physical characteristics of gases - ms. tabors … · web viewat high temperatures, the gas...

Name: ______________________Chemistry 1 Notes, 2012–13; P. Holloman

Topic 8 – Gases & Kinetic-Molecular Theory

2.1.5 – Explain the relationships among pressure, temperature, volume, and quantity of gas, both qualitative and quantitative.

I. Ideal Gases, Real Gases & KMT Ideal gases are gases which conform perfectly to all 5 assumptions of the Kinetic – Molecular

Theory (KMT) of gases:1. Gases are “point masses” with negligible volume.

(i.e. – Gas molecules themselves take up essentially no volume/space at all, especially compared with the distances separating one gas molecule from another. There is a lot of empty space between gas molecules.)

2. Gas particles are in constant motion, moving rapidly in straight lines in all directions. Thus they have KE (in fact, much more KE than either liquids or solids).

3. Collisions between gas particles or between gas particles and container walls are elastic no KE lost in the collision.

4. There are no forces of attraction or repulsion between gas particles.5. The average KE of a gas is directly proportional to the temperature (K) of the gas.

when T decreases, KE decreases when T increases, KE increases

Properties of gases you (hopefully) already know: Gases have no definite shape or volume. They expand to fit the shape of their

container, and they can also be compressed a great deal. Gases are fluids. They flow, and they can also diffuse. Gases are much less dense than solids or liquids.

A real gas is a gas that does not completely obey all the assumptions of the kinetic theory of gases, stated above. There is really no such thing as an “ideal gas” because all gas molecules will at least experience

van der Waal’s attractions (& they experience inelastic collsions, etc.). Real gases behave most like ideal gases at low pressure and high temperature:

At low pressures, the gas particles are spread out, and their volume is more negligible, relative to the container volume. Also, since the gas molecules are farther apart, they are usually able to avoid intermolecular forces of attraction.

At high temperatures, the gas molecules are zipping around so quickly that intermolecular attractions are not easily established, and gas molecules readily overcome them (continuing to move in straight lines).

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Recall Avogadro’s Law again here:

Avogardro’s Law – equal volumes of gases at the same temperature & pressure contain an equal number of particles (and thus an equal # of moles)

For example, this means that 22.4 liters of helium and 22.4 liters of radon (assuming both are at STP) would both contain 6.022 x 1023 atoms of gas, despite the fact that the mass of radon is more than 50 times greater than that of helium.

This fact can be expressed in the following formula:

nV = k

n1

V 1 =

n2

V 2 , where “n” = # of moles of gas & “V” = volume of gas

5.00 L of a gas is known to contain 0.965 mol. If the amount of gas is increased to 1.80 mol, what new volume will result (at an unchanged temperature and pressure)?

There are two important implications of Avogadro’s Law: All gases show the same physical behavior. A gas with a larger volume must consist of a greater number of particles.

TEMPERATURE & PRESSURE CONVERSIONS

In all of this discussion, don’t forget that the pressure of a gas is due to gas particles colliding with their container walls.

3 ways to measure pressure:(1) mm Hg (also called torr)(2) atmospheres of pressure (atm)(3) pascals (Pa) – often kilopascals (kPa)

Average atmospheric pressure at sea level at 0C = 1 atm = 760 mm Hg = 101.3 kPa

The average atmospheric pressure in Denver, CO = .830 atm.

Express this in: (1) mm Hg (2) kPa

Remember that the volume of a gas depends on its T & pressure. So to be able to accurately compare gases, we often compare them at: 1 atm of pressure and 0C = STP (standard temperature & pressure).

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For all gas laws, remember to convert the temperature to K!

Remember the relationship between K and C: K = C + 273

II. Boyle’s Law Boyle’s Law – At constant T, the volume of a sample

of gas varies inversely with the pressure.

PV = k P1V1 = P2V2

For a fixed mass of an ideal gas (the “fixed mass” part is important – you must assume no molecules can enter or escape): As volume , pressure (when T is constant). As the V decreases, concentration of the particles increases, resulting in more collisions with

the container walls, and thus greater pressure. Since pressure and volume are inversely proportional, decreasing the volume by one-half

would double the pressure.

A helium-filled balloon has a volume of 70.0 L and 800. mm Hg pressure. What volume will it occupy at 450. mm Hg, assuming constant temperature?

III. Charles’ Law Charles’ Law – At constant P, the volume of

a sample of gas varies directly with the Kelvin temperature.

