Gas Laws
Boyles Law (12.2): Pressure and Volume 1 atm = 760 torr = 760 mm Hg = 14.7 psi = 101.325 kPa In Boyle’s experiments he took a given quantity of gas, changed the volume and measured how the gas pressure responded. See data table on pg. 363 PV = k P = Pressure V = Volume k = constant for Boyles data k = 1.41 x 103 hg x in.3
Boyles Law You will not need to know a value for “k.” If you need it you can calculate it for any given problem. Calculate k for these examples: 1. You have a gas pressure of 2 atm in a .5 L bottle. 2. A test tube contains 0.035 L of Ne gas at a pressure of 250 torr.
Boyles Law: Changing pressure: What if the pressure or volume changes? The new volume and pressure will have the same constant as the old volume and pressure (assuming the temperature and mol of gas has not changed) Old volume x old pressure = k V1P1=k New volume x new pressure = k V2P2=k V1P1= V2P2
As the volume decreases, the particles collide with the sides of the container more often (pressure)
Practice Problems 1. There is 35 ml of air in a syringe it is at 1 atm. Mr. Bonifaci squeezes the syringe so that it has a volume of 20 ml. What is its pressure?
Practice Problems 2. A little boy is holding a balloon (it is 2.3 L big and has a pressure of 10.2 atm). His mean big sister grabs it and begins to squeeze it. Before it pops and the little boy screams it has a pressure of 35.9 atm. What is its volume? 3. A pick-up truck’s tires contain 23.5 L of air at a pressure of 3.2 atm. You and your ten best friends hop in the back of the truck (but you are not going to drive anywhere, that would be dangerous). The added weight squeezes the tires to a volume of 19.5 L. What is the new tire pressure?
Pattern When the volume gets smaller… The pressure increases. When the volume gets bigger… The pressure decreases.
Homework Homework: Read 12.2, # 14, 15, 17 (a,b), 19 (a), 23, 24
Charles Law: Volume and Temperature (12.3) Charles experimented by changing the temperature of a gas and measuring the resulting volume. (See graphs pg. 367) Note: Amount of gas (mol) and pressure must be constant.
Charles Law: Volume and Temperature He observed that the cooler the gas, the less volume. The kinetic theory of matter explains this by saying that slower moving particles will make less collisions and therefore push outward less (less volume).
Charles Law: Volume and Temperature Notice the graphs reach a volume of 0 L at -273 C. We call this absolute zero. This is the temperature in which matter (theoretically) stops moving and has no volume. In Kelvin it is 0 K. Remember: C + 273 = K
Charles Law Charles Law Mathematically: V V=bT or T = b V=Volume V=Volume T=Temperature (MUST BE IN K) b=constant
Charles Law If the mol of gas and pressure do not change, then: Old Volume / Old Temp = b V1 / T1 = b New Volume / New Temp =b V2 / T2 = b V1 / T1 = V2 / T2
Practice 4.0 L of gas is collected at 278 K and then heated to 351 K. The pressure is constant at 1 atm. Does the gas expand or shrink? What is the new volume?
Practice A sample of gas is gathered at 55 degrees C (1 atm). Its volume measures 9.5 L. We put the gas in the freezer and it cools to -10 degree C. What is its new volume? A balloon has a temperature of 40 C and a volume of 2.1 L. A student puts it in the freezer and later measures a new volume of 1.5 L. What temperature was the balloon when the student measured it the 2nd time?
Homework: Read 12.3, answer # 25, 29-31
Avogadro’s Law: Volume and Moles (12.4) Avogadro discovered that the volume of gas and the number of molecules of gas were related. Remember: 1 mol of gas take up 22.4 L at STP. However, there is still a relationship when gas is not at STP. Both temperature and pressure must remain constant
Avogadro’s Law: Volume and Moles (12.4) V1 V2 n1 = n2 V= volume n= mol
Practice Problems Image we have 45.2 L of gas containing 2.5 mol of N2. The temperature is 18 C and the pressure is 1 atm. The sample is separated and 2.5 L of gas is captured in a second container. How many mol of N2 are in this new container?
Practice Problems A gas has a temperature of 90 C and is a 1.3 atm. It has a volume of 13.5 L and contains 43 g of N2 gas. How many mol would 63.2 L of gas contain at the same temperature and pressure? Challenge Problem: We have a 12.2 L sample of O2 containing .5 mol of gas. The pressure is 1 atm and the temperature is 25 C. If all the O2 is converted to O3. What is the new volume of O3?
Homework: HW: read 12.4. Answer: 41-44, 33, 109, 121
Ideal Gas Law: (12.5) Over the last few days we have seen how several variables affect the volume of gas. What were they?
Ideal Gas Law: (12.5) Over the last few days we have seen how several variables affect the volume of gas. What were they? Boyles law: V1P1= V2P2 Charles law: V1 / T1 = V2 / T2 Avogadro’s law: V1 V2 n1 = n2
Ideal gas law: These can be combined into the equation: PV = nRT PV = nRT P = Pressure (in atm) V = Volume (in L) n = mol of gas T = Temperature (in K) R = universal gas constant = 0.08206 L atm/K mol
Ideal Gas Law This is called the ideal gas law because a gas that obeys this equation is said to behave ideally. Most gases obey this equation at pressures of 1 atm or lower and temperature 0 C and higher.
Practice A sample of O2 gas has a volume of 9.02 L, a temperature of 5 C, and a pressure of 1.9 atm. How many moles of gas are within this sample?
Practice What is the volume of a balloon containing 5x103 mol of gas, at 40 C, and 850 torr?
Practice Imagine that we have a 3.5 L container. Within it is .240 mol of gas at 25 C and 1.68 atm. The gas is transferred to a smaller container (1995 ml). The temperature and amount of gas are constant. What is the new pressure? A sample of methane gas has a pressure of 0.454 atm, a volume of 3.48 L and is a -15 C. The conditions change and the new pressure is 0.616 atm and the gas warms to 36 C. What is the new volume?
Homework Homework: Read 12.5 Answer: 49, 53, 56
Complex Gas laws Problems When doing a gas laws problem: List all information given in the problem If only 2 variables change (if a variable stays constant or does not change, ignore it) use the appropriate law. P and V = Boyle’s T and V = Charles’ n and V = Avagadro’s If nothing is changing and you are given 3 of the 4 variables, use the ideal gas law to find the 4th If 3 of the variables are changing use the ideal gas law (use the final variables).
Practice: A sample of B2H6, has a pressure of .454 atm at a temperature of -15 C and a volume of 3.48 L. If conditions change so that the temperature is 36 C and the pressure is .616 atm, what will be the new volume?