Flashcards in Section 1: Gases Deck (42):

1

## Central Theme of Chemistry

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• The macroscopic properties and behavior of substances that we can see or easily measure are the result of atomic or molecular-scale (i.e. microscopic or sub-microscopic) properties and behavior.

• Chemists use the observable changes in the properties/behaviour of matter to understand their microscopic causes

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## What is a gas?

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– fills and assumes the shape of its container.

– diffuses and mixes in all proportions with other gases.

3

## Molecules in a gas

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- are separated by large distances and interact weakly with each other, if at all.

- At T ~300K and Atmospheric pressure... Gas densities are strongly dependent on T & P, unlike solids and liquids.

4

## The four variables/parameters that describe any gas:

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– number of moles

• proportional to mass

– temperature

– volume

– pressure

5

## Pressure

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• Confined gases exert pressure.

• Detected as an outward force

Pressure: Force (N) per unit area (m^2)

6

## Atmospheric Pressure

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• Atmosphere – air

– N2, O2, Ar, CO2, H2O

• Extends roughly 100 km into space.

7

## Imploding Can

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- boil water inside popcan

- add it to cold water, the gaseous water molecules that are flying around in the can, when they hit the cold water they stick to the can

- you essentially form a vacuum inside of the can

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## Evangelista Torricelli

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• 1608-1647 (Northern Italy)

• Discovers atmospheric pressure

• Builds world’s first barometer (allows you to take quantitative measurements of atmospheric pressure)

9

## The barometer

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• Fill test-tube with Hg (mercury).

• Invert the tube.

• Place open end in

container of Hg.

• Height of Hg falls to 76 cm.

My notes:

- has two pieces:

- normally a dish that contains liquid mercury

- and a long (1m) test tube

- fill test tube with Hg, then invert that tube into the liquid Hg. At sea level, the column of Hg will drop such that the heigh falls to 76cm

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## Why does the Hg drop in the barometer?

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• Hg level changes until pressure from Hg column = atmospheric pressure

•

≈ 760mm (sea-level)

– does not depend on diameter of tube.

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## Pressure exerted by a column of liquid at its base

### - does not depend on the area of the column

12

## Liquid Pressure: Columns

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P=ghd

- The pressure exerted by a liquid depends on:

• The height of the column of the liquid and the density of the liquid

13

## Manometers

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- on right, have a confined gas that you need to get the pressure of

- beside that, the P of the gas pushing down

- on the left hand side, it is open to atmosphere

- the right hand side its the pressure of the gas and the presure due to mercury

- the left hand side is the pressure of atmosphere and pressure of the mercury

- this must mean these two pressures are equal since the meniscus is the same level

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## Simple gas laws

### relationships between pairs of gas properties (P, V, T, n)

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## Ideal Gas

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• a gas that obeys the simple gas laws perfectly.

• Real gases can behave like ideal gases over a range of conditions

16

## Boyle's Law

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• In 1662, Robert Boyle discovers the first gas law

using a manometer.

• Varies the volume and pressure of a fixed amount of air at constant temperature.

-experimented with a trapped volume of air

- he varied the pressure that was acting on the air at a constant temperature

- he used manometer, poured in Hg, he changed the pressure by adding more Hg

17

## Boyle's Law: Volume and Pressure

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For a fixed amount of an ideal gas at a fixed temperature, the volume is inversely proportional to the pressure.

- PV= constant

18

## Charles's Law

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• Jacques Charles (1746-1823)

• Gas expands when heated at a constant pressure. (and compresses when cooled)

19

## Charles's Law: Volume and Temperature

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- volume is directly proportional to the temperature

- the difference between the curves, is just different amounts of gas

- relationship is LINEAR

- made another observation: all crossed zero at exactly the same number (-273.15 ºC or 0 Kelvin)

V/T= constant

20

## Avogadro's Law

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• The volume occupied by an ideal gas (at given T & P) depends only on the number of molecules present; the type of molecule is not relevant

• Equal numbers of molecules occupy equal volumes.

*At the same T & P*

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## Avogadro's Law: When gases are behaving idealy

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• Gases are mostly empty space.

• The size of the molecules doesn’t much matter.

