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States of Matter

“State” refers to form or physical appearance – whether the sample of matter exists as solid, liquid, orgas.

The state of a sample of matter reflects the relative strength of Intermolecular forces at work.

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GasGas characteristics:•Weak intermolecular attractions (often London dispersion forces);•Large distances between molecules

(or atoms if Noble gases);•No definite shape of its own – fills

the container instead;•Low density (mass to volume ratio)

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SolidSolid characteristics:characteristics:

•Stronger intermolecular forces or Stronger intermolecular forces or high mass compared to liquids high mass compared to liquids

and gases;and gases;•Molecules or particles in very close Molecules or particles in very close

proximity to each other;proximity to each other;•Maintains own shape withoutMaintains own shape without container;container;•High density relative to gases.High density relative to gases.

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Liquid Liquid characteristicscharacteristics::•Stronger intermolecular forces Stronger intermolecular forces than gases or higher mass;than gases or higher mass;•Distance between molecules Distance between molecules larger than in solids, smaller larger than in solids, smaller than than in gases;in gases;•Takes shape of container but Takes shape of container but does not always fill entire does not always fill entire volume;volume;•Density < solid, but > gas.Density < solid, but > gas.

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About GasesAbout Gases

Gas properties we can measure:Gas properties we can measure:

PressurePressure

VolumeVolume

TemperatureTemperature

Moles (quantity of matter)Moles (quantity of matter)

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Gas molecules are in constant motion and collide with walls of container.

PressurePressure =

force of collision ÷ area of container wall, or

Pressure = Force/Area

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Gas pressure can be measured with a barometer

Top of tube sealed

Pan of mercury (Hg); open top

Bottom of tube open to Hg

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The force of the atmosphere pushing down on the surface of the mercury supports a vertical column of Hg above the level of the open surface.

atmosphere

Hg

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atmosphere

Hg

The distance the column of Hg rises above the surface can be measured in inches or millimeters….

Column height

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atmosphere

Hg

Column height

The pressure of the atmosphere at sea level is 1 atmosphere (atm) =30 inches Hg = 760 mm Hg

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The pressure of any gas can be measured in a device similar to the barometer, called a manometer.

Gas pressures are thus measured in atmospheres or mm Hg in the science lab (not inches of Hg).

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The volumevolume of a gas is taken to be the volume of the container enclosing it since the gas fills all the available space.

Gas volumes are typically measured in Liters (L).

Note: 1000 milliliters (ml) = 1 L

1 cc = 1 cm3 = 1 mL

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TemperatureTemperature of gases may be given in °C, but calculations must use the temperature on the Kelvin scale.

The lowest possible temperature at all is called absolute zero.

It is written 0 K (0 kelvins). At this temperature, molecules are no longer moving around from place to place.

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Comparing Celsius and Kelvin Scales

0 K -273° C

0° C273 K

100° C373 K

kelvins = °C + 273

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The quantity or amount of a gas is described by the number of molesnumber of moles, symbolized as nn.

We will see how the number of moles of a substance is calculated in a later chapter. For now, the number will be given if it is needed in a problem.

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The ideal gas lawideal gas law describes the relationship among pressure, volume, temperature, and number of moles for many gases.

If we multiply pressure and volume, and divide by temperature times number of moles, the ratio has a constant value, R, the gas constant:

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P·Vn·T

= R Ideal Gas Law

( · means “multiplied by” or “times”)

This equation means that any combination of pressure, volume, temperature, and number of molesdescribing a gas under a particular set of circumstances gives an unchanging number for R.

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The ideal gas law can be used in two ways:

(1) To calculate a new value for a property as others are changed, or

(2) To calculate a value for one of the properties of a gas if all the others are known under one set of conditions.

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Changing conditions of a gasSince R has an unchanging value, changes in P, V, n or T are proportionally related.

Let’s write values for one set of conditions as P1, V1, n1, and T1.For a second set of conditions writeP2, V2, n2, and T2.

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This allows us to say that

P1·V1 P2·V2=n1·T1 n2·T2

Here is a sample problem to illustrate how this is used…

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A balloon is filled with 3.0 L gas at 50° C. What is the volume of the gas if the temperature is lowered to 0 ° C?

Notice that nothing is said about pressure or number of moles of gas. We assume the pressure and number of moles of gas does not change. So, P1 = P2 and n1 = n2.

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P1·V1 P2·V2

n1·T1 n2·T2

=

If in general,

Then when P1 = P2 and n1 = n2 the general equation becomes just

V1 V2

T1 T2

=

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In this problem we already know V1, T1, and T2. We want to find V2. Solve the equation on the last slide by cross-multiplication and division:

V1·T2 = V2·T1 (cross multiply)

V1·T2

T1

= V2 (after dividing)

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Now the correct numbers and units can be put into the equation to solve the answer.

WARNINGWARNING: temperature must be in kelvins !!! (we can’t use °C here)

So T1 = 50 + 273 = 323 k

T2 = 0 + 273 = 273 k

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Plugging in:

(3.0 L )·(273 k)

(323 k)= 2.5 L

This makes sense: a balloon shrinks or contracts when it is cooled, so the volume should be smaller.

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We also use the ideal gas law to calculate a value for one of the properties of a gas if all the others are known under one set of conditions… this requires thatwe know the numerical value of R, the gas constant.

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When P is given in atmospheres,

V in Liters,

T in kelvins, and

n as a pure number,

Then, R =0.0821 L·atm/(mole·kelvin)

Do not memorize this number, it will be provided on exams!

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Example

A steel tank having a volume of 25 L is filled with gas at room temperature (25° C) to a pressure of 1500 pounds per square inch (psi).

If 1 atmosphere = 14 psi, how many moles of gas are in the tank?

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First, convert all values to the proper units for the ideal gas equation.

kelvins = 25 + 273 = 298

1 atm ?

14 psi 1500 psi=

? = 1 atm·1500 psi/14psi = 107 atm

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So if P·V = n·R·T,

Then (P·V)÷(R·T) = n

(107 atm)·(25 L)

(0.0821 L·atm/mole·K)·(298 K)=

109 moles of gas

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Some final thoughts about gases…

Since the attractive forces between gases are so weak, most of the space between gas molecules is empty. Each gas molecule acts pretty much independently.

John Dalton (he of atomic theory fame) recognized this. He demonstrated that:

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In a mixture of gases, each gas independently exerts its own pressure. As a result, the total pressure of the mixture is the simple sum of the pressure of each gas present. We write:

Ptotal = P1 + P2 + P3 +…Pz for z number gases in the mixture.

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The pressure of each gas in the mixture (P1 or P2 or P3, etc.) is called the partial pressure of the gas.

Since all the gases in the mixture have the same total volume and temperature, the partial pressure is related to how many moles of the gas are in the mixture.

Ntotal = n1 + n2 + n3 +…nz.

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Practical application:

Earth’s air is about 79% N2, 20% O2, and the remaining 1% is CO2, H2O, He, Ar, etc…

Thus, the partial pressure of O2 in the air is about 0.20 atmosphere.