The Gas Laws

Some things about gases: Some things about gases: Gases have mass It is easy to compress a gas Gases fill their containers completely Gases diffuse through each other easily Gases exert pressure The pressure of a gas depends on its temperature

Gases may be… Monoatomic: Made of one atom, like He Gases may be… Monoatomic: Made of one atom, like He Diatomic: Made of two atoms, like Cl2 or H2 *This is the case for Br, I, N, Cl, H, O, F Also known as Miss BrINClHOF (Brinklehoff) Polyatomic: Made up of more than two atoms, like CO2, NO2, or CH4 (methane)

Gases exhibit certain behaviors: Gases exhibit certain behaviors: Gases are composed of a large number of particles that behave like hard, spherical objects in a state of constant, random motion. Basically, gas particles are like billiard balls in a 3-D pool table, and they are all moving all over the place all the time in different directions

These particles move in a straight line until they collide with another particle or the walls of the container. Then they bounce off, and move again- these collisions are elastic

A word about Ideal Gases here…. Gases in the real world are different than ideal gases… which is what we use for gas laws (all that stuff about IMFs earlier? We need to ignore that for gases, or else these gas laws wouldn’t apply…but real gases in the real world do not behave like this ideal gas that we need to use for calculations….)

These particles are much much (double much intended) smaller than the distance between particles. Most of the volume of a gas is therefore empty space. Compared to the container, the volume of the gas is zero. So, we say the volume of the container is the volume of the gas

There is no force of attraction between gas particles or between the particles and the walls of the container. Keep in mind- things aren’t repelled, either….no attraction, no repulsion…

Collisions between gas particles or collisions with the walls of the container are perfectly elastic. None of the energy of a gas particle is lost when it collides with another particle or with the walls of the container. This is why gases take the shape of their container! The energy of the system is constant as long as the pressure and temperature remain constant.

The average kinetic energy of a collection of gas particles depends on the temperature of the gas and nothing else. Think back to the fact that temperature is a measure of Kinetic Energy (the random motion of molecules)

Kinetic Molecular Theory of Gases (KMT) Kinetic Molecular Theory of Gases (KMT) Gases consist of very small particles , each of which has a mass The distance separating gas particles is very large- so much so that we say the volume of the gas is negligible as compared to the volume of the container (the gas itself has no volume)

KMT, continued Gases have mass Gases have no volume exert no force on one another Gas particles are in random, rapid, constant motion Collisions with other gas particles or the walls of the container are elastic The average KE of a gas depends on the temperature of the gas Gas particles

Measuring Gases Volume =V Temperature =T Pressure =P We measure gases in several ways… Volume =V Temperature =T Pressure =P Number of Moles =n

Volume (V) We usually measure volume in We usually measure volume in Liters (L), but sometimes in other metric units 1L = 1000mL 1L = .001m3 We will use these conversions- be sure to know them!

What is Temperature? Temperature is a measure of heat; more specifically it is the (average) measure of the random kinetic energy of the molecules in an object Kinetic energy: Energy of motion More motion = More KE = Higher temperatures Less Motion= Lower KE = Lower temperatures

Temperature (T) For most scientists, the Celsius scale is used For most scientists, the Celsius scale is used However, we need to use the Kelvin scale for gas laws

Why? Why this strange and bizarre scale that uses a boiling point of 373K and a freezing point of 273K for water? Well, kiddies, it’s because our “normal” temperature scales are based upon numbers that make sense to use (or not) (like freezing at 0°C and boiling at 100 °C) or are a bit more convoluted (like the Fahrenheit scale, where zero comes from the temperature of ice, water and NH4Cl and body temperature was 98 °F and still water with ice was 32 °F. )

An Absolute Temperature Scale The Kelvin scale bases temperature on an absolute scale, where temperatures correspond to the amount of motion of the particles Absolute zero (O K) is when there is no molecular motion (at all) Scientists have gotten close to O K, but not quite there

So why do we need to use it again? Calculations using temperature of zero could be undefined or have no value (which really can’t be) Can’t have negative volumes (from using negative temperatures) The Kelvin scale avoids all of these issues

The Kelvin Scale Is based in Absolute Zero, which is -273°C 0K= -273°C Is based in Absolute Zero, which is -273°C 0K= -273°C 273K=0°C To convert between K and °C, °C + 273 =K or K -273 = °C It’s that simple, which is good since no gas laws calculations can use °C

Pressure (P) Gas pressure is created by the molecules of gas hitting the walls of the container. This concept is very important in helping you to understand gas behavior. Keep it solidly in mind. This idea of gas molecules hitting the wall will be used often. Pressure is force measured over an area P=Force/ area and yes, Physics children, Force = mass (acceleration)

Units of Pressure atmospheres (atm) millimeters of mercury (mm Hg) atmospheres (atm) millimeters of mercury (mm Hg) Pascals (= Pa) kiloPascals (= kPa) Standard pressure is defined as: 1 atm 1atm =760.0 mm Hg 1 atm=101.325 kPa

Measuring Pressure of Gases Manometers

Manometers Measure the pressure of a gas as compared to the outside world

Moles (n) We’ve been here before. Calm down about it. We’ve been here before. Calm down about it. Remember that 1 mole is 6.02E23 pieces of something- in this case, usually molecules of gas (but sometimes atoms, if not a diatomic gas). Also, 1 mol gas at STP= 22.4L (= means occupies, takes up, etc)

