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Lecture Handout 5: Gases (Online Text Chapter 6) I.  The Structure of a Gas

A.  Gases are composed of particles that are flying around very fast in their container(s).

1.  The particles travel in straight lines until they encounter either the container wall or another particle; then they bounce off.

2.  There is a lot of empty space between particles.

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B.  As the gas particles move and strike a surface, they push on that surface

1.  If we could measure the total amount of force exerted by gas molecules hitting a surface at any one instant, we would know the pressure the gas is exerting.

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II.  Measuring Air Pressure A.  We measure the effect of

particle collisions with the walls of the container or on a surface.

B.  We measure air pressure with a barometer.

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C.  What would happen if the column of mercury were replaced by a column of water?

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D.  What happens to the height of the column of mercury in a mercury barometer as you climb to the top of a mountain?

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E.  Units of Pressure

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F.  Ex: A high-performance bicycle tire has a pressure of 132 psi. What is the pressure in mmHg?

G.  Ex: Convert 45.5 psi into kPa

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H.  Manometers 1.  Manometers are U-shaped tubes, partially filled

with a liquid, connected to the gas sample on one side and open to the air on the other.

2.  Two types: Open ended manometer is open to the atmosphere and measures the pressure difference between a the pressure of a gas and atmospheric pressure.

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III.  Gas Laws A.  Boyle�s Law

1.  Experiment

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2.  Data

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3.  Boyle�s Law: Molecular View a.  Pressure is caused by the molecules

striking the sides of the container.

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4.  Ex: A cylinder with a movable piston has a volume of 7.25 L at 4.52 atm. What is the volume at 1.21 atm?

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5.  Ex: A balloon is put in a bell jar and the pressure is reduced from 782 torr to 0.500 atm. If the volume of the balloon is now 2.78 x 103 mL, what was it originally?

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B.  Charles� Law 1.  Experiment

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B.  Charles� Law 2.  Data

y = 0.158x + 40.718 R² = 0.97935

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50

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40 50 60 70 80 90 100

Hei

ght o

f Gas

Bub

ble

(mm

)

T (°C)

Height of an Air Bubble vs. Temperature

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B.  Charles� Law 3.  Data: different axes

y = 0.158x + 40.718 R² = 0.97935

0

10

20

30

40

50

60

-300 -250 -200 -150 -100 -50 0 50 100 150

Hei

ght o

f Gas

Bub

ble

(mm

)

T (°C)

Height of an Air Bubble vs. Temperature

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4.  Ex: A gas has a volume of 2.57 L at 0.00 °C. What was the temperature at 2.80 L?

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5.  Ex: The temperature inside a balloon is raised from 25.0 °C to 250.0 °C. If the volume of cold air was 10.0 L, what is the volume of hot air?

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6.  Combined Gas Law

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C.  Ideal Gas Law 1.  By combining the gas laws we can write a

general equation

2.   n is the number of moles of gas 3.   R is called the gas constant 4.  When P is in atm and V is in Liters:

€

R = 0.08206L atmmol K

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4.  Ex: How many moles of gas are in a basketball with total pressure 24.3 psi, volume of 3.24 L at 25°C?

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D.  Standard Conditions 1.  Because the volume of a gas varies with

pressure and temperature, chemists have agreed on a set of conditions to report our measurements so that comparison is easy – we call these standard conditions:

2.  STP = Standard Temperature and Pressure:

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3.  Ex: What volume will 1.00 mol of O2 occupy at 1.00 atm and 273 K?

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4.  Ex: A gas occupies 10.0 L at 44.1 psi and 27 °C. What volume will it occupy at 1.00 atm and 273 K?

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5.  Ex: Calculate the volume occupied by 637 g of SO2 (MM 64.07) at 6.08 x 104 mmHg and –23 °C.