VT = k

V 1

T 1 =

V 2

T 2

For a fixed mass of an ideal gas: As temperature , volume (when P is constant). As we just discussed, higher temperatures higher average velocity of gas particles, and

thus more energetic collisions between gas particles and container walls. To maintain constant pressure, there must be fewer collisions per unit area. Therefore, volume of the gas must increase.

Temperature and volume are directly proportional, so doubling the temperature would double the volume of the gas.

A helium-filled balloon has a volume of 55.0 L at 25.0C and 133 kPa. What volume will it occupy at and 10.0C and 133 kPa?

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IV. Gay-Lussac’s Law Gay-Lussac’s Law – At constant V,

the pressure of a sample of gas varies directly with the Kelvin temperature.

PT = k

P 1

T 1 =

P 2

T 2

For a fixed mass of an ideal gas: As temperature , pressure (when V is constant). At higher temperatures, the particles have a higher average velocity, and thus collide with

container walls with greater force (i.e. – each collision is more energetic). Since gas molecules are moving faster, as long as the volume is held constant, they will collide more frequently with the container walls.

Temperature and pressure are directly proportional, so doubling the temperature would double the pressure of the gas.

A helium-filled balloon is under a pressure of 1.55 atm at 25.0C. What pressure would the gases in the balloon exert at 20.C at constant volume?

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V. Combined Gas Law When the amount of a gas is fixed:

P 1 V 1

T 1 =

P 2 V 2

T 2

A helium-filled balloon has a volume of 50.0 L at 25.0C and 820. mm Hg. What volume will it occupy at 650. mm Hg and 10.0C?

A helium-filled balloon is under a pressure of 112 kPa at 32.0C. By how many degrees would the temperature have to drop in order for the pressure exerted by the gas in the balloon to decrease by 20 kPa?

When you read a problem and one of these components (P, V, or T) is missing, just assume that it was held constant and therefore would cancel out (divide out in the equation).

Also, all temperatures in gas law problems must be in Kelvin!

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VI. The Ideal Gas Law

PV = nRT

P = pressure n = # of moles of gasV = volume R = a constant (ideal gas constant)

T = temperature (K)

3 values for R: 0.0821

L ¿atmmol ¿ K = 62.4

L¿mm Hgmol ¿K = 8.314

L¿ kPamol¿ K

Obviously, the only difference in units for each R value is the unit for pressure. So when you are setting up these problems, choose the unit for R which has the same pressure unit as the pressure in the problem.

The purpose of the units for R is to cancel out all the other units in the problem. Therefore, V must be in liters (L), because R has liters in it, which must cancel out.

What is the volume in liters occupied by 0.250 mol of oxygen at 20.0C and 740 mm Hg pressure?

What mass in grams of chlorine (Cl2) is contained in a 10.0 L tank at 27C and 3.50 atm of pressure?

What pressure in atmospheres is exerted by 54.7 g of sulfur dioxide gas in a 4.08 L container at 35.0C?

How do you know when to use the Combined Gas Law and when to use the Ideal Gas Law?

Combined Gas Law – you will be given at least 2 of P, V, or T (i.e. – 2 temperatures, 2 pressures, and/or 2 volumes)

Ideal Gas Law – you will see some mention of either moles or grams (and only one P, V, and T)

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VII. Dalton’s Law of Partial Pressures You’ve got a mixture of different gases in a container.

Each exerts a specific amount of pressure. The pressure of each gas in a mixture = partial pressure of that gas.

Dalton’s Law of Partial Pressures – the total pressure of a mixture of gases = the sum of all the partial pressures of the component gases

If you have a mixture of gases:

PT = P1 + P2 + P3 + …

Gases collected by water displacement are never pure – they’re always mixed with water vapor molecules as they evaporate from the H2O surface.

Patm = Pgas + PH2O (note: PT = total pressure is the same as: Patm = atmospheric or barometric pressure)

Water vapor pressure varies with temperature. So, you must know T and the barometric pressure at the time of the experiment & use a reference table to find water vapor pressure at that T. (see next page…)

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2KClO3(s) 2KCl(s) + 3O2(g) The oxygen was collected from this decomposition by water displacement. The barometric pressure during the experiment was 731.0 mm Hg and the T was 20.0C. What was the partial pressure of the oxygen collected?

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physical characteristics of gases - ms. tabors … · web viewat high temperatures, the gas...

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