States of Matter & Gas Laws (Chapter 1.1) PDF

# Chapter 1.1: Behaviour of Gases ## States of matter - Solid - Liquid - Gas ## Solid - Have definite shapes - Not compressible - Atoms and molecules are held together in a framework called the crystal lattice - Position of the atoms and molecules is fixed within the crystal lattice - Degree of...

# Chapter 1.1: Behaviour of Gases ## States of matter - Solid - Liquid - Gas ## Solid - Have definite shapes - Not compressible - Atoms and molecules are held together in a framework called the crystal lattice - Position of the atoms and molecules is fixed within the crystal lattice - Degree of disorder is very low - Atoms and molecules in solids undergo vibrational motion - Reflection of the kinetic energy the particle possesses - Greater the motion, the higher the temperature of the substance - Solid is held together by forces such as London dispersion forces, dipole-dipole, ion-dipole, hydrogen bonding, electrostatic forces (ionic compounds) as well as metallic bonding (in metals) ## Liquid - Substances in the liquid state take on the shape of the container - Liquids are incompressible - The atoms and molecules are not held together as tightly as in solids - The degree of disorder is increased compared to solids - Atoms and molecules of liquids also possess vibrational motion - Possess rotational motion - Greater the kinetic motion, the higher the temperature of the substance - Particles are able to change position, and this is what allows liquids to flow and change shape - Forces that hold liquid substances together include London dispersion forces, dipole-dipole, ion-dipole, and hydrogen bonding ## Gases - Substances in the gaseous state do not have a definite state and take the shape of the container - Gases are compressible unlike solids and liquids - The space between particles is large enough for this - If a compressed gas is enough, gases can be condensed into a liquid - Gas molecules are not held together at all, the particles are free to move in space - Attractive forces are very weak, mostly London Dispersion forces - They have a high degree of disorder - Gas molecules possess vibrational, rotational, as well as translational motion - The higher the kinetic energy of the particles, the higher the temperature - The kinetic energy is high enough that gases are not as affected by gravity as other materials - The translational motion is random and in all directions - They will fill the container - The size of the molecule affects what state the molecule will be in - The greater the size of the molecule, the more intermolecular forces can be exerted - This means that the particle will be more likely to attract each other, thereby sticking together and forming liquids or solids - **Examples:** - Methane: is a gas at room temperature (natural gas) - Octane: is a liquid at room temperature (gasoline) - Isocane: is a solid at room temperature # Kinetic Molecular Theory of Gases - The volume of an individual gas molecule is negligible compared to the volume of the container holding the gas. This means that individual gas molecules, with virtually no volume of their own, are extremely far apart and most of the container is "empty" space. - There are neither attractive nor repulsive forces between gas molecules. - Gas molecules have high translational energy. They move randomly in all directions, in straight lines. - When gas molecules collide with each other or with the container wall, the collisions are perfectly elastic. This means that when gas molecules collide, somewhat like billiard balls, there is no loss of kinetic energy. - The average kinetic energy of gas molecules is directly related to the temperature. The greater the temperature, the greater the average motion of the molecules and the greater their average kinetic energy. - The kinetic molecular theory of gases describes a hypothetical ideal gas. - Postulated because under normal environmental conditions, gases behave in a similar and predictable fashion. - Allows for calculations with high degree of accuracy. - Gas particles will actually take up space, but the space is so insignificant compared to the container that they can be considered not to take up space. # Chapter 11.2 Boyle's Law ## Robert Boyle - 25 January 1627 - 31 December 1691 - Stated that the volume of a given amount of gas, at constant temperature, varies inversely with applied pressure. - As pressure increases, the volume of a gas decreases and vice versa. - If the data of volume and pressure is graphed, the following is shown: * Diagram with pressure on the y-axis and 1/V on the x-axis. - If instead, we graph pressure versus 1/volume, a different line can be observed. * Diagram with pressure on the y-axis and 1/V on the x-axis. - We can observe that Va 1/P - The volume of a gas is proportional to the inverse of the pressure exerted on the gas. - It is difficult to deal with proportionality. - Can be replaced by constant, k, so that: V = KX or PV = K - This relationship is true for all gases. - Important fact is that temperature has to be constant. ## How can this be used? - If one knows the initial conditions of a gas, then it is possible to calculate either one variable if there is a change in the other. - P₁ x V₁ = K - PF x Vf = K - Since k is constant, P₁ x V₁ = K = PF x Vf - P₁ x V₁ = PF x Vf # Chapter 11.2 Gas Pressure & Volume ## What is pressure? Pressure: The force exerted on an object per unit of surface area. - P = F/A - P = Pressure - F = Force exerted - A = Area of the object - SI unit for pressure is measured in pascals. - 1 Pa = 1 Nm² - Pressure is often reported in kilopascals, or kPa. - The pressure of a gas is determined by the kinetic motion of the particles. - As the particles move, they will collide with the surface of the container. - The collision is what exerts the pressure on the container. - Scientists estimate the atmosphere to have a mass of about 5.1 x 10⁸kg - The atmosphere is being pulled towards the surface of the earth by gravity. - This is what exerts pressure on all objects on earth. - This is the atmospheric pressure. ## History on pressure of Gases - Galileo Galilei: 15 February 1564 - 8 January 1642 - Developed the suction pump. - Can lift water up to 10m using air - Any greater distance, the water column would collapse and the pump would not work. - Torricelli started working with mercury. - Mercury is 13.6 x denser than water. - Filled a dish with water. - Filled a gas tube of 1.0 cm in diameter with mercury and immersed the open end in the dish. - Some of the mercury ran out, but approximately 760mm remained in the tube. - Concluded that air could push up mercury 760mm in the glass tube. * Diagram of a tube filled with mercury, with air pressure at the bottom of the tube. - Performed this experiment over and over. - Noticed that the level of mercury was changing enough to be noticeable. - Couldn't explain this. - Considered the experiment a failure. - However, Torricelli had just invented the barometer ## Units of Pressure - There are numerous ways to measure pressure. - The SI unit is Pa. - Also in use are: - mmHg (milimetre mercury) or inches Hg (inches of mercury) - torr, 1 torr = 1 mmHg - atm (1 atmosphere of pressure) - Psi, pounds per square inch - Bar, exactly equal to 100,000 Pa (100 kPa) ## Standard Atmospheric Pressure - Measured at sea level at 0°C (273.15K). - 1 atmosphere - 101.3 kPa - 1,013. 25 mbar - 760 mmHg - 29.9212 inches Hg - 14.696 psi # Chapter 11.3 Charles Law ## Jacques Charles - 12 November 1746 - 7 April 1823 - French scientist - Was interested in hot air balloons. - First to fill balloons with hydrogen gas. - Investigated the expansion rates of different gases. - Found all gases expand at the same ratio. - For each degree increase in temperature, any gas would expand by 1/273rd of the volume at 0°C. - Therefore, if a gas at 0°C were to be heated to 273°C, its volume would double. - For this to be true, the pressure and the amount of gas has to be constant. - Charles found that regardless of the gas, the x-intercept of graphs of temperature versus volume would always be -273°C. ## The Kelvin Scale and Absolute Zero ## Lord Kelvin - William Thomson, 1st Baron Kelvin - 26 June 1824 - 17 December 1907 - Scottish scientist. - Realized, at -273°C all molecular motion would stop, and there is no kinetic energy present in the particles. - The hypothetical volume of gas would be "0", zero. * Diagram of a graph with volume on the y-axis and temperature (°C and K) on the x-axis - Real gases do have a volume at this low temperature. - Would be condensed into a liquid. - But this is the basis for the Kelvin Temperature Scale. - -273°C is absolute "0", zero, or 0K. - Today, the accepted value has been refined to -273.15°C - Since it is an absolute value, Kelvin doesn't have degrees. - There is no negative value for Kelvin. - In studying gases, temperature can only be reported in Kelvin. - To convert from Celsius into Kelvin: **Temperature in °Celsius + 273** ## Charles Law - The volume of a fixed mass of a gas is proportional to its temperature when the pressure is kept constant. - VaT - V = KT or V₁/T₁ = Vf/Tf # Chapter 11.3 Gay-Lussac's Law ## Joseph Louis Gay-Lussac - 6 December 1778 - 9 May 1850 - French scientist - Worked on gases - Worked on the relationship of temperature and pressure in gases when the volume is constant. ## Gay-Lussac's Law - The pressure of a fixed amount of gas, at constant volume, is directly proportional to its Kelvin temperature. - PaT or P/T = K - P₁/T₁ = Pf/Tf ## Safety - Gases are normally stored under pressure in cylinders. - Cylinders are thick-walled metal containers. - Each has a maximum pressure it can withstand. - Have to be tested every 5-10 years. - Cylinders have safety valves to regulate internal pressure. - If internal pressure rises too high, a spring in the valve releases some gas to release the pressure. - Other cylinders have fusible plugs, which will melt at a temperature lower than where dangerous reactions can occur. - Gas cylinders must be stored in fire-resistant storage rooms. - These rooms have to be ventilated. - Gas cylinders also need to be tied down so they cannot tip over and damage the valve which could accidentally release gas. # Chapter 11.4 The Combined Gas Law ## Combined Gas Law - Review of the gas laws so far: - Boyle's Law: P₁V₁ = PfVf - Charles Law: V₁/T₁ = Vf/Tf - Boyle's Law is derived from the fact that Va 1/P. - This holds true when temperature is kept constant. - Can be rewritten as: Va 1/PxT, when T is recorded in Kelvin. - Va 1/PxT or VaT/P - Va T/P - Introduces a constant, K3 - V = T/P x K3 - P₁V₁/T₁ = K3 - PFVF/Tf = K3 - P₁V₁/T₁ = PFVF/Tf OR PV/T = K3 - STP, Standard temperature and pressure - Temperature is 0°C or 273 K - Pressure is 1 atm of pressure or 101.3 kPa ## Dalton's Partial Pressure Law - Total pressure of a mixture of gases is the sum of the pressures of each of the individual gases. - Ptotal= P₁ + P₂ + P₃ + ... + Pn