Module 8: Gases

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Module 8 Gases

• By Alyssa Jean-Mary
• Source Modular Study Guide for First Semester
  Chemistry by Anthony J. Papaps and Marta E.
  Goicoechea-Pappas

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Substances that Exist as Gases

• All the elements and some common compounds that
  exist as gases under standard laboratory
  conditions (T 25C and P 760 torr) are listed
  in the table above.

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Properties of Gases

• Compressibility a gas can be compressed into
  smaller volumes in other words, the density of
  a gas can be increased by applying pressure (but
  if too much pressure is applied, the gas will
  become a liquid or a solid)
• Indefinite shape of volume a gas fits the
  container it is in
• Expansion a gas expands without limit, until it
  completely and uniformly fills the volume of the
  container it is in
• Mixibility or diffusion gases diffuse into each
  other completely in other words, they can mix
  together easily
• Low density the density of a gas is small it
  is expressed in g/L
• The average kinetic energy (KE) of gaseous
  molecules is directly proportional to absolute
  temperature of these molecules - KE a T (K).
  Thus, if the temperature is the same, the kinetic
  energy of different gas molecules is also the
  same.
• The terms to describe the amounts and properties
  of gases are
• T temperature (expressed in Kelvin (K))
• P pressure
• V volume
• n number of moles

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Characteristics of Ideal Gases

• The equations in this module apply only to ideal
  gases or to gases who behave very similarly to
  ideal gases
• The characteristics of an ideal gas are
• It has a negligible volume
• It has no attractive forces between molecules
• It undergoes elastic collisions
• Real gases can behave as ideal gases by avoiding
  the following
• extremely low temperatures
• very small volumes
• very high pressures

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Pressure

• Pressure is force per unit area
• Common units of pressure
• atmosphere (atm)
• torr
• millimeters of mercury (mmHg)
• pascal (Pa)
• bar
• The following equalities allow conversion between
  units of pressure
• 1.00 atm 760 torr 760 mmHg 1.01 x 105 Pa
  1.01 bar
• At sea level, the pressure is 760 torr (1 atm)
• Below sea level, it is greater than this
• Above sea level, it is lower than this
• A barometer is a device that is used to measure
  pressure
• The pressure of the atmosphere is equal to the
  height of the mercury Patm h (mmHg)
• A manometer is a partially filled glass tube of
  mercury, with one arm open to the atmosphere
  (side P1) and the other arm (side P2) attached to
  a gas tank
• The pressure of the gas in the tank is equal to
  the pressure of the atmosphere plus the
  difference in the height of the mercury on the
  two sides Pgas P1 ?h

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Examples Using a Manometer

• What is the pressure (in Pascals) of a gas if the
  difference in the height of mercury from one arm
  to the other in a manometer is 45mm and the
  pressure of the atmosphere is 1.03atm?

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Standard Temperature and Pressure (STP) and
Standard Molar Volume

• STP (standard temperature and pressure)
• T 0.00C (273.15K)
• P 1 atm (760 torr)
• At STP, 1 mol of an ideal gas occupies 22.4L

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Gas Laws

• Boyles Law volume is indirectly proportional to
  pressure, keeping temperature and number of moles
  constant - V a 1/P (at constant T and n)
• For example, if the volume is doubled, and the
  temperature and the number of moles are kept
  constant, the pressure is cut in half
• Charles Law volume is directly proportional to
  absolute temperature, keeping pressure and number
  of moles constant V a T (K) (at constant P and
  n)
• For example, if the volume is doubled, and the
  pressure and the number of moles are kept
  constant, the temperature (in K) is also doubled
• Avogadros Law volume is directly proportional
  to the number of moles, keeping the pressure and
  temperature constant V a n (at constant T and
  P)
• For example, if the volume is doubled, and the
  pressure and the temperature are kept constant,
  the number of moles is also doubled

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Examples Using the Gas Laws

• Example 1 If the volume of a gas is 50mL, what
  happens to this volume if
• at constant temperature and number of moles, the
  pressure is increased from 2atm to 6atm?
• at constant temperature and number of moles, the
  pressure is decreased from 8atm to 4atm?
• at constant pressure and number of moles, the
  temperature is increased from 55K to 110K?
• at constant temperature and number of moles, the
  pressure is decreased from 255K to 85K?
• at constant temperature and pressure, the number
  of moles is increased from 1mol to 4mol?
• at constant temperature and pressure, the number
  of moles is decreased from 8mol to 2mol?
• Example 2 If there are 4.0g of Lithium and 2.0g
  of Helium, which occupies the larger volume at
  STP?

