LECT05. Ideal Gas Calculations - Weebly

1 31 Introduction to Chemical Engineering Calculations Lecture 5. Ideal Gas Calculations Prof. Manolito E Bambase Jr. Department of Chemical Engineering. University of the Philippines Los Ba os 5 Ideal Gas Calculations What is an Ideal gas? An Ideal gas is an imaginary gas that obeys exactly the following relationship: PV = nRT. where P = absolute pressure of the gas V = total volume occupied by the gas n = number of moles of the gas R = Ideal gas constants in appropriate units T = absolute temperature of the gas SLIDE. Prof. Manolito E Bambase Jr. Department of Chemical Engineering. University of the Philippines Los Ba os 2. 5 Ideal Gas Calculations The Ideal Gas Constant, R. R = cal/(gmol)(K). = Btu/(lbmol)(0R). = (psia)(ft3)/(lbmol)(0R). = (kPa)(m3)/(kmol)(K). = J/(gmol)(K). = (atm)(cm3)/(gmol)(K). = (atm)(L)/(gmol)(K).

2 = (in. Hg)(ft3)/(lbmol)(0R). = (atm)(ft3)/(lbmol)(0R). SLIDE. Prof. Manolito E Bambase Jr. Department of Chemical Engineering. University of the Philippines Los Ba os 3. 5 Ideal Gas Calculations Standard Conditions for the Ideal Gas Several arbitrarily specified standard states of temperature and pressure have been selected by custom. System TS PS VS nS. SI K kPa m3 1 kmol Am. Eng. 4920R 1 atm ft3 1 lbmol Natural Gas K psia ft3 1 lbmol Industry SLIDE. Prof. Manolito E Bambase Jr. Department of Chemical Engineering. University of the Philippines Los Ba os 4. 5 Ideal Gas Calculations Example 5-1. Ideal Gas calculation Butane (C4H10) at 3600C and atm absolute flows into a reactor at a rate of 1100 kg/h. Calculate the volumetric flow rate of this stream. Method A. Computation using a known value of R. The Ideal gas equation in terms of flowrate: PV nRT V n.

3 Or P RT. t t t t .. P V = n RT. SLIDE. Prof. Manolito E Bambase Jr. Department of Chemical Engineering. University of the Philippines Los Ba os 5. 5 Ideal Gas Calculations Example 5-1. Ideal Gas calculation Solving for volumetric flowrate: . n RT. V=. P. Obtaining the molar flowrate from mass flowrate: . m 1100 kg / h n= kmol / h MW 58 kg / kmol Using absolute temperatures and pressure: T = 633 K and P = 3 atm SLIDE. Prof. Manolito E Bambase Jr. Department of Chemical Engineering. University of the Philippines Los Ba os 6. 5 Ideal Gas Calculations Example 5-1. Ideal Gas calculation Using the following value of R: L atm 1000gmol L atm R gmol K 1kmol kmol K. The volumetric flowrate is . n RT ( / h)( L atm / kmol K)(633K). V= . P 3atm L 1m3 m3. V =328, 329. h 1000 L h SLIDE. Prof. Manolito E Bambase Jr. Department of Chemical Engineering.

4 University of the Philippines Los Ba os 7. 5 Ideal Gas Calculations Example 5-1. Ideal Gas calculation Method B. By comparison to standard conditions PV nT.. PS VS n STS. Using a basis of 1 hr, then n = 19 kmol The following standard conditions will be used. PS = 1 atm VS = m3. nS = 1 kmol TS = 273 K. SLIDE. Prof. Manolito E Bambase Jr. Department of Chemical Engineering. University of the Philippines Los Ba os 8. 5 Ideal Gas Calculations Example 5-1. Ideal Gas calculation Solving for V: n T P . V S VS. n S TS P . 633K 1atm 3. V 273K 3atm 1kmol . V 329m 3. In terms of volumetric flowrate m3. V = 329. h SLIDE. Prof. Manolito E Bambase Jr. Department of Chemical Engineering. University of the Philippines Los Ba os 9. 5 Ideal Gas Calculations Example 5-2. Ideal Gas at Two Different Conditions Ten cubic feet of air at 700F and 1 atm is heated to 6100F.

5 And compressed to atm. What volume does the gas occupy in its final state? Let 1 denote the initial state of the gas and 2 the final state. P1V1 n1T1 T1.. P2 V2 n 2T2 T2. Solving for V2: 0. P1 T2 3 atm 1070 R 3. V2 V1 ft 530 0 R ft P T. 2 1 atm . SLIDE. Prof. Manolito E Bambase Jr. Department of Chemical Engineering. University of the Philippines Los Ba os 10. 5 Ideal Gas Calculations Example 5-3. calculation of Ideal Gas Density What is the density of N2 at 270C and 100 kPa in SI units? PV nT.. PSVS n STS. Solving for (n/V) and obtaining the density from this : n n S P TS . MW MW. V VS PS T . 1kmol 100 kPa 273K kg kg 3 28 3. 300 K kmol m SLIDE. Prof. Manolito E Bambase Jr. Department of Chemical Engineering. University of the Philippines Los Ba os 11. 5 Ideal Gas Calculations Ideal Gas Mixtures and Partial Pressures In a mixture of Ideal gases, the partial pressure of a gas component is the pressure that would be exerted by a that component if it existed by itself in the same volume as occupied by the mixture and the same temperature of the mixture.

6 PiVtotal = niRTtotal where Pi and ni are the partial pressure and number of moles of component i. SLIDE. Prof. Manolito E Bambase Jr. Department of Chemical Engineering. University of the Philippines Los Ba os 12. 5 Ideal Gas Calculations Ideal Gas Mixtures and Partial Pressures For the gas mixture: PtotalVtotal = ntotalRTtotal Dividing the two equations, Pi VT n i RTT ni or Pi PT yi PT. PT VT n T RTT nT. According to Dalton, PA + PB + PC + .. = Ptotal SLIDE. Prof. Manolito E Bambase Jr. Department of Chemical Engineering. University of the Philippines Los Ba os 13. 5 Ideal Gas Calculations Example 5-4. Ideal Gas Mixtures and Partial Pressures A flue gas analyzes CO2, O2, and N2. The mixture is at 4000F and 765 mmHg pressure. Calculate the partial pressure of each component. Component y Pi (mmHg). CO2 (765) = O2 (765) = N2 (765) = Total 765 mmHg SLIDE.

7 Prof. Manolito E Bambase Jr. Department of Chemical Engineering. University of the Philippines Los Ba os 14.