How do gases behave
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How Do Gases Behave?. What is a solid, liquid or gas?. Help Marvin the Martian understand what a solid, liquid and gas are! Draw what solids, liquids, gases look like Describe physical/chemical properties What would happen if we changed pressure? What would happen if we changed temperature?.

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How Do Gases Behave?

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How Do Gases Behave?


What is a solid, liquid or gas?

  • Help Marvin the Martian understand what a solid, liquid and gas are!

  • Draw what solids, liquids, gases look like

  • Describe physical/chemical properties

  • What would happen if we changed pressure?

  • What would happen if we changed temperature?


What is Pressure?

  • Pressure = Force/Area

  • 1 atmosphere (atm)

  • 760 Torr

  • 760 mmHg

  • 1.01 Bar

  • 101,327 Pascal

  • 101.3 Kpa

  • 14.7 lbs/in2

  • Measured with

    a barometer


MANOMETER

  • Column of mercury to measure pressure.

  • h is how much lower or higher the pressure is than outside.

  • Pgas = Patm - h

  • Pgas = Patm + h

h

h


What is Temperature?

  • Average Kinetic Energy (1/2 mv2) of an atom or molecule

  • Measured in Fahrenheit, Celsius or Kelvin (SI)

  • F = (C x 1.8) + 32

  • K = C + 273

  • 0 Kelvin: absolute zero (atom stops moving completely)

  • Is there a maximum temperature in the universe?


Kinetic Molecular Theory

  • Theory explains why ideal gases behave the way they do.

  • Assumptions that simplify the theory, but don’t work in real gases.

    • The particles are so small we can ignore their volume.

    • The particles are in constant motion and their collisions cause pressure.

    • The particles do not affect each other, neither attracting or repelling.

    • The average kinetic energy is proportional to the Kelvin temperature.

    • The molecules move in straight path and all collisions are elastic


What is an Ideal Gas?

  • An ideal gas or perfect gas is a hypothetical gas consisting of identical particles of:

    • Negligible volume

    • With no intermolecular forces

    • Atoms or molecules undergo perfectly elastic collisions with the walls of the container

  • Ideal gas law calculations are favored at low pressures and high temperatures.

  • Real gases existing in reality do not exhibit these exact properties, although the approximation is often good enough to describe real gases.


What is Boyle’s Law?

  • In the mid 1600's, Robert Boyle studied the relationship between the pressure P and the volume V of a confined gas held at a constant temperature.

  • Boyle observed that the product of the pressure and volume are observed to be nearly constant.

  • The product of pressure and volume is exactly a constant for an ideal gas.

  • P * V = constant

  • This relationship between pressure and volume is called Boyle's Lawin his honor.


BOYLE’S LAW

V

P (at constant T)


Slope = k

V

1/P (at constant T)


22.41 L atm

O2

PV

CO2

P (at constant T)


20.5 L of nitrogen at 25ºC and 742 torr are compressed to 9.8 atm at constant T. What is the new volume?

P1V1=P2V2

(0.98 atm)(20.5 L) = (9.8 atm)(V2)

20.09 atm*L/9.8 atm= V2

2.1 L = V2

30.6 mL of carbon dioxide at 740 torr is expanded at constant temperature to 750 mL. What is the final pressure in kPa?

(30.6mL)(740Torr)=(750 mL)(P2)

22,644 mL*Torr/750 mL= P2

30.2 Torr =P2

(30.2 Torr) (1 atm/760 Torr) (101.3 kPa/1 atm)=

3059.3 kPa/760= 4.03 kPa


What is Charles’ Law?

  • The relationship between temperature and volume, at a constant number of moles and pressure, is called Charles and Gay-Lussac's Law in honor of the two French scientists who first investigated this relationship.

  • Charles did the original work, which was verified by Gay-Lussac. They observed that if the pressure is held constant, the volume V is equal to a constant times the temperature T, or:

  • V / T= constant


CHARLES LAW

He

CH4

H2O

V (L)

H2

-273.15ºC

T (ºC)


Examples

What would the final volume be if 247 mL of gas at 22ºC is heated to 98ºC , if the pressure is held constant?

