Engineering Chemistry 14/15 Fall semester Instructor: Rama Oktavian Email: [email protected] Office Hr.: M.13-15, Tu. 13-15, W. 13-15, Th. 13-15,

Engineering Chemistry

14/15 Fall semester

Instructor: Rama OktavianEmail: [email protected] Hr.: M.13-15, Tu. 13-15, W. 13-15, Th. 13-15, F. 09-11

Outlines

1. Gas: Properties 1. Gas: Properties

2. Gas laws: Boyle and Charles law 2. Gas laws: Boyle and Charles law

3. Ideal gas law 3. Ideal gas law

Review

Mass conservation law

Fluorite, a mineral of calcium, is a compound of the metalwith fluorine. Analysis shows that a 2.76-g sample of fluorite contains 1.42 g of calcium. Calculate the (a) mass of fluorine in the sample; (b) mass fractions of calcium and fluorine in fluorite; (c) mass percent of calcium and fluorine in fluorite.

Dolomite is a carbonate of magnesium and calcium. Analysis shows that 7.81 g of dolomite contains 1.70 g of Ca. Calculate the mass percent of Ca in dolomite. On the basis of the mass per cent of Ca, and neglecting all other factors, which is the richer source of Ca, dolomite or fluorite

Review

Mass conservation law

Gas state

State of matter

There are 4 states of matter

Gas state

State of matter

Properties of solid

Microscopic view of a solid

retains a fixed volume and shape

rigid - particles locked into place

not easily compressible

little free space between particles

does not flow easily

rigid - particles cannot move/slide past one

another

Gas state

State of matter

Properties of liquid

Microscopic view of a solid

assumes the shape of the part of the

container which it occupies

particles can move/slide past one another

not easily compressible

little free space between particles

flows easily

particles can move/slide past one another

Gas state

State of matter

Properties of gas

Microscopic view of a solid

assumes the shape and volume of its

container

particles can move past one another

compressible

lots of free space between particles

flows easily

particles can move past one another

Microscopic properties

Gas state

State of matter

Properties of gas

Microscopic view of a solid

Properties that can be observed and

measured

Macroscopic properties

• Properties of bulk gases

• Observable

– Pressure, volume, mass, temperature..

How to make relation between those

macroscopic properties of gas??

The general form of an equation of state isp=f(T,V,n)

Gas state

Gas properties

Gases Exert Pressure: What is Pressure?

Pressure is defined as the force exerted divided by the area it acts over

Pressure = Force/Area

The SI unit of pressure, the pascal(Pa), is defined as 1 newton per metre-squared:1 Pa =1 N m−2

1 Pa =1 kg m−1s−2

1 atm =1.013 25 ×105Pa exactly 1 bar =105Pa

Gas properties

Gases Exert Pressure: What is Pressure?

Pressure is defined as the force exerted divided by the area it acts over

Pressure = Force/Area

Self-test 1.1 Calculate the pressure (in pascals and atmospheres) exerted

by a mass of 1.0 kg pressing through the point of a pin of area 1.0 ×10−2

mm2 at the surface of the Earth.

Gas properties

Pressure measurement

Barometer – device that measures

atmospheric pressure

Invented by Evangelista Torricelli in 1643

the height of the mercury column is proportional to the external pressure

Gas properties

Pressure measurement

Derive an equation for the pressure at the base of a column of liquid of mass density ρ(rho) and height h at the surface of the Earth.

p=F/A F = mg m = ρV

V = Ah m = ρAh F = mg = ρAhg

the pressure is independent of the shape and cross-sectional area of the column.

Gas properties

Pressure measurement

Gas properties

Pressure measurement

A manometer measures the pressure of a gas in a container

Gas pressure is the force exerted by the collisions of gas particles with a surface

Gas properties

Pressure measurement

Atmospheric pressure

By definition the average pressure at sea level will support a column of 760 mm of mercury. (760 torr)

g = 9.81 m.s-2 h = 0.76 m

ρ = 13.6 g.cm-3 = 13.6 kg.L-1 = 13.6x103kg.m-3

P = 9.81x0.76x13.6x103 = 1.013x105 Pa (N.m-2)

Gas properties

Pressure measurement

Atmospheric pressure problem

If we made a barometer out of water, what would be the height of the water column if the pressure is 745 torr?

