1. Write down the ideal gas law and define all its variable and parameters. 2. Calculate the values and units of the ideal gas law constant R.

Transcription

1 Ideal Gases Objectives:. Write dow the ideal gas law ad defie all its variable ad parameters.. Calculate the values ad uits of the ideal gas law costat R. 3. Calculate the value of oe variable,, T, or, from a give set of values. 4. Calculate the desity ad specific gravity of a gas. 5. Defie ad use partial pressure i gas calculatios. 6. Solve material balaces ivolvig gases.

2 Ideal gas law Lats, The most famous ad widely used equatio that relates,, ad T for a gas is the Ideal gas law: or Where = absolute pressure of the gas = Specific molar volume (volume per mole) of the gas = total volume occupied by the gas R= ideal (uiversal)gas costat = umber of moles of the gas T= absolute temperature of the gas Ideal gas law i three dimesios as a surface. The -T plae shows straight lies for costat values of,. = (costat) T. The - plae shows curves for costat values of T,. = Costat 3. The T- plae shows straight lies for costat,. = (costat) T

3 Ideal gas coditios The major coditios for a gas to behave as predicted by the ideal gas are:. The molecules of a ideal gas do ot occupy ay space.. No attractive forces exist betwee the molecules so that the molecules move completely idepedetly of each other. 3. The gas molecules move i radom, straight-lie motio, ad the collisios betwee the molecules, ad betwee the molecules ad the walls of the cotaier are perfectly elastic. Gases at low pressure ad/or high temperature meet these coditios. From a practical veiw poit withi reasoable error you ca treat air, oxyge, itroge, hydroge, carbo dioxide, methae, ad eve water vapor uder most of the ordiary coditios you ecouter as ideal gases Gas costat (uiversal / ideal) R.987 cal /g mol K.987 TU / lb mol R 0.73 psia ft 3 / lb mol R 8.34 ka m 3 / kg mol K 8.34 J / g mol K pressure moles volume temperature Lt 8.06 atm cm 3 / g mol K atm L / g mol K.9 i Hg ft 3 / lb mol R atm ft 3 / lb mol R ft lb f / lb mol R moles L T 3 3

4 Commo Stadard Coditios for the Ideal Gas Several Specified stadard coditios or S.C. or S.T.. for stadard temperature ad pressure have bee specified for gases System T / SI 73.5 K 0.35 ka.45 m 3 / kg mol Uiversal Scietific 0.0 C 760 mm Hg.45 liters / g mol Natural Gas Idustry 60 F psia ft 3 / lb mol merica Egieerig 3 F atm ft 3 / lbmol Example: Use of stadard coditios to calculate volume from mass Calculate the volume, i cubic meters, occupied by 40 kg of CO at stadard coditios assumig CO, acts as a ideal gas. asis: 40 kg of CO 40 kg CO kg mol CO.4 m 3 CO 44 kg CO kg mol CO =0.4 m 3 CO at S.C. 4

5 5 Ideal Gas I may processes goig from a iitial state to a fial state, it is coveiet to use the ratio of the ideal gas laws i the respective states, ad thus elimiate R as follows: T T Let be oe gas ad be aother: W / / W ) )( ( W W T T sp gr. If T =T = W W sp.gr : iitial state : fial state

6 How to use ideal gas equatio? i: iitial state f: fial state i = f 6

7 Ideal gas mixtures ad partial pressure artial pressure: Each compoet of a gas mixture exerts a pressure that it would exert if it were i the cotaier aloe. T + = T (mole balace) + t costat T & : + = T Dalto s Law of partial pressure i = T magat s Law of partial volumes Likewise for costat & T i = T 7

8 Ideal gas mixtures ad partial pressure Suppose moles of substace, moles of, C moles of C, ad so o, are cotaied i a volume at a temperature T ad total pressure. If there are moles of all species i the volume at pressure ad temperature T, the:... ( y y...) y Dalto s law y The partial pressure of a compoet i a ideal gas mixture is the mole fractio of that compoet times the total pressure. Likewise for costat & T: y y... ( y y...) magat s law 8

9 Example: Effect of T ad o volumetric flow rate Te cubic feet of air at 70 F ad atm is heated to 60 F ad compresses to.5 atm. What volume does the gas occupy i its fial state? 9

10 Example: aterial balaces o a evaporator-compressor Liquid acetoe (C 3 H 6 O) is fed at a rate of 400 L/mi ito a heated chamber, where it evaporates ito a itroge stream. The gas leavig the heater is diluted by aother itroge stream flowig at a measured rate of 49 m 3 (ST)/mi. The combied gases are the compressed to a total pressure =6.3 atm gauge at a temperature of 35 C. The partial pressure of acetoe i this stream is a=50 mmhg. tmosphertic pressure is 763 mmhg.. What is the molar compositio of the stream leavig the compressor?. What is the volumetric flow rate of the itroge eterig the evaporator if the temperature ad pressure of this stream are 7 C ad 475 mmhg gauge? 0

11 Example: aterial balaces for a process ivolvig combustio gas aalyzed 6.4 % CO, 0.% O, 39 % CO, 5.8 % H, 0.6 % CH 4, ad.% N. It etered the combustio chamber at 90 F ad a pressure of 35 i. Hg, ad was bured with 40 % excess air (dry), which was at 70 F ad a atmospheric pressure of 9.4 i. Hg; 0 % of the CO remaied ubured. How may cubic feet of air were supplied per cubic foot of eterig gas? How may cubic feet of product gas were produced per cubic foot of eterig gas if the exit gas was at 9.4 i. Hg ad 400 F?