247 ml/295 K = X ml/371 K

91,637 mL * K = 295 X * K

91,637 mL * K/295 K= X

310 mL = X

If the volume of oxygen at 21 °C is 785 L, at what temperature would oxygen occupy 804 L?

785 L/294 K = 804 L/X K

785 X = 236,376

X = 236,376/785

X= 301 K = 28 °C


Combined Gas Law

  • Combining Charles’s Law and Boyle’s Law in a single statement:

  • P1V1/T1 = P2V2/T2

  • 39.8 mg of caffeine gives 10.1 mL of nitrogen gas at 23°C and 746 mmHg. What is the volume of nitrogen at 0°C and 760 mmHg?

  • First change temperature to Kelvin

  • V1 = 10.1mL P1 = 746 mmHg K1 = 296 K

  • V2 = ? P2 = 760 mmHg K2 = 273 K

    10.1 * 746/296 = V2 * 760/273

    V2 = 9.14 mL


Other Gas Laws

  • Gay-Lussac Law

    • At constant volume, pressure and absolute temperature are directly related.

    • P/T = k (constant)

  • Avogadro’s Law

    • At constant temperature and pressure, the volume of gas is directly related to the number of moles.

    • V /n= k (n is the number of moles)


Gas Law Summary

What equation would we get if we combined them all?


What is the Ideal Gas Law?

  • Combining Boyle’s Law, Charles’ law & Avogadro’s Law we derive the Ideal Gas Law:

  • P V = n R T

  • P = Pressure (atm)

  • V = Volume (L)

  • n = # moles (0.0821 L atm /mol K)

  • R = Gas Constant

  • T = Temperature (K)

  • Ideal gas law calculations are favored at low pressures and high temperatures

  • Tells you about a gas NOW.

  • The other laws tell you about a gas when it changes.


Let’ Try It!

  • Example:

  • If we had 1.0 mol of gas at 1.0 atm of pressure at 0°C (STP), what would be the volume?

  • PV = nRT

  • V = nRT/P

  • V = (1.0 mol)(0.0821 L atm/mol K)(273 K)/(1.0 atm)

  • V = 22.41 L

  • 1 mole of ANY gas at STP will occupy 22.4 Liters of volume


Gas Density and Molar Mass

  • D = m/V

  • Let M stand for molar mass

  • M = m/n

  • n = m/M

  • PV = nRT

  • PV = (m/M) RT

  • P = mRT/VM = (m/V)(RT/M)

  • P = d RT/M

  • PM/RT = d (density)


Examples

  • What is the density of ammonia at 23ºC and 735 torr?

  • Units must be: atm, K

  • 735 torr(1 atm/760 torr) = 0.967 atm

  • 23 + 273 = 296 K

  • Molar mass of NH3 = 17.0 g

    d = 0.967 * 17.0 g

    (0.0821 L* atm/mol * K)(296 K)

    d = 0.676 g / L


Gases and Stoichiometry

  • Reactions happen in moles

  • At Standard Temperature and Pressure (STP, 0ºC and 1 atm) 1 mole of gas occupies 22.42 L.

  • If not at STP, use the ideal gas law to calculate moles of reactant or volume of product.


Examples

  • Consider the following reaction:

  • Suppose you heat 0.0100 mol of potassium chlorate, KClO3, in a test tube. How many liters of oxygen can you produce at 298 K and 1.02 atm?

  • Break it into 2 problems, one involving stoichiometry and the other using the ideal gas law


0.0100 mol KClO3 X 3 mol O2/2 mol KClO3

= 0.0150 mol O2

Now that you have the moles of oxygen use the ideal gas law to calculate the volume:

V = nRT/P

0.0150 mol x 0.0821 L * atm (K * mol) x 298 K

1.02 atm

V = 0.360 L


  • Using the following reaction

  • Calculate the mass of sodium hydrogen carbonate necessary to produce 2.87 L of carbon dioxide at 25ºC and 2.00 atm.

    n = PV/RT = (2.00 atm)(2.87 L)

    (0.0821 L*atm/K*mol)(298 K)

    n= 0.235 mol CO2

    0.235 mol CO2 (1 mol NaHCO3) ( 84.0 g)

    (1 mol CO2 ) (1 mol NaHCO3)

    19.7 g NaHCO3


Dalton’s Law

  • The total pressure in a container is the sum of the pressure each gas would exert if it were alone in the container.

