reminder: angel quiz 8 due on thur 10/20 - pennsylvania ...courses.chem.psu.edu/chem110fall/lecture...

Jensen Chem 110 Chap 10 Page: 1

Week 8: Lectures 22 – 24

Lecture 22: W 10/12

Lecture 23: F 10/14

(Special lecture by Dr. Ben Lear)

Lecture 24: M 10/17

Reading:

BLB Ch 10.1 – 10.9

Homework:

BLB 10: 23, 30, 45, 5, 71, 75, 82, 83, 84;

Supp 10: 1 – 15

Reminder:

No Angel Quiz on Thur 10/13

ALEKS Objective 8 due on Tue 10/18 Angel Quiz 8 due on Thur 10/20

Jensen Office Hour: 501 Chemistry Building

Thursday 10/13: cancelled

Tuesday 10/18: 10:30 – 11:30 am


Gas Molecules’ Characteristics

! Gas molecules are constantly moving

expand in whatever volume is available

mix completely with one another

! They are far apart (10 times as far as they are big)

can be easily compressed

! They move in straight lines

! They collide with each other

! They collide with walls: pressure

! Higher temperature yields faster motion

! Lower temperature yields slower motion and

eventually condensation

Gases are described in terms of: pressure (P),

temperature (T), volume (V), # moles (n)

All gases behave similarly at low pressure

Gases will mix in all proportions with other gases to

form homogeneous mixtures


Pressure

• Pressure: force per unit area

Force: Kg•m•s–2

, or Newton (N); Unit area: m2

• SI unit for pressure: 1 N•m–2

= 1 Pa (Pascal)

• Standard Atmospheric Pressure**:

1 atm = 1.013 x 105 Pa

1 atm = 760 torr (or mm Hg)

[1 atm = 14.7 lb/in2]


Measuring Pressure

Barometer used to measure Patm

The key idea is balance force on area

Patm " height (h) of column of liquid

Measure P in terms of height of Hg

1 atm = 760 torr “=” 760 mm Hg

[know this conversion!]

Patm PHg

Patm = PHg

dl= density of liquid (here: Hg)

g = gravitational constant

Patm = constant x h

Patm = Fatm/A

PHg = Fl/A = gdlh

so,


Mercury Manometer

Used to measure the difference in pressure

between open or closed end and that of a gas

in a vessel.

Closed Ended: Pg = h (mm Hg)

Open Ended: Which P is greater?

Pgas = Patm __ Ph Pgas = Patm __ Ph


Example: The height of the column of

mercury in the open-ended manometer shown is found to be 65 mm. If the external

pressure is 1.06 atm, what is the gas

pressure inside the bulb?

A. 0.85 atm

B. 0.97 atm

C. 1.15 atm

D. 1.71 atm

E. The pressure cannot be

determined from the information given.


Understanding Gases

State of gas is described by:

• n = moles of gas

• P = pressure

• V = volume of container

• T = (absolute) temperature (K = °C + 273.15)

STP: standard temperature & pressure

(T = 273.15 K; P = 1 atm)

Three foundational relationships:

! Boyle!s Law (P and V)

! Charles! Law (V and T)

! Avogadro!s Law (V and moles)

Combining these three to one equation

The ideal Gas Law (P, V, T, and moles):

P V = n R T


! Boyle’s Law (volume & pressure)

V of a fixed amount of gas at constant T is inversely

proportional to P

V " 1/P or

PV = constant

(T,n fixed)

! Charle’s Law (volume & temperature)

V of fixed amount of gas at constant P is

proportional to the absolute temperature

V " T or

V/T = constant

(P,n fixed)

Note: T in absolute

temperature (K)!

K = °C + 273.15

V 1/2V


! Avogadro’s Law (volume & moles)

V of gas at constant T and P is proportional to the

number of moles of gas:

V " n or

V/n = constant

(P,T fixed)

So far: V ! 1/P (Boyle!s law)

V ! T (Charles!s law)

V ! n (Avogadro!s law)

Combining these three to one equation:

Units of R (gas constant) are very important!

Ideal Gas Law: P V = n R T

V

n


Using Ideal Gas Law: P V = n R T

! Given 3 quantities, solve for the 4th

Example: What is the volume occupied by

1 mol of gas at exactly 0°C and 1atm (STP)?


Practice Example: How many molecules

comprise one breath of air with a volume of 2.5 L at body temperature (37 ºC) and a

pressure of 750 mm Hg?

A. 5.8 x 1022 B. 4.4 x 1025

C. 6.2 x 1024

D. 6.7 x 1022

E. 6.0 x 1023


! Changes in P, V, T

Given: initial conditions of Pi, Vi, Ti

final conditions of any two quantities

Find: Value for the third final value

Example: A sample of gas at 25 °C and

1.0 atm in a 2.5 L vessel is allowed to

expand until the pressure is 0.85 atm and

the temperature is 15 °C. What is the final

volume of the gas?


Practice Example: At 27 °C and 1.00 atm, a sample of He gas (2.35 mol) occupies 57.9 L.

What is the volume of this sample at 150 °C

and 1.00 atm?

A. 0.709 L

B. 1.41 L

C. 41.1 L

D. 57.9 L

E. 81.6 L


Summary: Ideal Gas Law PV = nRT

At STP (What T and P? _________________),

1mol of any gas has molar volume VSTP = _____ L.


