Physical Chemistry I(TKK-2246)

13/14 Semester 2

Instructor: Rama OktavianEmail: rama.oktavian86@gmail.comOffice Hr.: M.13-15, Tu. 13-15, W. 13-15, Th. 13-15, F. 09-11

Outlines

1. Ideal gas properties 1. Ideal gas properties

2. Molar mass of gas 2. Molar mass of gas

3. Molar mass of volatile component 3. Molar mass of volatile component

4. Gas mixture 4. Gas mixture

Review

Learning check

A sealed flask with a capacity of 1 dm3 contains 5 g of ethane. The flask is so

weak that it will burst if the pressure exceeds 1 MPa. At what temperature will the

pressure of the gas reach the bursting pressure ?

Review

Learning check

A perfect gas undergoes isothermal compression, which reduces its

volume by 1.80 dm3. The final pressure and volume of the gas are 1.97 bar and 2.14

dm3, respectively. Calculate the original pressure of the gas in (a) bar,

(b) Torr

Review

Learning check

A large cylinder for storing compressed gases has a volume of about 0.050 m3. If

the gas is stored under a pressure of 15 MPa at 300 K, how many moles of

gas are contained in the cylinder ?

What would be the mass of oxygen in such a cylinder ?

Review

Learning check

A manometer consists of a U-shaped tube containing a liquid. One side

is connected to the apparatus and the other is open to the atmosphere. The

pressure inside the apparatus is then determined from the difference in

heights of the liquid. Suppose the liquid is water, the external pressure is

770 Torr, and the open side is 10.0 cm lower than the side connected to the

apparatus. What is the pressure in the apparatus? (The density of water at

25°C is 0.99707 g cm−3.)

Ideal gas and Real gas

Ideal gas

The ideal gas law is used to describe the behavior of an ideal gas.

Ideal gas: hypothetical gas that obeys kinetic molecular theory and the ideal gas law

Ideal gas and Real gas

Ideal gas

RTVp

The ideal gas law was useful in determining the properties of a specific sample of gas at constant T, P, V, and n.

We often need to know how a change in one (or more) properties impacts the other properties for a sample of a gas

Ideal gas and Real gas

Real gas

RTVp deviations from the perfect gas law because molecules interact with one another

Repulsive forces are significant only when molecules are almost in contact

Attractive intermolecular forces have a relatively long range and are effective over several molecular diameters

Ideal gas and Real gas

Real gas

The compression factor Z

For ideal gas 1Z

1 ZP

1 ZPP moderate Z < 1

Ideal gas and Real gas

Real gas

The compression factor Z

RT

VPZ

Ideal gas and Real gas

Equation of state for Real gas

Virial equation of state

How to describe this P-V behavior?

Ideal gas and Real gas

Equation of state for Real gas

Virial equation of state

RT

VPZ

Ideal gas and Real gas

Equation of state for Real gas

Virial equation of state

Ideal gas and Real gas

Equation of state for Real gas

Virial equation of state

The second virial coefficient B′ can be obtained from measurements of the density ρ of a gas at a series of pressures. Show that the graph of p/ρ against p should be a straight line with slope proportional to B′.

Molar mass of ideal gas

Determination of molar mass for ideal gas

Ideal gas equation

nRTPV

M

wn

RTPP

RT

V

wM

Intensive properties and measurable

Molar mass of ideal gas

Determination of molar mass for ideal gas

Gas density

RTPP

RT

V

wM

Density is higher 1. for gases with a higher molar mass Gases2. at higher pressures3. at lower temperatures

Molar mass of ideal gas

Determination of molar mass for ideal gas

Example

if chemical analysis of a gas yields an empirical formula (CH 2 )n, then the molar mass must be some multiple of 14 g/mol ; the possibilities are 28, 42, 56, 70, and so on. If a molar mass determination using Eq. (2. 20) yields a value of 54 g/mol, then we may conclude that n = 4 and that the material is one of the butenes.

Molar mass of ideal gas

Determination of molar mass for ideal gas

Problem : Calculation of Molecular Weight of a Natural Gas - Methane

A sample of natural gas is collected at 25.0 C in a 250.0 ml

flask. If the sample had a mass of 0.118 g at a pressure of 550.0 torr,

what is the molecular weight of the gas?

Use the ideal gas law to calculate n, then calculate the molar mass.

Molar mass of ideal gas

Determination of molar mass for ideal gas

Problem

At 100°C and 1.60 kPa, the mass density of phosphorus vapour is

0.6388 kg m−3. What is the molecular formula of phosphorus under these

conditions?

Molar mass of ideal gas

Determination of molar mass for ideal gas

Problem

A series of measurements are made in order to determine the molar mass of an

unknown gas. First, a large flask is evacuated and found to weigh 134.567 g. It is

then filled with the gas to a pressure of 735 torr at 31°C and reweighed; its mass

is now 137.456 g. Finally, the flask is filled with water at 31°C and found to weigh

1067.9 g. (The density of the water at this temperature is 0.997 g/mL.) Assuming

that the ideal-gas equation applies, calculate the molar mass of the unknown gas.

Gas mixture

Air is an example of an ideal gas mixture and has the following approximate composition.

Component % by Volume N2 78.10 O2 20.95 Argon 0.92 CO2 + trace elements 0.03

Gas mixture

Properties of gas mixture

k gasesT = Tm V = Vm

P = Pm m = mm

The total mass of the mixture mm and the total moles of mixture Nm are defined as

m m N Nm ii

k

m ii

k

1 1

and

Gas mixture

Properties of gas mixture

Volume concentration

Unit : mol/m3

Volume concentration molarity

Gas mixture

Properties of gas mixture

The composition of a gas mixture is described by specifying either the mass fraction mfi or the mole fraction yi of each component i.

mfm

my

N

Nii

mi

i

m

and

Note that

mf yii

k

ii

k

1 1

1 = 1 and