powerpoint to accompany chapter 9a gases. brown, lemay, bursten, murphy, langford, sagatys:...

PowerPoint to accompany

Chapter 9a

Gases

Brown, LeMay, Bursten, Murphy, Langford, Sagatys: Chemistry 2e © 2010 Pearson Australia

Characteristics of Gases Like liquids and solids, they:

Still have mass and momentum Have heat capacities & thermal conductivities Can be chemically reactive

Unlike liquids and solids, they: Expand to fill their containers Are highly compressible Have extremely low densities


Pressure

Pressure is the amount of force applied to an area.

Atmospheric pressure is the weight of air per unit of area.

P =FA


Units of Pressure

Pascals 1 Pa = 1 N/m2 = 1 Kg/ms2

Bar 1 bar = 105 Pa = 100 kPa

mm Hg or torr The difference in the heights in mm (h) of

two connected columns of mercury Atmosphere

1.00 atm = 760 torr


Standard Pressure

Normal atmospheric pressure at sea level.

This is ambient pressure, equal all around us, so not particularly felt

It is equal to: 1.00 atm 760 torr (760 mm Hg) 101.325 kPa 14.696 psi


Manometer

Figure 9.2

Used to measure the difference between atmospheric pressure & that of a gas in a vessel.


Manometer calculation:

Patm= 102 kPa

Pgas> Patm

Pgas= Patm + h

Pgas= 102 kPa + (134.6mm – 103.8mm)Hg

Pgas= 102 kPa + (32.6mm Hg) Note 1mmHg = 133.322 Pa Pgas= 102 kPa + (32.6x133.322x10-3 kPa)

Pgas= 106 kPa = 1.06 bar =1.06/1.013 atm

Pgas= 1.046 atm


Boyle’s Law

The volume of a fixed quantity of gas at constant temperature is inversely proportional to the pressure: V ~ 1/P

Figure 9.4


As P and V are inversely proportional

A plot of V versus P results in a curve.

Since

V = k (1/P)

This means a plot of V versus 1/P will be a straight line.

PV = k

Figure 9.5


Charles’s Law: initialwarm balloon, T big, V big


Charles’s Law: finalcold balloon T & V little


Charles’s Law

The volume of a fixed amount of gas at constant pressure is directly proportional to its absolute temperature.

VT = k

A plot of V versus T will be a straight line.

Figure 9.7V = kT


Avogadro’s Law The volume of a gas at constant temperature

and pressure is directly proportional to the number of moles of the gas.

Mathematically, this means: V = kn

Figure 9.8


Ideal-Gas Equation

So far we’ve seen that:V 1/P (Boyle’s law)

V T (Charles’s law)

V n (Avogadro’s law)

Combining these, we get, if we call the proportionality constant, R:

nTP V = R

i.e. PV = nRT (where R = 8.314 kPa L/mol K)


V = k (1/P)

nTP V = R V

P


Ideal Gas Law Calculations

Heat Gas in Cylinder from 298 K to 360 K at fixed piston position. (T incr. so P increases)

Same volume, same moles but greater P P1 = (nR/V1)T1 or P1/T1 = P2 / T2

P2 = P1T2 / T1

P2 = P1(T2 /T1 ) = P1(360/298) = 1.2081P1



Move the piston to reduce the Volume from 1 dm3 to 0.5 dm3. (V decreases so P increases)

Same moles, same T, but greater P P1V1 = (nRT1) = P2V2

P2 = P1V1 / V2 = P1 (V1 / V2)

P2 = P1(1.0/0.5) = P1(2.0)



Inject more gas at fixed piston position & T. the n increases so P increases)

Same volume, more moles but greater P P1 = n1(RT1/V1) or P1/n1 = P2 / n2

P2 = P1 n2 / n1 for n2 = 2 n1

P2 = P1(2)



R = (PV / nT) When kPa and dm3 are used as is common R = 8.314 kPa dm3 / mol K or J/mol K It is useful to write the ideal gas law this way

so that R is the constant and other variables can change from initial to final conditions

This again reduces the gas law to a simple arithmetic ratio calculation

The only tricks are to ensure all units are consistent or converted as needed.


V = (nRT/P) = 1mol (8.314kPa dm3 /molK)(273.15K)/100 kPaV/mol = 22.71 dm3 = 22.71L


Gas Densities and Molar Mass

If we divide both sides of the ideal-gas equation by V and by RT, we get:

nV

PRT=

Most of our gas law calculations involve proportionalities of these basic commodities.


Gas Densities and Molar Mass

We know that moles molar mass = mass

So multiplying both sides by the molar mass () gives:

n = m

PRT

mV = i.e. =

PRT


Molecular Mass

We can manipulate the density equation to enable us to find the molar mass of a gas:

Becomes

PRT =

RTP =


End of Part 9a Ideal Gas Law

powerpoint to accompany chapter 9a gases. brown, lemay, bursten, murphy, langford, sagatys:...

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