Measurements of Pressure

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1 Measurements of Pressure ì ì ì Pressure can have a variety of methods of measurement These include the atmosphere (atm), the kilopascal (kpa), mm of Mercury (mm of Hg), milibars (mb), and pounds per square inch (psi) You must know how to convert between kpa/psi, mmhg/atm, and psi/atm

2 Conversion Factors ì Here are the conversion factors for the various pressure units: ì 1atm = 760 mm of Hg = psi = bar = Pascal = Kpa = 760 Torr ì ì Basically mm of Hg is the same as Torr And Kpa is just 1000x larger than Pa.

3 Try the following ì Convert the following ì 1 atm to mm of Hg ì 500 mm of Hg to atm ì 400 Torr to mm of Hg ì 300kpa to atm ì 3 atm to mm of Hg

4 CHAPTER 14 GASES & ATMOSPHERE Mr.Yeung

5 Objective 3 basic laws Boyle s law Charles law Gay-Lussac s law Combining the above laws Combined gas law Ideal gas law

6 Intro Gases There are more spaces between the particles in a gas than liquids and solids

7 Thinking in gases In gases, think of the kinetic theory The movement of the molecules has the ability to Expand (heat up a balloon) Take shape (use gas to fill up any thing) Change in volume (change the pressure of a balloon)

8 Four variables used to describe a gas Pressure (P) in kilopascals, or others Volume (V) in liters Temperature (T) in kelvin Number of moles (n)

9 Gases at STP (Standard Temperature Pressure) When gases are said to be at STP, it means it is at 0 C (273K), 101.3kPa or 1atm.

10 Overall gas laws There are 4 gas laws: Boyles law Charles law Gay-lussac s law Combined gas law Ideal gas law (involves moles)

11 Boyle s Law Variables: Pressure & Volume Constant variable: Temperature P 1 V 1 = P 2 V 2 GayLussac s Law Variables: Pressure & Temperature Constant variable: Volume Temperature in Kelvin P 1 T 1 = P 2 T 2 Charles Law Variables: Temperature & Volume Constant variable: Pressure Temperature must be in Kelvin! V 1 T 1 = V 2 T 2

12 Boyle s law He states for a given mass of gas at constant temperature, the volume of the gas varies inversely with pressure. P 1 V 1 = P 2 V 2 P = Pressure V = Volume Assuming the same amount of mols and at the same temperature Inversely proportional means the higher the pressure, the lower the volume

13 Note: There is still the same number of gas molecules from the first one to the other. The number of gas molecules do not change, it is the space that the molecules can move around decreased (with added pressure!

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15 Low pressure = high volume Know this graphical relationship in Boyle s law!!! Increase in pressure = low volume

16 Why is it a linear relationship? (straight line?) Graphing pressure vs 1/volume gives a linear relationship The graph is pressure and the inverse of volume. Since the relationship between pressure and volume is an INVERSE relationship, graphing the inverse of volume will give you a straight line.

17 Example A balloon contains 30.0L of helium gas at 103 kpa. What is the volume of the helium when the balloon rises to an altitude where the pressure is only 25.0 kpa? P 1 = 103 kpa V 1 = 30.0 L P 2 = 25.0 kpa Unknown: V 2 =?L

18 Answer V2 = (V1 * P1)/P2 V2 = (30.0L * 103kPa)/25.0kPa = 1.24 X 10 2 L

19 Charles Law ü You buy a helium balloon for your lovely girlfriend for Valentines day. You take the balloon outside into the -30C temperature, and the balloon shrunk half its size. You walk back to the store and see the balloon in it s regular size. What just happened?

20 Charles law ü As the temperature of the enclosed gas increases, the volume increases, if the pressure is constant (same). So the hotter it gets, the more volume (more space the gas molecules has to move around) you get and vice versa Or the colder it gets, the molecules distance within each other decreases, the size of the balloon shrinks.

21 Know this graphical representation!

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24 Charles Law Symbolic V 1 = V 2 T 1 T 2 V = volume (L) T = Temperature (K)

25 Why does the temperature have to be in Kelvin? When he collected his results, he extrapolated (extended) and found that when the volume was equaled to 0L, it was at degrees Celsius. Converting Celsius to Kelvin 273K = 0C DO NOT USE Unit ANALYSIS for this because Celsius and Kelvin are not proportional to each other. If you increase 5 degrees C, it does not increase 5 degrees Kelvin! So basically just add 273 to get Kelvin from Celsius a) 15C b) 45C c) -23C d) 0C 288K 318K 230K 273K

26 Problem A balloon inflated in a room at 24 C has a volume of 4.00L. The balloon is then heated to a temperature of 58C. What is the new volume if the pressure remains constant?

27 Answer V1 = 4.0L T1 = 24C T2 = 58C V2 =? Convert to Kelvin T1 = = 297K T2 = = 331K Use Charles equation V2 = (V1 * T2)/T1 V2 = (4.0L * 331K)/297K =4.46L

28 Gay-Lussac s Law Gay-Lussac's Law states: that the pressure of a sample of gas at constant volume, is directly proportional to its temperature in Kelvin. Increased temperature = increased pressure Constant variable: Volume (doesn t change), so think about a enclosed can, the volume doesn t change when heated.

29 Gay-Lussac s law Equation: Examples: P 1 T 1 = P 2 T 2 Exploding beer kegs, aerosol cans, or soda cans in the heat.

30 Gay-Lussac law example Example: 10.0 L of a gas is found to exert 97.0 kpa at 25.0 C. What would be the required temperature (in Celsius) to change the pressure to standard pressure keeping a constant volume? P1: 97.0 kpa T1: 25C = 298 P 1 T 1 = P 2 T = T 2 P2: kpa T2: Change your temperatures to Kelvin! T 2 = K

31 Combined Gas Law Consider the following: If the top diagram is similar to a see-saw What happens when P is held constant? T and V move together (Proportional) What happens when T is held constant? P moves up and V moves down and vice versa (Inverse relationship)

32 The combined gas law can be expressed as: P = Pressure V = in Litres T = in Kelvin Here s an example: P 1 V 1 T 1 = P 2 V 2 T 2 If a gas occupies a volume of 25L at 25ºC and 1.25atm, calculate the volume at 128ºC and 0.75atm

33 Step 1: Change temp to Kelvin 25ºC = 298K 128ºC = 401K Step 2: Solve for V 2 using the CGL V 2 = P 1 V 1 T 2 = (1.25atm)(25L)(401K) P 2 T 1 (0.75atm)(298K) V 2 = 56.1L