container increases drastically!



Increasing the temperature, may help the gas behave ideally by giving them more energy to withstand attractive/repulsive forces.


Taking all these in consideration, Johannes van der Waals realized the limitations and proposed an equation that accounts for the behavior of REAL GASES.

He accounted for the intermolecular forces of attraction by increasing the pressure by a correction factor.

He accounted for the free volume disparity by decreasing the volume through another correction factor.

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PVDW +n2aV 2

Vcontainer − nb( ) = nRT


A 215 g (4.89 moles) sample of dry ice (CO2 (solid))was allowed to evaporate in a rigid 1.98-L vessel at constant temperature of 299 K.

Calculate for Pressure based on ideal gas Law

Calculate for pressure based on VDW equation

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PVDW +n2aV 2

Vcontainer − nb( ) = nRT

In Summary Chapter 5

Gases in summary:

1.  Gases have different properties than solids and liquids (What are they?)

2.  Gases are usually measured using pressure (How do you measure pressure? – Barometer, Manometer, conversions)

3.  The behavior of most gases can be observed using the different Gas Laws, which combine to form the Ideal Gas Law (What are these laws? Know how to do problem solving with these laws)

4.  The Ideal Gas Laws can be applied to determine other quantities like molecular weight of a gas, density of a gas, partial pressure and mole fractions of gas mixtures and stoichiometry in reactions of gases.

5.  The behavior of gases can be understood at the molecular level by the Kinetic Molecular Theory (What are the postulates?)

6.  Gases may deviate from the Ideal Gas Law because of interactions between molecules and molecular volume. A better approximation of gas behavior is given by Van der Waals equation.

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Chem 7 Chapter 5 - KimikaPostulate 1: Particle Volume Postulate 2: Particle Motion Postulate 3: Particle Collisions What are the implications of these statements? Gases are point particles