22

## Standard Temperature and Pressure (STP)

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• Standard temperature: 0°C = 273.15 K

• Standard pressure: 1 bar = 0.9869 atm

• Avogadro: one mole (6.02 • 1023) of molecules of any ideal gas occupy the same volume at STP: ~22.7 L

23

## Ideal Gas equation

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PV=nRT

T= always in K

R= depends on what units you have

• You can rewrite n as m/M, that way you can either solve for m or M

24

## 4 Parameters describe a gas

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• Pressure

• Volume

• Number of moles

• Temperature

- if you know 3/4, you can use the gas law to calculate the 4th

25

## General Gas Law

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• When problem involves gases under two different conditions

• Given some of these parameters, we will want to calculate the unknowns

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## How to use General Gas law

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• Use:

(P1V1)/(n1T1)= (P2V2)/(n2T2)=R

• Cancel the parameters that are equal on two sides of the equation.

• Substitute known values (check units).

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## Boyles Law (Equation)

### P1V1=P2V2

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## Charles Law (Equation)

### V1/T1=V2/T2

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## Amonton's Law (Equation)

### P1/T1=P2/T2

30

## Gas density

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d=m/V

= MP/RT

units: gL^-1

31

## Gay- Lussac's Law

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• gases react in volumes proportional to small whole numbers.

Why?

- volumes are proportional to the stoichiometric coefficients in chemical equation (V is proportional to n- Avogadro)

32

## Partial Pressures

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nA+nB= nTOT

- made up of two species

- apply ideal gas law (PV=nTOTRT)

• mole fraction of A:

- fraction of molecules that are A xA=nA/nTOT

- same for nB

-mole fractions sum to 1

33

## Dalton's Law of Partial Pressures

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“The total pressure exerted by a gaseous mixture is equal to the sum of the partial pressures of each individual component in a gas mixture.”

- Pa+Pb=Ptotal

• components of a gaseous mixture exert the same pressure as they would in the absence of the other components.

- you use nTOT, in this situation as well

- Use pressure fractions, to determine how much pressure is being used by both species

34

## Astronauts

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Humans need PO2

between 120 torr and 380 torr. (altitude sickness when pressure drops below 120)

• Astronauts are supplied 100% O2 with P ≈ 160 torr.

• helps prevent suit ballooning.

• If regular air with Ptot=160 torr were used, PO2=32 → hypoxia.

• If 100% O2 at 760 torr were used → hyperoxia

35

## Behaviour of ideal gases can be explained by a simple model:

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• Large number of particles (molecules)

• following Newton’s laws of motion (random, straight lines until they collide with another molecule or edge of container).

• separated by large distances

• collisions are brief

• no long-range forces between particles

• gas has internal energy only due to kinetic energy of particles

• total energy is constant

36

## Microscopic description of Pressure

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- collisions of particles with walls of container

P=1/3(N/V)(mu^2)

N= number of particles

u^2= average square velocity

m= mass of one particle

- get this equation from force of momentum of particles

- using that force, then dividing by area to get the pressure

37

## Microscopic description of Temperature

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– depends on the kinetic energy of the

particles.

T= 2/3(Na/R)(1/2mu^2)

38

## Root mean square velocity

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• close to the average speed of the

particles.

- increasing temp by 4, increases u by 2

- increasing molar mass by 4, decreases u by 2

u= (3RT/M)^0.5

39

## Are air molecules ‘displaced’ by hundreds of meters in a single second?

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NO... because

• Air molecules have enough kinetic energy to travel long distances quickly.

• But they continually collide with other air molecules and change direction.

• Instead of travelling in a straight line... molecules follow a much longer path, due to collisions

40

## Distributions of Molecular Speeds

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• Velocity of individual particles are constantly altered by collisions.

• Particles have a wide distribution of speeds.

41

## Maxwell-Boltzmann Distribution

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- left hand side is oven (choose temp) contains gas. there is a little hole in the side which means the gas particles are free to escape. then goes through slits to form into a beam, this enters measurement end of instrument (two rotating discs with two slots (one in each) that are offset.)

- the gas particle will go through the first slot; in order to go thru the second slot only if its velocity is just right (meaning that the time it takes for the particle to get from first slit to second slit is equal to distance between plates over the velocity of the gas particle, has to be the same time the second lit rotates.

Results:

- small number of detections at low speed

- the max depends on the temp (highest temp)

• Distribution shifts to slower speeds for larger molecules (as we have seen), so the lower the mass, the faster the speed.

• Distribution shifts to higher speeds for higher temperatures.

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