Gas+Laws

G**ases have many distinctive properties, including the principal three:**
 * __Properties of Gases __**
 *  1.Gases are easy to compress, because gas molecules are so far apart. In most cases, doubling the pressure of a gas cuts its volume in half. **
 *  2.Gases expand to fill their containers. **
 *  3.Gases occupy more space than liquids or solids. **
 *  Other properties of gases include: **
 *  4.Gases, which do not have a definite shape or volume, expand to fill their containers. For this reason, the volume of a gas can be assumed to be the volume of the container it is in. **
 *  5.Gases have very low densities. For example, 1 mole of liquid water at 298 Kelvin and 1 atmosphere occupies a volume of 18.8 cubic centimeters, and the same amount of water vapor occupies 30,200 cubic centimeters. **
 *  6.All gases respond in the same way to changes in temperature and pressure, either expanding or contracting, and this change is very predictable. **
 *  7.At standard temperature (0 degrees Celsius) and standard pressure (1 atmosphere), every gas occupies 22.4 Liters of volume. **


 *  __Charles' Law__ **
 *  The quantitative __#|relationship__ between volume and temperate was discovered by the French scientist Jacques Charles in 1787. [[image:http://exploration.grc.nasa.gov/education/rocket/Lessons/vtgraph.gif width="162" height="175" align="right" caption="Charles' Law"]]His experiments sho[[image:http://thm-a04.yimg.com/image/85728db720ebd75a width="124" height="125" align="left" caption="Jacques Charles"]]wed that all gasses expand the same amount when heated through the same temperature interval. Charles found that the volume changes by 1/273 of the original volume for each Celsius degree at constant pressure. The same goes for cooling gas, but the volume decreases by 1/273 of the original amount. The relationship between Kelvin Temperature (K= 273.15+ °C) and gas volume is known as Charles' law. Charles law states that the volume of a fixes mass of gas at constant pressure varies directly with the Kelvin temperature. **


 *  Charles' Law can be written as V=kT or V/T = k. The value of T is the Kelvin temperature, and k is a constant. The value of K depends on the quantity of gas and the pressure. **


 *  Another form that can be useful for volume-temperature problems is V1/T1 = V2/T2 where V1 and T1 represent initial condition and V2 and T2 represent a new set on conditions. **


 *  __Avogadro’s Law__ **
 *  Avogadro’s Law is a gas law named after the scientist Amedeo Avogadro who discovered that equal volumes of gases, as the same temperature and pressure, contained the same amount of molecules. **
 * <span style="font-family: 'Times New Roman','serif'; font-size: 12pt; line-height: 115%;"> Written mathematically, **
 * <span style="font-family: 'Times New Roman','serif'; font-size: 12pt; line-height: 115%;">= where P=Pressure, V= Volume, N= number of molecules, and T= Temperature Since Pressure and Temperature are constant they can be cancelled out, causing the equation **


 * <span style="font-family: 'Times New Roman','serif'; font-size: 13.2pt; line-height: 115%;">__Graham’s Law__ **
 * <span style="font-family: 'Times New Roman','serif'; font-size: 12pt; line-height: 115%;"> Graham's Law states that the rate of effusion of a gas is inversely proportional to its molecular weight. This was discovered by a Scottish physical chemist named Thomas Graham. **


 * <span style="font-family: 'Times New Roman','serif'; font-size: 12pt; line-height: 115%;"> [[image:Graham.GIF width="124" height="160" align="left" caption="Thomas Graham"]] [[image:grahamsequation.png]]Where r is the velocity of the gas, and M is the molecular weight. **


 * <span style="font-family: 'Times New Roman','serif'; font-size: 12pt; line-height: 115%;"> Graham’s Law is used to relate the relative velocities of gases. We can compare velocities of two gases to determine how much faster one gas is moving than the other. From Physics we know that: **


 * <span style="font-family: 'Times New Roman','serif'; font-size: 12pt; line-height: 115%;"> KE=1/2mv^2 **
 * <span style="font-family: 'Times New Roman','serif'; font-size: 12pt; line-height: 115%;"> Another formula we can use is: **


 * <span style="font-family: 'Times New Roman','serif'; font-size: 12pt; line-height: 115%;"> KE=(3/2)RT **
 * <span style="font-family: 'Times New Roman','serif'; font-size: 12pt; line-height: 115%;"> Where R=gas constant and T=temperature in Kelvin **


