Gas Laws Introduction

Review of Gases Ideal gases: In constant, random motion Travel in a straight line until colliding with other gas molecules or the walls of the container All collisions are perfectly elastic (KE and Momentum are conserved) Gases diffuse throughout a container until there is an equal concentration throughout the container

Gas Pressure Caused by collisions with walls of the container Each time a molecule hits the wall of a container, the molecule exerts a force on the wall and the wall exerts an equal and opposite force (momentum conserved) For a given volume, more molecules means a higher pressure, due to a higher number of collisions. More moles = more constant Volume. Pressure is measured in Pascals (Pa) and Atmospheres (atm). 1 Pa = 1 N/m 2. like a ¼ of a pound spread over 4 desktops 1 atm = 101,325 Pa or Kpa 1 atm = 760mmHg = 760 torr

Concept Questions What effects do changes in the amount of gas and in the volume of the container have on gas pressure? What is the effect of temperature change on the pressure of a contained gas? What would you have to do to the volume of a gas to reduce its pressure to ¼ of the original pressure at constant pressure? Keeping the temperature constant, how could you increase the pressure in a container by one hundredfold? The manufacturer of an aerosol deodorant packaged in a 150- mL container wishes to produce a container of the same size that will hold twice as much gas. How will the pressure of the gas in the new product compare with that of the gas in the original container?

Boyle’s Law – P & V Boyle’s law relates Pressure and Volume P 1 * V 1 = P 2 * V 2 Can be rewritten to solve using Cross-Multiply and Divide Boyle’s law is inversely proportional, with constant temperature as Volume increases, Pressure decreases Examples include bike pumps and syringes.

Boyle’s Law Example A party balloon at 1 atm, with a volume of 15 L is put in a vacuum where the pressure is decreased to 0.33 atm. What will the new volume of the balloon be?

Charle’s Law – T & V Charle’s Law relates Temperature and Volume Temperatures should be done in Kelvin (K). Written as: Charle’s Law is dependent on conditions of constant pressure. Charle’s Law is directly proportional. If you increase the temperature of a balloon, it will inflate. If you decrease the temperature of a balloon, it will shrink. Liquid Nitrogen and balloon. Liquid Nitrogen and balloon Plunger Fire Starter

Charle’s Law Example If a sample of gas occupies 100L at 40°C, what will be it’s volume at 80°C if the pressure stays the same? Notice: a doubling of the temperature in Celsius doesn’t cause a doubling of the Volume. It’s important to always put the temperatures in Kelvin first!!!

Gay-Lussac’s Law – P & T Relates Pressure and Temperature. Written as: Pressure and Temperature are directly proportional. If you throw a pop can into a fire, what happens to the pop can? Can in fire.

Gay-Lussac’s Law Example The pressure inside a can of Coke at 4°C is roughly 343kPa. What will the pressure be when the can reaches 100°C, roughly the boiling point of the soda? =461.8kPa

Combined Gas Law Links relationship between Pressure, Temperature and Volume.

Combined Gas Law Example A car tire is pumped up in the summer (T=29°C) to a pressure of Kpa. The volume of the tire is 26L. What will the pressure be in the winter (T=-5°C) assuming that the volume of the tire stays the same? = Kpa

Combined Gas Law Example 2 In a car engine, when the fuel/oxygen mix is introduced to a spark, combustion occurs and the result is very hot expanding gases, that drive the pistons and eventually make the car move. If the fuel oxygen mix starts at a temperature of 27°C and occupies.050L while compressed in the cylinder to 1034 kPa, what will be the pressure after combustion when the gases are now at 2100°C and they’ve expanded to.75 L?

Example 2 continued… The resulting pressure is still significantly high enough to allow the exhaust gases to quickly exit the exhaust valves as the piston finishes the fourth phase of the cycle.

Standard Temperature & Pressure (STP) STP are conditions of pressure and temperature that are set to compare gases and reactions at. There are several values for STP, but we will use the conditions of 0°C and 1 atm of pressure. When doing Stoichiometry we used the number 22.4L/mol to convert from volume to moles L/mol only works at STP, though. In the real world, temperatures and pressures can change, so to know how many moles of gas there are for a given set of conditions we use…

The Ideal Gas Law Combines all gas laws with Avogadro’s Hypothesis. Avogadro’s Hypothesis – “Under conditions of constant Temperature and constant Pressure, equal volumes of all gases contain the same number of molecules/atoms” It’s where we get the 22.4 L/mol number in Stoichiometry. 10L of O 2 will have the same number of molecules as 10L of C 3 H 8.

PV=nRT PV = nRT  pronounced “pvnert” P = pressure V = volume n = number of moles T = Temperature R = Ideal Gas constant. Has several values based on what units the other measurements are done in.

PV=nRT Example A sample of CO 2 at 30°C and 2.5atm occupies a volume of 40L. How many moles of CO 2 are there in the sample?