Bell Ringer Quiz A gas bubble is squeezed with 7.42 atm of pressure. The bubble started at a size of 2.7 L under STP conditions. What is the size of the bubble once it is squeezed? 0.36 L Knowing that Charles’ Law deals with temperature and volume, what does 2.6 L change to when the temperature is decreased from 200 K to 100 K? 1.3 L What are the following elements: Hf, Os, Pb, Au, Rn, Fr, W Hafnium, Osmium, Lead, Gold, Radon, Francium, Tungsten

Gay-Lussac Gas Law Ideal Gas Law Important Concepts: Gay-Lussac Gas Law Ideal Gas Law Kinetic Theory of Gases Ideal Behavior of Gases

Boyle’s Law Review Boyle’s Law relates pressure and volume P1V1= P2V2 The relationship between pressure and volume is known as what type of relationship? Inverse Relationship What two variables are held constant for Boyle’s Law? Number of particles and temperature

Charles’ Law Review Charles’ Law relates volume and temperature The relationship between volume and temperature is known as what type of relationship? Directly Proportional What is held constant for Charles’ Law? Number of particles and pressure

Absolute Zero and Kelvin Scale Absolute zero is the temperature at which the volume of a gas becomes zero when the a plot of the volume versus temperature for a gas are extrapolated. As expected, the value of absolute zero obtained by extrapolating the data is essentially the same as the value obtained from the graph of pressure versus temperature in the preceding section. Absolute zero can therefore be more accurately defined as the temperature at which the pressure and the volume of a gas extrapolate to zero. A plot of the volume versus the temperature of a gas (when the temperatures obtained are converted from Celsius to the Kelvin scale) becomes a straight line that passes through the origin. Any two points along this line can therefore be used to construct the following equation, which is known as Charles' law. Before using this equation, it is important to remember that temperatures must be converted from C to K

Gay-Lussac’s Law Gay-Lussac was a French Chemist who discovered the relationship between temperature and pressure He kept volume and the number of particles constant His testing found that as temperature increases the pressure inside a fixed volume increases This relationship is known as a directly proportional relationship

Gay-Lussac’s Law Gay-Lussac’s Law states that pressure in directly proportional to temperature in a closed volume that does not change He found that the relationship between pressure and temperature was always constant He found that Knowing this he set both sides equal and derived his law:

Example Problem #1 If a container is heated from 100 K to 135 K that had an initial pressure of 689 torr, what is its pressure after being heated? T1 = 100 K T2 = 135 K P1 = 689 torr P2 = x torr

Practice Problem #1 If a steel container has an internal pressure of 300.2 kPa with a temperature of 273 K is submersed in water. The new pressure inside the container is 101.13 kPa. The container and the water reach equilibrium. What is the temperature of the water? T1 = 273 K T2 = x K P1 = 300.2 kPa P2 = 101.13 kPa

Combined Gas Law Boyle’s, Charles’, and Gay-Lussac’s Laws deal with pressure, volume, and temperature. In the natural world, is it possible to separate pressure, volume, and temperature? In the natural world, these three variables are intertwined and need to be accounted for when dealing with gas properties To account for this inseparability, a gas law was devised to incorporate all three variables. This gas law is known as the combined gas law which states the following

Example Problem #2 If a balloon was inflated with He at STP conditions and had a volume of 1.0 L was released and reached an elevation where the pressure was 0.86 atm and 238.1 K, what would the new volume of the balloon be? T1 = 273 K T2 = 238.1 K P1 = 1 atm P2 = 0.86 atm V1 = 1.0 L V2 = x L

A New Gas Law With the discovery of the combined gas law, we are now able to take the final step in the gas laws. Let’s make some observations and deductions about the gas laws. What was always kept constant in all 4 gas laws? Number of particles When each gas law was solved for one half of the equation what was seen to be true? It was found to be a constant If each gas law keeps the number of particles the same, what would happen if we changed the number of particles? A new gas law would need to be derived

Deriving the Ideal Gas Law If we add in more gas particles to a balloon, what do you predict will happen to the pressure, temperature, and volume of the balloon? The pressure would increase The volume would increase The temperature would increase Since all of these variables increase with an increase in particles what is the relationship between these variables? Directly proportional

Ideal Gas Law Knowing that volume, pressure, and temperature are directly proportional to the number of particles, we can add number of particles (n) to our previously discovered combined gas law to make this relationship: Without even knowing it, we have derived what is known as the Ideal Gas Law The constant k in the above equation is known as the gas constant actually known as R R is equal to 0.082057461(L*atm)/(K* ) mol is back!!

Ideal Gas Law Now that we know that k = R for the ideal gas law we can now setup the Ideal Gas Law For this law scientists made n equal to moles and not number of particles to make the math easier to handle Knowing the ideal gas law makes remembering the other 4 gas laws pointless… WHY!?!

WHY?!? Remembering the other gas laws becomes pointless because if you set the ideal gas law equal to R and the set it equal to itself anything that is held constant on both sides will cancel out. Do you see the other gas laws?

Example Problem #3 A vessel contains 2.87 moles of CO. The volume of the container is 3.8 L and it has a temperature of 243 K. What is the pressure inside the container?

Quiz

Question 1 What does STP stand for AND what are the values associated with it? Saturated temperature point AND 0 0C at 1 atm Standard temperature and pressure AND 0 0C at 1 atm Standing Tempo Pianissimo and 100 0C at 0 atm Standard temperature and pressure AND 100 0C at 0 atm

Question 2 What causes gases to not behave ideally? High Pressure Bad upbringing Being to hot Low temperature Low pressure Improper measuring

Question 3 What happens to the molecules of gas if the temperature is increased AND what happens to the pressure? The molecules slow down The molecules stick together The molecules speed up The pressure decreases The pressure increases The pressure stays the same

Question 4 What is the direct measure of average kinetic energy? Density Pressure Volume Temperature Conductivity

Question 5 What is an ideal gas? A gas that interacts with its neighbor gas particles, can stop, and stick together A gas that elastically bounces, has constant motion, no attraction or repulsion A gas that elastically bounces but stops from time to time A unstoppable particle that cannot be contained except by the incredible hulk