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E.  Mixtures of Gases 1.  When gases are mixed together, their

molecules behave independently of each other

a.  all the gases in the mixture have the same volume

all completely fill the container

b.  all gases in the mixture are at the same temperature

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2.  Therefore, in certain applications, the mixture can be thought of as one gas

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3.  Dalton�s Law of Partial Pressures a.  The pressure of a single gas in a mixture of

gases is called its partial pressure. b.  The sum of the partial pressures of all the

gases in the mixture equals the total pressure:

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c.  The partial pressure of any one gas, PA, is equal to its mole fraction, χA, times the total pressure:

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4.  Ex: Determine the mass of Ar in a mixture of He, Ne and Ar with: PHe=341 mmHg, PNe= 112 mmHg, PT = 662 mmHg, V = 1.00 L, T = 298 K.

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5.  Ex: Find the partial pressure of neon in a mixture with total pressure 3.9 atm, volume = 8.7 L, temperature = 598 K, and 0.17 moles Xe.

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6.  Ex: Find the mole fractions and partial pressures in a 12.5 L tank with 24.2 g He and 4.32 g O2 at 298 K.

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7.  Ex: Find the mole fraction of neon in a mixture with total pressure 3.9 atm, volume 8.7 L, temperature 598 K, and 0.17 moles Xe.

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IV.  Collecting A Gas A.  Mostly done in lab over water.

1.  Ex: Zn(s) + 2 HCl(aq) H2(g) + ZnCl2(aq)

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2.  The partial pressure of the water vapor, called the vapor pressure, depends only on the temperature.

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3.  Ex: 1.02 L of O2 collected over water at 293 K with a total pressure of 755.2 mmHg. Find the mass of O2.

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4.  Ex: 0.12 moles of H2 is collected over water in a 10.0 L container at 323 K. Find the total pressure.

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V.  Gas Problems with Stoichiometry A.  The ideal gas law allows us to convert from the

volume of the gas to moles: then we can use the coefficients in the equation as a mole ratio

P, V, T of Gas A mole A mole B P, V, T of Gas B

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1.  Ex: What volume of H2 is needed to make 35.7 g of CH3OH at 738 mmHg and 355 K? CO(g) + 2 H2(g) → CH3OH(g)

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2.  Ex: How many grams of H2O form when 1.24 L H2 reacts completely with O2 at 1.00 atm and 273 K? O2(g) + 2 H2(g) → 2 H2O(g)

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3.  Ex: What volume of O2 at 0.750 atm and 313 K is generated by the thermolysis of 10.0 g of HgO? 2 HgO(s) → 2 Hg(l) + O2(g)

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V.  The Kinetic Molecular Theory of Ideal Gases

A.  Gases are composed of particles that are flying around very fast in their container(s).

B.  The size of a particle is negligible compared to the volume of the gas.

1. 

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C.  The collision of one particle with another (or with the walls of the container) is elastic.

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D.  The average kinetic energy of a particle is proportional to the temperature in Kelvin.

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4.  Gas particles have a distribution of Kinetic Energy values called the Boltzmann Distribution that is the same for all particles at the same temperature.

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5.  But all gases have different masses and therefore different velocities even at the same temperature

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6.  Ex: Draw a Boltzmann Distribution using molecular speed on the x-axis for methane at T = 300 K and at T = 500 K.

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7.  Ex: Draw a Boltzmann Distribution using molecular speed on the x-axis for methane and neon at the same temperature.

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VI.  Diffusion and Effusion

A.  The process of a collection of molecules spreading out from high concentration to low concentration is called __________.

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B.  The process by which a collection of molecules escapes through a small hole into a vacuum is called __________.

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C.  Diffusion and effusion both occur more rapidly for molecules with higher velocities.

D.  Ex: Which will diffuse more rapidly: oxygen gas or argon gas?

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VII.  Real Gases

A.  At STP, most gases are pretty close to ideal:

1.  Ideal gas law assumes

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B.  At low temperatures and high pressures, gases act less ideal.

1.  At low temperatures, the speed of the particles is lower.

2.  At high pressures, the particles are forced closer together so that IMF are more important.