13. Matter Very SimpleYear 13

Learning Objectives Before the unit

I have learned

I have revised

I can show my understanding of effects, ideas and relationships by describing and explaining cases involving:

• The behaviour of ideal gases • The kinetic theory of ideal gases • Absolute (Kelvin) temperature as proportional to the average energy per particle, with average energy » kT as a useful approximation

• Energy transfer producing a change of temperature (in gases, liquids and solids) • Random walk of molecules in a gas; distance gone in N steps related to I can use the following words and phrases accurately when describing effects and observations:

• Absolute temperature • Ideal gas • Root mean square speed • Internal energy I can sketch, plot and interpret: • Graphs showing relationships between p, V and T for an ideal gas I can make calculations and estimates involving: • The universal gas law equation pV = NkT where N =nNA and Nk = nR ; number of moles n and Avogadro constant NA

• The equation for the kinetic model of a gas: • Temperature and energy change using ΔE = mcΔƟ

13. Matter Very Simple

Why does the balloon not expand?

www.phet.colorado.edu

Boyle’s Law

CpV

m = constantT = constant

pm = constantT = constant

VNCp

NCpV

/

No term for type of particle, therefore independent!

TV

m = constantp = constant

Tp

V = constantm = constant

The ideal gas law

NkTpVNTpV

NkTpV

measurable

unknown

NkTpV

NkTpV

The Gas Constant

6 x 1023 Avogadro Number, NA

9 MILES DEEP

Avogadro Number

• Number of particles in one mole of a substance

• E.g. 2 g of H2, 32 g of O2

Ideal gas law

nRTpVkNRkTnNpV

A

A

k

• NA was determined in 1909 so k could be calculated

• Determine k

particleper JK1038.1

mol10022.6molJK314.8

1-23

1-23

-1-1

k

NRkA

What does it mean?

Quick Check Questions

• Have a go at Q1-6 for Thursday

Pg 100 Q1

• Show that the pressure of an ideal gas doubles if its volume is halved

Vp

CNkTVNkTp

NkTpV

1

Pg 100 Q2

• A gas cylinder contains 100 litres of oxygen at room temperature and a pressure of 30 atm. Show that the cylinder can provide 6000 litres of oxygen at atmospheric pressure

2211

21

2

22

1

11

VpVpTT

TVp

TVp

NkTpV

NkTpV

litres 6000atm 1litres 200atm 30

2

2

2211

VV

VpVp

Pg 100 Q3

• A meteorological balloon has a volume of 2 m3 at ground level. Show that the designer should expect it to have a volume of 8 m3 at a height where the atmospheric pressure us 25 % of that at ground level, if the temperature remains the same.

2211

21

2

22

1

11

VpVpTT

TVp

TVp

NkTpV

NkTpV

32

23

21

2111

2211

m 8

m 24

441

V

V

VV

VpVp

VpVp

Pg 100 Q4

• In fact, in Q3 the temperature falls to -30 oC compared to 20 oC at ground level. Show that the designer should expect the balloon to have a volume of about 6.6 m3 at a height when the atmospheric pressure is 25 % of that at ground level.

2

22

1

11

TVp

TVp

NkTpV

NkTpV

32

3

2

23

2

1

m 6.6293

K243m 24293K243K

m 24

243293

VK

V

V

KTKT

Pg 100 Q5

• One mole of any ideal gas occupies a volume of about 22 litres at room temperature and pressure. Show that a small matchbox of air contains about 1020 molecules.

mol 000682.0

cm 15cm 22000

2

2

33

22

22

11

11

nn

RTnVp

RTnVpnRTpV

20

1-23

1-1-

10JK 1038.1

molJK 314.8mol 000682.0

N

N

knRN

nRNk

nRNkTpV

NkTpV

Pg 100 Q6

• 28 g of N2 contains 1 mole of molecules. Show that at a temperature of 546 K the nitrogen will occupy a volume of 22 litres at a pressure of 2 atm.

atmpKKatmp

TTpp

Tp

Tp

RTnVp

RTnVpnRTpV

2273

5461

2

2

1

212

2

2

1

1

22

22

11

11