 * <span style="font-family: 'Times New Roman','serif'; font-size: 12pt; line-height: 115%;"> Using these two formulas we can determine the velocity of a given gas and then plug them into the Graham’s Law formula to determine the relative velocity of two gases. **


 * <span style="font-family: 'Times New Roman','serif'; font-size: 12pt; line-height: 115%;"> __Example:__ **


 * <span style="font-family: 'Times New Roman','serif'; font-size: 12pt; line-height: 115%;"> We can determine the relative velocities of hydrogen and oxygen by looking at their molar masses: **


 * <span style="font-family: 'Times New Roman','serif'; font-size: 12pt; line-height: 115%;"> V1/V2 = √32/√2 → V1/V2=4 **


 * <span style="font-family: 'Times New Roman','serif'; font-size: 12pt; line-height: 115%;"> This means that the hydrogen is moving 4 times faster than the oxygen. **


 * <span style="font-family: 'Times New Roman','serif'; font-size: 12pt; line-height: 115%;">__Dalton's Law of Partial Pressures__ **
 * John Dalton was an English Chemist who proposed the atomic theory. he found that in the absence of a chemical reaction, the pressure of a gas mixture is the sum of the individual pressures of each gas alone. The pressure of each gas in a mixture is called the partial pressure of that gas. Dalton's law of partial pressures states that the total pressure of a mixture of gases is equal to the sum of the partial pressures of the component gasses.**


 * Dalton's law can be written as [[image:http://upload.wikimedia.org/math/3/2/c/32cf78bb87a3eb4edc5c562a67ebc8f0.png]] or [[image:http://upload.wikimedia.org/math/c/b/4/cb45ddd733b18f16ea8bb954e3193256.png]]**


 * __Combined Gas Law__**


 * Now that we know Boyle's Law, Charles' Law, and Lussac's Law, we can use the combined gas law to find the volume, pressure, or temperature in °C, of any given gas.**
 * The combined gas law is written as (P1V1)/T1=(P2V2)/T2 [[image:reich-chemistry/combined.gif width="148" height="70" align="right"]]**


 * In some cases, a variable may be held constant. When the pressure is held constant, the equation turns into V1/T1=V2/T2. When the temperature is held constant, the equation is P1V1=P2V2. When the volume is held constant P1/T1=P2/V2. However, when the value of every variable is given, you must use the combined gas law.**


 * __Ideal Gas Law__**


 * The Ideal gas law is: PV=nRT where P=pressure in either atm or kpa, V= volume in liters, n=number of moles, R=gas constant, and T=temperature in kelvin.**
 * Depending on the unit of pressure, the R value changes.**
 * When P is in atm, R= 0.08206. When P is in kpa, R= 8.314.**
 * Example: What is the volume of any gas at 1 atm and 0°C?**
 * PV=nRT (1)(V)=(1)(0.08206)(0+273) V=22.4 L[[image:http://www.chemistryland.com/CHM130/Web-PowerPoints/Gases_PV_nRT.jpg width="215" height="171" align="right"]]**


 * We already know that n=the number of moles. We also know that moles= mass/molar mass. Therefore, by only knowing either the mass or the molar mass, we can find n.**
 * The new equation is PV=(mass/molar mass)RT**
 * Example: What is the mass of chlorine if its molar mass is 71 g/mol the pressure is 2 atm, the volume is 5 L, and the temperature is 295°K**
 * (2)(5)=(mass/71)(0.08206)(295) 10=(mass/71)(24.2) 0.41=mass/71 mass=29.3 g.**


 * __Gas Stoichiometry__ **
 * Now that we have learned the Ideal Gas Law – PV=nRT where P=Pressure; V=Volume; n=number of moles; R=gas constant; and T=Temperature in Kelvin – we can use this law in Stoichiometry. In order to understand gas stoichiometry lets review what stoichiometry is. When balancing equations we determine the number of moles needed of each compound or element to complete the reaction. From here we can look at the ratios of moles. The ratio of moles will be constant for the reaction. Therefore, if we know the number of moles we have of one compound we can determine the number of moles of every other compound.**


 * Take for example the reaction of C2H5OH and O2 to form CO2 and H2O.**


 * The reaction is written as: C2H5OH + 3O2 -> 2CO2 + 3H2O**


 * The mole ratios are 1:3:2:3**


 * Given 100 grams of C2H5OH how many grams of the other three compounds do you have?**


