Chapter 12 The Ideal Gas Law PDF

Chapter 12 Exploring Gas Laws Chapter 11.1: The Ideal Gas Law  Law of Combining Volumes: When gases react, volumes of the reactants and products, measured at equal temperatures and pressures, are always in whole number ratios.  Formulated by Joseph Louis Gay-Lussac  Example: 2...

Chapter 12 Exploring Gas Laws Chapter 11.1: The Ideal Gas Law  Law of Combining Volumes: When gases react, volumes of the reactants and products, measured at equal temperatures and pressures, are always in whole number ratios.  Formulated by Joseph Louis Gay-Lussac  Example: 2 volumes of hydrogen gas react with one volume of oxygen gas to produce two volume of water vapour.  Law of Multiple proportions: the masses of the elements that combine can be expressed in small whole number ratios.  Formulated by John Dalton  Amedeo Avogadro, 9 August 1776 – 9 July 1856, was an Italian scientist  Contributed to the molecular theory now known as Avogadro’s Law.  Combined the ideas of Gay-Lussac and John Dalton  Related the volume of a gas to the amount that is present calculated from the mass.  Avogadro’s Law: equal volumes of gases under the same conditions of temperature and pressure will contain equal numbers of molecules  Based on Avogadro’s Law, one mole of a gas occupies the same volume as one mole of another gas at the same temperature and pressure.  Molar volume: is the space that is occupied by one mole of a gas and is expressed as L/mol Example:  A resealable 1.30 L container has a mass of 7.43g. Nitrogen gas (N2(g)) is added to the container until the pressure is 98.0 kPa at 22.0°C. Together, the container and the gas have a mass of 6.18 g. Calculate the molar volume of nitrogen gas at STP.  Solution:  What is required?  Volume of one mole of nitrogen at STP  Given:  P1 = 98.0 kPa  P2 = 101.3 kPa  V1 = 1.30 L  V2 = ?  T1 = 22.0°C, or 295 K  T2 = 0°C or 273 K  m1 = 1.45 g (6.18 g – 4.73 g)  m2 = 1.45 g (mass does not change)  Step 1: calculate number of moles of nitrogen gas 𝑚 1.45 𝑔  n= = = 0.0517 mol 𝑀 28.02 𝑔/𝑚𝑜𝑙  Step 2: find the volume of nitrogen at STP, using the Combined Gas Law 𝑃1𝑉1 𝑃2𝑉2  = 𝑇1 𝑇2 𝑃1𝑉1 𝑇2  V2 = × 𝑇1 𝑃2 98.0 𝑘𝑃𝑎 ×1.30 𝐿 ×273 𝐾  V2 = 295 𝐾 ×101.3 𝑘𝑃𝑎 = 1.16 L  Step 3: Find the molar volume 𝑉 1.16 𝐿  Molar volume = = = 22.4 L/mol 𝑛 0.0517 𝑚𝑜𝑙  Therefore: the molar volume of nitrogen gas is 22.4 L/mol at STP Homework:  Practice Problems:  Questions 1-4 on page 477  Questions 5-11 on page 482 Volumes of Real Gases:  At STP gases behave like ideal gases.  At high pressure and/or low temperatures gases no longer behave like ideal gases.  This is because gas molecules have a volume of their own.  There is attraction between gas molecules.  Molecules don’t necessarily move in straight lines.  Collisions are not completely elastic, there is loss of energy.  In these conditions of low temperature and/or high pressure, gases have smaller volumes.  Molecules are closer together allowing for attraction.  Smaller volumes of the gas also means that the volume of the gas particles becomes more important. The Ideal Gas Law  Vαn 𝑇  Vα 𝑃 𝑛 ×𝑇  Therefore: V α 𝑃 nRT  Introduce a constant, R, V = 𝑃 𝑃𝑉  R= 𝑛𝑇 The Universal Gas Constant, R  One mole of a gas at STP:  P = 101.3 kPa  T = 273 K  V = 22.4 L  n = 1.00 mol 𝑃𝑉  R= 𝑛𝑇 101.3 𝑘𝑃𝑎 ×22.4 𝐿 𝑘𝑃𝑎 × 𝐿  R= = 8.314 1.00 𝑚𝑜𝑙 ×273 𝐾 𝑚𝑜𝑙 ×𝐾 The Universal Gas Law  PV = nRT Homework  Practice Problems:  Questions 12-15 on page 487-488.  Section Review Questions:  Questions 1-7 on page 488. Chapter 12.3: Gas Law Stoichiometry  Volume to volume stoichiometry  When gases react with other gases Gay-Lussac’s law of combining volumes can be used to solve these problems  As usual, it requires a balanced chemical equation  Example: what volume of ammonia gas can be produced from 12.0 L of nitrogen and excess hydrogen gas at same temperature and pressure?  N2(g) + 3 H2(g)  2 NH3(g)  There is a 1 mol N2(g) to 2 mol 2 NH3(g) ratio between nitrogen and ammonia 𝑥 𝐿 𝑁𝐻3 𝑔 2 𝑚𝑜𝑙  Therefore, ( ) = 1 𝑚𝑜𝑙 12.0𝐿 𝑁2 𝑔 ( )  x = 24.0 L  Using the ideal gas law it is possible to solve problems in stoichiometry when gases are involved.  Solve the problem by first converting the volumes into number of moles  Compare the moles  Then convert back to volumes  Often reactions occur in solutions which then release gas  If this is the case, the pressure of water vapour needs to be considered  This can be corrected for using Dalton’s partial pressure law  Pgas = Ptotal – Pwater vapour  Use the table for water vapour pressure to correct for this Homework  Practice Problems:  Questions 25-28 on page 503  Questions 29-34 on page 506  Questions 35-39 on page 511  Section Review Questions 1-8 on page 514