Gay-Lussacs Ideal Gas Law Examples

Gays Gay-Lussacs gas law  is a special case of the  ideal gas law  where the volume of the gas is held constant. When the volume is held constant, the pressure exerted by a gas is directly proportional to the absolute temperature of the gas. The law is also known as Gay-Lussacs law of pressure temperature. Gay-Lussac formulated the law between 1800 and 1802 while building an air thermometer. These example problems use  Gay-Lussacs law to find the pressure of gas in a heated container as well as the temperature you would need to change the pressure of gas in a container. Key Takeaways: Gay-Lussac's Law Chemistry Problems Gay-Lussacs law is a form of the ideal gas law in which gas volume is kept constant.When volume is held constant, pressure of a gas is directly proportional to its temperature.The usual equations for Gay-Lussacs law are P/T constant or Pi/Ti   Pf/Tf.The reason the law works is that temperature is a measure of average kinetic energy, so as the kinetic energy increases, more particle collisions occur and pressure increases. If temperature decreases, there is less kinetic energy, fewer collisions, and lower pressure. Gay A 20-liter cylinder contains 6  atmospheres (atm)  of gas at 27 C. What would the pressure of the gas be if the gas was heated to 77 C? To solve the problem, just work through the following steps:The cylinders volume remains unchanged while the gas is heated so Gay-Lussacs gas law applies. Gay-Lussacs gas law can be expressed as:Pi/Ti Pf/TfwherePi and Ti are the initial pressure and absolute temperaturesPf and Tf are the final pressure and absolute temperatureFirst, convert the temperatures to absolute temperatures.Ti 27 C 27 273 K 300 KTf 77 C 77 273 K 350 KUse these values in Gay-Lussacs equation and solve for Pf.Pf PiTf/TiPf (6 atm)(350K)/(300 K)Pf 7 atmThe answer you derive would be:The pressure will increase to 7 atm after heating the gas from 27 C to 77 C. Another Example See if you understand the concept by  solving another problem: Find the temperature in Celsius needed to change the pressure of 10.0 liters of a gas that has a pressure of 97.0 kPa at 25 C to standard pressure. Standard pressure is 101.325 kPa. First, convert  25 C to  Kelvin  (298K).  Remember that the Kelvin temperature scale is an  absolute temperature  scale based on the definition that the  volume  of a  gas  at constant (low)  pressure  is directly proportional to the  temperature  and that 100 degrees separate the  freezing  and  boiling points  of water. Insert the numbers into the equation to get: 97.0 kPa / 298 K 101.325 kPa / x solving for x: x (101.325 kPa)(298 K)/(97.0 kPa) x 311.3 K Subtract 273 to get the answer in Celsius. x 38.3 C Tips and Warnings Keep these points in mind when solving a  Gay-Lussacs law problem: The volume and quantity of gas are held constant.If the temperature of the gas increases, pressure increases.If temperature decreases, pressure decreases. Temperature is a measure of the kinetic energy of gas molecules. At a low temperature, the molecules are moving more slowly and will hit the wall of a  containerless  frequently. As temperature increases so do the motion of the molecules. They strike the walls of the container more often, which is seen as an increase in pressure.   The direct relationship only applies if the temperature is given in Kelvin. The most common mistakes students make working this type of problem is forgetting to convert to Kelvin or else doing the conversion incorrectly. The other error is neglecting  significant figures  in the answer. Use the smallest number of significant figures given in the problem. Sources Barnett, Martin K. (1941). A brief history of thermometry. Journal of Chemical Education, 18 (8): 358. doi:10.1021/ed018p358Crosland, M. P. (1961), The Origins of Gay-Lussacs Law of Combining Volumes of Gases, Annals of Science, 17 (1): 1, doi:10.1080/00033796100202521Gay-Lussac, J. L. (1809). Mà ©moire sur la combinaison des substances gazeuses, les unes avec les autres (Memoir on the combination of gaseous substances with each other). Mà ©moires de la Socià ©tà © dArcueil 2: 207–234.  Tippens, Paul E. (2007). Physics, 7th ed. McGraw-Hill. 386–387.