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Combined Gas Laws

• (P1V1 / n1T1) (P2V2 / n2T2)
• If one of the terms is constant, it is eliminated
  from both sides of the equation for example
• If n is constant, (P1V1 / T1) (P2V2 / T2)
• If n and T are constant, (P1V1) (P2V2)
• Units used for this equation
• Pressure (P) and Volume (V) can be in any unit as
  long as P1 and P2 have the same units V1 and V2
  have the same units
• Temperature (T1 and T2) must have the units of
  Kelvin (K)

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Examples Using the Combined Gas Laws

• Example 1 If a sample of oxygen has a volume of
  45.2L, a pressure of 2.6atm, and a temperature of
  33C, what volume will it occupy at STP?
• Example 2 If the pressure of a gas at 56C is
  cut in half and its volume is tripled, what will
  the resulting temperature be?
• Example 3 If a gas has a pressure of 250torr and
  a volume of 67mL, what will the new volume (in L)
  be if the pressure increased to 0.658atm if the
  temperature is held constant?

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Ideal Gas Equation

• PV nRT
• R gas constant 0.0821 (Latm)/(moleK) 62.4
  (Ltorr)/(moleK)

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Examples Using the Ideal Gas Equation

• Example 1 If 2.6g of nitrogen gas at 23C has a
  volume of 55mL, what is its pressure (in mmHg)?
• Example 2 If 0.556mol of neon gas has a volume
  of 25L and a pressure of 4.1atm, what is its
  temperature (in C)?

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Molar Mass and Density of Gases

• The ideal gas equation (PV nRT) can be
  rewritten to include molar mass (M)
• Since n g/M, PV (g/M)RT
• The ideal gas equation (PV nRT), rewritten to
  include molar mass (PV (g/M)RT), can be
  rewritten to find density
• Since d m/V g/V, d PM/RT

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Examples of Calculating Molar Mass and Density

• Example 1 If 5.62g of a gas has a pressure of
  55torr, a volume of 60mL, and a temperature of
  75C, what the molar mass of this gas?
• Example 2 What is the density of argon at STP?

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Daltons Law of Partial Pressures 1

• At constant volume and temperature, the total
  pressure exerted by a mixture of ideal gases is
  equal to the sum of the partial pressures of
  these gases
• PT PA PB PC
• where PT total pressure, PA partial pressure
  of gas A, PB partial pressure of gas B, PC
  partial pressure of gas C
• Using the ideal gas equation (PV nRT) and
  solving for P (P nRT/V), with V and T being
  constant (along with R), PT nART/V nBRT/V
  nCRT/V , but since T and V are constant (along
  with R), PT (nA nB nC )(RT/V)
• where nA number of moles of gas A, nB number
  of moles of gas B, nC number of moles of gas C

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Daltons Law of Partial Pressures Relationship
Between Total Pressure and Individual Partial
Pressures

• If a sample contains gases A and B
• If PA is divided by PT
• PA/PT (nART/V) / ((nAnB)RT/V), but since T and
  V, along with R, are constant, they cancel out,
  so PA/PT nA/(nAnB) XA, where XA is the mole
  fraction of A
• A mole fraction is the ratio of moles of one
  component in a sample to the number of total
  moles in the sample. A mole fraction is a
  dimensionless quantity (i.e. it has no units). A
  mole fraction can be any number between 0 and 1,
  but the sum of all the mole fractions in a sample
  must be equal to 1, so, if there are just two
  components present (gases A and B), XA XB 1
• By rearranging PA/PT nA/(nAnB) XA, the
  partial pressure of A can be found PA
  (nA/(nAnB))PT XAPT using this same method,
  the partial pressure of B can also be found PB
  (nB/(nAnB))PT XBPT
• So, in this sample of gases A and B, the
  following equation can be used to find the total
  pressure of the sample PT PA PB
  (nAnB)(RT/V) XAPT XBPT