Application of the Ideal Gas Law:

Density and Molar Mass

Ideal Gas Law: P V = n R T


Density and Molar Mass

At the same T and P, density is

_______________ to molar mass.

Example: Which of these gases has a density of 3.42 g/L at 30°C and 1.2 atm?

A. He

B. Cl2

C. F2

D. Kr

E. Xe


Practice Example: What is the density of

ammonia (NH3) gas in a 4.32 L container at 837 torr and 45 °C?

A. 3.86 g/L

B. 0.717 g/L C. 0.432 g/L

D. 0.194 g/L

E. 4.22 x 10–2 g/L


Gas Mixtures: Partial and Total Pressure

Partial pressure: the pressure a gas would

have if it was the only gas in the container

Dalton!s law of partial pressures:

total pressure of the gas mixture is equal

to the sum of partial pressures

Mole fraction: dimensionless & must sum to 1

Partial pressure:


Example: 3.0 L of He at 5.0 atm and 25°C

is combined with 4.5 L of Ne at 2.0 atm and 25°C at constant T into a 10L vessel. What

is the partial pressure of the He in the 10L

vessel?

What is the total pressure in the 10 L

vessel?


Practice Example: What is the partial

pressure of O2 in the vessel below?

Ptot = 756 torr Gas Mole fraction

T = 300.0 °C Ar 0.320

VTOT=5.00 L N2 0.270

CO2 0.150

Ne 0.160

O2 ?

A. 75.6 torr

B. 242 torr

C. 380 torr

D. 680 torr E. 756 torr

How many moles of CO2 are in this vessel?


Collecting gases over water

Ptotal = Pgas + PH2O

barometric pressure vapor pressure

If you know the barometric pressure, you can

determine the partial pressure of gas by using

the vapor pressure of H2O (Appendix B, Pvap of

H2O)


Example: A student collected 201 mL of H2

over water at 27 oC and a barometric pressure of 733 torr. The vapor pressure of

water at 27 oC is 26.74 torr. How many

grams of H2 were collected?

A. 20.0 g

B. 1.80 x 10!2 g

C. 130 g

D. 8.61 x 10!3 g E. 1.52 x 10!2 g


Kinetic Molecular Theory (KMT)

KMT explains why gases behave the way they do;

look at gases on a molecular level

The 5 key postulates of KMT

1. Molecules move in straight lines; but their

directions are ____________.

2. Molecules are small (The volume they occupy is

small compared to the total volume) – they have

_______ volume.

3. There are _______ intermolecular forces

(molecules do not attract or repel each other).

4. Molecules experience elastic collisions

5. Mean kinetic energy # " T (in K)


Temperature and Molecular Speed

# = average kinetic energy of molecule

u = average (root mean square) speed of molecule

m = mass of molecule (in kg)

" Distribution of molecular speeds: Some

molecules move more slowly; some move faster.

" When T increases, less molecules move

_________, more molecules move __________, so

the average molecular speed _______________.


KMT explains the behaviors of ideal gases

• At constant n and V; P increases as T increases.

T increases, # __________ , u ___________;

more collisions per unit time & harder collisions

so P increases

• At constant n and T, P decreases as V increases.

Constant T means constant # & u.

longer distances between collisions & fewer

collisions per unit time with walls

so P decreases (Boyle!s Law)


Average Molecular Speed, Molar Mass, and

Temperature

" At the same T, different gases have ________ average kinetic energy (#).

" At the same T, different gases have _________

average speeds (u)

" At a given temperature, the _______ a gas is, the

________ its average molecular speed will be.


Average Molecular Speed and Molar Mass

Example: What is the average speed of O2 at

20 °C? Note: use R = 8.314J/(mol•K) and M in

kg/mol.


Practice Example: All three gas containers

below have V = 1 L and T = 25 °C. Which of the following statements is/are true?

1. The average molecular speed is the same

in all three samples.

2. The pressure is the same for all three samples.

3. The average molecular kinetic energy is

the same in all three samples.

A. 1 only

B. 2 only

C. 3 only D. 1 and 2

E. 2 and 3


Other Properties of Gases

• Effusion: leakage of gas

through a small opening

• Diffusion: spread of gas

through space or second

substance.

Rate of effusion (or diffusion) " 1

M

Usually we compare the effusion (or diffusion)

rate of two gases:

Graham!s law:

$ Heavy molecules effuse (diffuse) more

slowly than lighter molecules


Effusion Rate and Molar Mass

Example: An unknown gas effuses at a rate of 0.112 times H2 gas at 25 °C. What is the molar

mass of the gas?


Practice Example: A sample of N2 gas (2.0 mmol) effused through a pinhole in 5.5 s. How long will it take for the same amount of CH4 to effuse under the same conditions?

A. 7.3 s B. 5.5 s C. 3.1 s D. 4.2 s E. 9.6 s


Collisions and Diffusion

" At STP molecules collide ~1010

times per

second. N2 speed = 500 m/s

but…

in 1 s it collides 1010

times

" This means that although molecular speeds

are high at STP, molecules don’t go very far

net distance traveled << (speed x time)

" Mean free path (MFP): distance between

collisions.

MFP is ~6x10

-8 m at 1 atm for air molecules

What happens to the MFP as density and P

decrease?

reminder: angel quiz 8 due on thur 10/20 - pennsylvania ...courses.chem.psu.edu/chem110fall/lecture...

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