The Combined Gas Law

Complete the beginning of your notes based on your knowledge of manipulating equations.

The left side of the combined gas law is where we write the initial state of the gas. This can be thought of as the “before” picture. The right side of the combined gas law is where we write the final state of the gas. This can be thought of as the “after” picture.

= Combined Gas Law P1V1 P2V2 n1T1 n2T2 The Combined Gas Law can be used to easily and quickly tell whether variables are inversely or directly proportional. Combined Gas Law P1V1 P2V2 n1T1 n2T2 = 4

Combined Gas Law P1V1 P2V2 n1T1 n2T2 = Being directly proportional means that the variables go up together and come down together. Notice that volume and temperature are directly proportional, and they are found on opposite sides of the division sign.

Notice that pressure and volume are Combined Gas Law P1V1 P2V2 n1T1 n2T2 = Being inversely proportional means that if one goes up, the other comes down. Notice that pressure and volume are inversely proportional, and they are found on the same side of the division sign.

Combined Gas Law Several simplified relationships have already been provided to you on your reference sheet. However, you may need to determine the relationship between two variables which do NOT have their own equation.

Combined Gas Law P1V1 P2V2 n1T1 n2T2 = = = P1 P2 n1 n2 2.0 atm P2 To derive any equation between two variables, simply scratch out whichever variables are being held constant. P1V1 P2V2 n1T1 n2T2 = Example: 5.0 moles of nitrogen gas are in a container with a pressure of 2.0 atmospheres. What would the pressure be if 7.0 moles were in a container with the same volume at the same temperature? P1 P2 n1 n2 = 2.0 atm P2 5.0 mol 7.0 mol = (5.0)P2 = 14.0 P2 = 2.8 atm 8

Combined Gas Law P1V1 P2V2 n1T1 n2T2 = = = P1 P2 T1 T2 To derive any equation between two variables, simply scratch out whichever variables are being held constant. P1V1 P2V2 n1T1 n2T2 = Example: The pressure of a container is 100. kPa at a temperature of 300. K. At what temperature would the pressure be 150. kPa if the volume and number of moles of gas are held constant? P1 P2 T1 T2 = 100. kPa 150. kPa 300. K T2 = (100)T2 = 45000 T2 = 450. K 9

While there are 3 major temperature scales, only 2 of these are commonly used by scientists: Celsius and Kelvin are the temperature scales used by most scientists. While you are familiar with Fahrenheit, it is not a widely used scale for science.

The Kelvin Temperature Scale Temperature is the measure of the average kinetic energy of the atoms or molecules. Temperature measures the average kinetic energy of a system, and kinetic energy is the energy of motion. This means that the lowest temperature that can be reached is when all of the molecules have stopped! This is absolute zero. 0 K = -273 oC

Converting Between Temperature Scales Absolute Zero 0 K = -273 oC Kelvin = oC + 273 oC = K - 273 Important Fact: In order for our gas law equations to work correctly, temperatures must ALWAYS be in Kelvin!

Convert the temperatures on your notes between Celsius and Kelvin. Notice that for any given temperature, the Kelvin measurement is ALWAYS LARGER.

So why is the combined gas law important? The combined gas law is important because it allows us to predict how gases will be affected be a change in temperature, pressure or volume by using a simple mathematical equation.