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Daltons Law of Partial Pressures Insoluble Gases

• Gases that are insoluble in water and that dont
  react with water can be collected over water.
• The partial pressure that a gas (for example,
  water vapor) exerts above its liquid is called
  its vapor pressure. Each liquid has its own
  characteristic vapor pressures that vary with
  temperature.
• When a gas is collected over water, there is
  water vapor present along with the gas above the
  water, so, at atmospheric pressure, with PT
  atmospheric pressure, PT Pgas Pwater, and,
  solving for Pgas, Pgas PT Pwater

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Examples Using Daltons Law of Partial Pressures

• Example 1 If a 25.0L flask contains 4.3g of
  oxygen gas and 2.6g of nitrogen gas at 35C,
• What is the total pressure (in atm) inside the
  flask?
• What is the partial pressure of each component in
  the mixture?
• What is the mole fraction of each component in
  the mixture?
• Example 2 If 253mL of a sample of oxygen gas are
  collected over water at 31C and 750.3torr, how
  many moles of oxygen are present in the sample?

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Grahams Law Diffusion and Effusion of Gases

• Diffusion the intermingling of gases
• Effusion the leaking out of a gas through a
  small hole or orifice
• RateA/RateB v(MB/MA)
• where RateA rate of effusion of gas A, RateB
  rate of effusion of gas B, MB molar mass of gas
  B, MA molar mass of gas A
• Rate Volume/time, so units mL/sec, L/min, etc.

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Examples Using Grahams Law

• Example 1 What is the ratio of effusion of O2 to
  H2?
• Example 2 If O2 effuses 5 times faster than an
  unknown gas, what is the molar mass of the gas?
• Example 3 If O2 effuses at a rate of 25.5 L/min,
  at what rate (in L/min) does N2 effuse?

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Stoichiometry in Reactions Involving Gases
Gay-Lussacs Law (Law of Combining Volumes)

• At constant temperature and pressure, the volumes
  of reacting gases can be expressed using the same
  simple whole number ratio used for expressing
  moles of reacting gases, meaning that V is
  directly proportional to n, if temperature and
  pressure are constant - V a n (at constant T and
  P). So, just as moles can be converted using the
  coefficients in a balanced chemical equation, so
  can volumes.
• If the reaction is performed at STP, 1 mole
  22.4 L.

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Examples of Solving Stoichiometry Problems Using
Gay-Lussacs Law

• Example 1 Consider the following balanced
  chemical equation
• 3 H2 (g) N2 (g) ? 2 NH3 (g)
• If 25.0L of H2 reacts with excess N2 at constant
  temperature and pressure, how many liters of NH3
  are produced?
• If 7.66g of N2 reacts with excess H2 at STP, how
  many liters of NH3 are produced?

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Stoichiometry in Reactions Involving Gases Using
the Ideal Gas Equation

• The concept map below represents the possible
  steps to solve a stoichiometry problem. Which
  steps are used depends on the information given
  in the problem and the information that needs to
  be solved for in the problem.

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Examples of Solving Stoichiometry Problems Using
the Ideal Gas Equation 1

• Example 1 Consider the following balanced
  chemical equation
• 2 KClO3 (s) ? 2 KCl (s) 3 O2 (g)
• If 2.56g of KClO3 decomposes at 55.0ºC and
  752.3torr, how many mL of oxygen gas are
  produced?
• If 75.0mL of KClO3 decomposes at 55.0ºC and
  752.3torr, how many grams of oxygen gas are
  produced?
• If a 2.563g impure sample of KClO3 decomposes to
  give 305mL of O2 at 55.0ºC and 752.3torr, with
  2.002g of residue left behind, calculate the
  following
• What is the gas constant, R?
• How many grams of pure KClO3 are present in the
  impure sample?
• What is the percentage of KClO3 in the impure
  sample?

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THE END