Gas properties

Pressure measurement

Variation in atmospheric pressure

– Changing weather conditions

Gas properties

Pressure measurement

Variation in atmospheric pressure

– Changing altitude

Gas laws

Boyle’s law

• Boyle’s Law is one of the laws in physics that concern the

behaviour of gases

• When a gas is under pressure it takes up less space:

• The higher the pressure, the smaller the volume

• Boyles Law tells us about the relationship between the volume of

a gas and its pressure at a constant temperature

• The law states that pressure is inversely proportional to the

volume

Gas laws

Boyle’s law

Pressure-volume relationship

pressure-volume behavior of gases were made by Robert Boyle in 1662

P a 1/V

P x V = constant

P1 x V1 = P2 x V2

Gas laws

Pressure and Volume: Boyle’s Law

• Volume and pressure are inversely proportional. – If one increases the other decreases.

Gas laws

Pressure and Volume: Boyle’s Law• Boyle’s Law and Breathing: Inhalation

During inhalation, the lungs expand the pressure in the lungs

decreases air flows towards the

lower pressure in the lungs

Gas laws

Pressure and Volume: Boyle’s Law• Boyle’s Law and Breathing: Inhalation

During exhalation• lung volume decreases• pressure within the lungs

increases• air flows from the higher

pressure in the lungs to the outside

Gas laws

Pressure and Volume: Boyle’s Law

A sample of chlorine gas occupies a volume of 946 mL at a pressure of 726 mmHg. What is the pressure of the gas (in mmHg) if the volume is reduced at constant temperature to 154 mL?

P1 x V1 = P2 x V2

P1 = 726 mmHg

V1 = 946 mL

P2 = ?

V2 = 154 mL

P2 = P1 x V1

V2

726 mmHg x 946 mL

154 mL= = 4460 mmHg

Gas laws

Pressure and Volume: Boyle’s LawGuide to Calculations with Gas Laws

Gas laws

Pressure and Volume: Boyle’s Law

Problem

A deep sea diver is working at a depth where the pressure is 3.0 atmospheres. He is breathing out air bubbles. The volume of each air bubble is 2 cm2. At the surface the pressure is 1 atmosphere. What is the volume of each bubble when it reaches the surface?

Gas laws

Charles’s law

• French chemist Jacques Charles discovered that the volume of a gas at

constant pressure changes with temperature.

• As the temperature of the gas increases, so does its volume, and as its

temperature decreases, so does its volume.

• The law says that at constant pressure, the volume of a fixed number of

particles of gas is directly proportional to the absolute (Kelvin) temperature

Gas laws

Charles’s law

Volume-temperature relationship

Variation of gas volume with temperatureat constant pressure

V a T

V = constant x T

V1/T1 = V2/T2

Gas laws

Charles’s law

Volume-temperature relationship

For two conditions, Charles’s law is written

V1 = V2 (P and n constant)

T1 T2

Rearranging Charles’s law to solve for V2 gives

T2 x V1 = V2 x T2

T1 T2

V2 = V1 x T2

T1

Gas laws

Charles’s law

Example problem

A balloon has a volume of 785 mL at 21 °C. If thetemperature drops to 0 °C, what is the new volume ofthe balloon (P constant)?

STEP 1 Set up data table:

Conditions 1 Conditions 2 Know PredictV1 = 785 mL V2 = ? V

decreases

T1 = 21 °C T2 = 0 °C

= 294 K = 273 K T decreases

Be sure to use the Kelvin (K) temperature in gascalculations.

Gas laws

Charles’s law

STEP 2 Solve Charles’s law for V2:

V1 = V2

T1 T2

V2 = V1 x T2

T1

Temperature factor decreases T

STEP 3 Set up calculation with data: V2 = 785 mL x 273 K = 729 mL

294 K

Gas laws

Charles’s law

A sample of oxygen gas has a volume of 420 mL at a temperature of 18 °C. At what temperature (in °C) will the volume of the oxygen be 640 mL (P and n constant)?

1) 443 °C

2) 170 °C

3) –82 °C

Gas laws

Avogadro’s lawAvogadro’s law states that the volume of a gas is

directly related to the number of moles (n) of gas

T and P are constant

V1 = V2 n1 n2

Ideal Gas law

The combination of those laws gives

Usually written as:

R is gas constant

Ideal Gas law

R is known as universal gas constant

Using STP conditions

nT

PVR

)15.273)(1(

)4.22)(1(

Kmol

LatmR

1).)(.(0821.0 KmolLatmR

Ideal Gas law

R is known as universal gas constant

Learning check

What is the value of R when the STP value for P is 760 mmHg?

Ideal Gas law

Problem

Learning check

A 5.0 L cylinder contains oxygen gas at

20.0°C and 735 mm Hg. How many grams

of oxygen are in the cylinder?

Ideal Gas law

Problem

Learning check

In an industrial process, nitrogen is heated to 500 K in a vessel of

constant volume. If it enters the vessel at 100 atm and 300 K, what

pressure would it exert at the working temperature if it behaved as a

perfect gas?