A few guys and their laws…. Dalton- Partial Pressures Boyle- Pressure and Volume Charles- Volume and Temperature Gay Lussac-Pressure and Temperature Graham- Rate of diffusion Avogadro- moles and volume

And a few laws with no guys… Ideal Gas Law- pressure, volume, temperature related to number of moles Combined Gas Laws- relate changes in pressure, temperature, and volume in a sealed container (no change in moles)

Avogadro’s Law You’ve heard of him before… You’ve heard of him before… He’s the guy who came up with the number of particles in a mole He related the volume of a gas to the number of moles 1mol= 22.4L gas at STP The more moles, the higher the volume

Dalton’s Law of Partial Pressures The total pressure in a sealed container of gas are the sum of all the partial pressures of the gases in the container PT= P1+P2+P3…. For as many gases are present

Using Dalton’s Law…. What is partial pressure of oxygen gas in a container of oxygen, nitrogen, and hydrogen, if the partial pressure of nitrogen is .68atm, the partial pressure of hydrogen is .24 atm, and the total pressure is 1.02atm? PT= P1+P2+P3 PT= Pnitrogen+Phydrogen+Poxygen 1.02atm= .68atm + .24 atm +Poxygen 1.02atm-.68atm-.24atm=Poxygen

Boyle’s Law Relates pressure and volume, while temperature and number of moles are constant (so they do not appear in the equation)

Boyle’s Law: P1V1=P2V2 In a closed rigid container of a gas at a constant temperature, the pressure times the volume remains constant (P1V1=k) Pressure and volume are inversely related The P1 is the pressure at the first volume (V1), while P2 is the pressure at the second volume (V 2).

Boyle’s Law: P1V1=P2V2 The product of pressure and volume remains constant as long as the temperature remains constant. (The number of moles must also remain constant.) Volume Pressure When volume is high, pressure is low When the volume is low, pressure is high

Using Boyle’s Law If a balloon with a volume of 3L is under a pressure of 1 atmosphere, determine the new volume if the pressure is changed to .8 atm. We are given P1, V1, and P2. We are asked to find V2 Two key words here are new and changed- to ID these measurements as linked (having the same subscript) What is the new volume?

Charles’ Law Charles’ law relates volume and temperature, at a constant pressure and number of moles in a flexible container. Since the pressure and number of moles are constant, they do not appear in the equation.

Charles’ law V1/T1=V2/T2 In a closed container of a gas at a constant temperature, the pressure times the volume remains constant (P1V1=k) The P1 is the pressure at the first volume (V1), while P2 is the pressure at the second volume (V 2).

Charles’ Law V1/T1=V2/T2 can be rearranged to read V1T2=V2T1 V1/T1=V2/T2 can be rearranged to read V1T2=V2T1 Why would we care to rearrange this? This means no division in the equation. You can use it either way, just remember that they are DIRECTLY PROPORTIONAL.

Charles’ Law As the temperature increases, the volume increases. As the temperature increases, the volume increases. As the temperature decreases, the volume decreases. Temperature and volume are proportionally related.

Chuck’s law (still…) Think again about temperature- it is the KE of the gas particles. Think about what the volume is a result of: the force that the gas molecules are exerting of the container Think about how if something hits another thing at a higher speed- it hits with more force. More force is pushing harder. Pushing harder means further. This means greater volume when we are dealing with a flexible container!

Combined Gas Law (Putting it all together) (P1V1)/ T1=(P2V2)/T2 Takes all other gas laws into account, even if you can’t see them here (they cross out of the equation) When in doubt about most of the guy’s laws, you can use this one, because when the pressure, volume, or temperature is constant, you have the law you need.

Gay Lussac’s Law Relates pressure and temperature, when volume is kept constant (P1/T1=k) P1/T1= P2/T2 Or P1T2=P2T1

Ideal Gas Law First, a few words about ideal gases: First, a few words about ideal gases: Ideal gases follow the gas laws at ALL pressures and temperatures Ideal gases cannot be liquefied by cooling and/ or applying pressure KMT assumes that all gas molecules have no attraction to each other, and has no volume These above statements aren’t true However, in most cases, all gases behave like ideal gases, so the gas laws hold true in most cases

The Ideal Gas Law PV=nRT n= number of moles R= ideal gas constant PV=nRT n= number of moles R= ideal gas constant R=.0821 atm L/ mol K R= 62.4 mmHg L/ mol K R= 8.31E3 Pa L/ mol K Why so many Rs? Different measurements of pressure

Graham’s Law of Effusion Diffusion: tendency of ions and molecules to move from an area of high concentration to an area of low concentration Effusion: Gases escaping from a tiny hole in a container (because of diffusion or pressure differences) The rate of effusion of a gas is inversely proportional to the square root of its molar mass

More on Graham’s Law… KE= ½mv2 KE= ½mv2 So, when two bodies having the same KE but different masses, the smaller one must be moving faster….why does this matter? If two gases in a container have the same temperature (the same KE), the lighter one must be moving faster

Graham’s Law Rate A √ molar mass B _______ = ______________ Rate A √ molar mass B _______ = ______________ Rate B √ molar mass A Lighter gases effuse faster- that’s why party balloons filled with He are must faster to deflate than those filled with air (air is mostly heavier N2 and O2)