 * To solve this we make our stoichiometry table and plug in what we know to determine what we don’t know.**
 * || **C2H5OH** || **O2** || **→** || **CO2** || **H20** ||
 * **grams** || **100 g** || **208.32 g** ||  || **190.96 g** || **117.18 g** ||
 * **molar mass** || **46 g/mol** || **32 g/mol** ||  || **44 g/mol** || **18 g/mol** ||
 * **moles** || **2.17 mol** || **6.51 mol** ||  || **4.34 mol** || **6.51 mol** ||


 * Knowing the mole ratios we can determine the number of moles of each other compound and from there determine the amount of grams based on the molar mass of that compound**


 * This concept can be applied to gases. As stated above the Ideal Gas Law is PV=nRT. In this equation we can determine the number of moles of a certain gas in a reaction. If we know the number of moles of the gas and the mole ratio of the gas to the other compounds in the reaction, we can determine the number of moles of each other compound in the reaction. This would be done by using simple stoichiometry.**


 * __Example:__**


 * How many grams of Nitrogen at 200 K and 3.25 atm would be required to produce 50 g of ammonia?**


 * To solve this we would set up a stoichiometry table and plug in the values we know.**


 * The reaction is:**
 * N2 + 3H2 -> 2NH3**


 * We know the mole ratio is 1:3:2--- therefore we know that 2.94/2 will give us the number of moles of nitrogen.**


 * || **N2** || **H2** || **→** || **NH3** ||
 * **grams** || **50 g** ||  ||   || **50 g** ||
 * **molar mass** || **17 g/mol** ||  ||   || **17 g/mol** ||
 * **moles** || **1.41 mol** ||  ||   || **2.94 mol** ||
 * 2.94/2 = 1.41**


 * Once we know the number of moles we can determine the number of grams needed.**


 * n= mass/molar mass --- 1.41=mass/28 --- mass=39.48 grams**


 * From here we can determine the volume of the gas using the ideal gas law.**


 * PV=nRT --- (3.25)V=(1.41)(.08206)(200) --- V=7.12**


 * __ Lussac’s Law __**
 * Lussac’s law was discovered by the French chemist Joseph Louis Gay-Lussac in 1802. The law states that the pressure of a fixed mass and fixed volume of a gas is directly proportional to the gas's temperature. This basically means that if a gas's temperature increases then so does its pressure, as long as the mass and the volume are held constant. This is possible because temperature is the measure of the kinetic energy of a substance, and as the kinetic energy increases, the particles of the substance move more quickly, exerting more force on the container holding the gas. This in turn exerts increased pressure. **
 * The law can be written as P/T=k **
 * Where: P is the pressure of the gas **
 * T is the temperature of the gas (in kelvins) **
 * k is a constant **
 * When comparing the substance under two separate sets of conditions, this law can be translated to: **
 * P1/T1=P2/T2 **
 * Example: **
 * Five grams of octane (C8H18) and enough oxygen to burn it are in an automobile cylinder compressed to 20 atm at 28°C. The mixture explodes and heats the cylinder to 150°C. What is the pressure in the (same sized) cylinder after the explosion? **


 * P1 = 20 atm, T1 = 301K, P2 = ?, T2 = 423 K **
 * P1 / T1 = P2 / T2 **
 * (20)/(301) = (P2)/(423) **
 * P2 = 28.4 atm [[image:http://www.grc.nasa.gov/WWW/K-12/airplane/Images/glussac.gif width="497" height="372"]] **


 * __ Boyle’s Law __**


 * Boyle’s law was first developed by amateur scientists Richard Towneley and Henry Power, but then confirmed and published by Robert Boyle. This law states that the absolute pressure and the volume of a gas are inversely proportional at a constant temperature. This means that as volume increases, pressure decreases, or vice versa. This works because, if the volume of a container is increased, there is a greater area in which the particles of gas inside the container can move. Since the particles have more space, there is less force exerted on the walls of the container by the particles and therefore, less pressure.**
 * The law can be written as: PV=k **
 * Where: P is the pressure**
 * V is the volume**
 * k is a constant**


 * When comparing the substance under two different sets of conditions, this law can be translated to:**


 * P1*V1=P2*V2 **


 * Example:**
 * What pressure is required to compress 196.0 liters of air at 1.00 atmosphere into a cylinder whose volume is 26.0 liters**
 * Boyles Law**
 * P1 = 1 atm, V1 = 196 L, P2 = ?, V2 = 26 lL**
 * (1) (196) = (P2) (26)**
 * P2 = 7.5 atm**