  • The total pressure is the sum of the partial pressures.

  • PTotal = P1 + P2 + P3 + P4 + P5 ...

  • For each P = nRT/V


Dalton's Law

  • PTotal = n1RT + n2RT + n3RT +... V VV

  • In the same container R, T and V are the same.

  • PTotal = (n1+ n2 + n3+...)RTV

  • PTotal = (nTotal)RT V


The Mole Fraction

  • Ratio of moles of the substance to the total moles.

  • symbol is Greek letter chi c

  • Because pressure of a gas is proportional to moles, for fixed volume and temperature then,

  • c1 = n1= P1nTotalPTotal


Calculating the Partial Pressure and Mole Fraction of a Gas Mixture

  • A 1.00 L sample of dry air at 25°C and 786 mmHg contains 0.925 g N2, plus other gases including oxygen, argon and carbon dioxide.

    • What is the partial pressure (in mmHg) of N2 in the air sample?

    • What is the mole fraction and mole percent of N2 in the mixture?


  • Convert grams into moles

    0.925 g N2 x (1 mol N2/28.0g N2)

    =0.0330 mol N2

  • Substitute into ideal gas law

    PN2 = nN2RT/V

    =0.0330mol x 0.0821 L*atm/K*mol x 298

    1.00 L

    =0.807 atm = 613 mmHg


  • The mole fraction of N2 in the air is

    = PN2/P = 613 mmHg/786 mmHg

    =0.780

  • Mole percent equals mole fraction x 100

    =0.780 x 100 = 78%

  • Air contains 78.0 mole percent of N2


Vapor Pressure

  • Water evaporates!

  • When that water evaporates, the vapor has a pressure.

  • Gases are often collected over water so the vapor pressure of water must be subtracted from the total pressure.

  • Vapor pressure varies by temperature and must be given in the problem or in a table.


  • Hydrogen gas is produced by the reaction of hydrochloric acid, HCl, on zinc metal:

    2HCl (aq) + Zn (s) —> ZnCl2 (aq) + H2 (g)

  • The gas is collected over water. If 156 mL of gas is collected at 19°C and 769 mmHg total pressure, what is the mass of hydrogen collected?


  • First find the Partial Pressure. The vapor pressure of water at 19°C is 16.5 mmHg

    P = PH2 + PH2O

    PH2 = P - PH2O

    PH2 =769 – 16.5 = 752 mmHg

  • Use the ideal gas law to find the moles of hydrogen collected.

    P: 752 mmHg x (1 atm/760 mmHg) = 0.989 atm

    V: 156 mL x (1 L/1000 mL) = 0.156 L

    T: 19 + 273 = 292 K

    R: 0.0821 L*atm/K*mol

    n: ?


  • Solve for moles:

    n = PV/RT

    = 0.989 x 0.156/0.0821 x 292

    =0.00644 mol H2

  • Convert moles to grams:

    0.00644 mol H2 x (2.02g/1 mol H2)

    =0.0130 g H2


What’s Diffusion and Effusion?

  • Only a few physical properties of gases depends on the identity of the gas.

  • Diffusion - The rate at which two gases mix.

  • Effusion - The rate at which a gas escapes through a pinhole into a vacuum.


What is Graham’s Law?

  • We know that Kinetic energy = 1/2 mv2

  • If two bodies of unequal mass have the same kinetic energy, which moves faster?

  • The lighter one!

  • Thus, for two gases at the same temperature, the one with lower molecular mass will diffuse/effuse faster.

  • The rate of effusion/diffusion of a gas is inversely proportional to the square root of its mass.


  • Calculate the ratio of effusion rates of molecules of carbon dioxide and sulfur dioxide from the same container and at the same temperature and pressure:

    Rate of effusion of CO2 = √Mm SO2

    Rate of effusion of SO2 √Mm CO2

    = √64.1/44.0 = 1.21

  • In other words, carbon dioxide effuses 1.21 times faster than sulfur dioxide.


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