Dimensional Consistency in Equations: Understanding Units and Concentrations

4. Equations must be dimensionally consistent . • What does this mean? • Let us take the eq p = gh + p0 Is it correct ? How do we make it correct? • Same for units, each term must have the same unit(s) as all other terms

5. The mole unit • What is 1 mole of Na ? Units? Are we using grams for mass ? or Kg? or lb? Then we call the mole by the mass we use • What is the mass of lbmole of H2SO4 ? • 98 lb H2SO4 = 44.45 Kg • How many gms in 6 gmoles of H3PO4? How many moles of H are available? Of P ? of O ?

6. = 438 g H3PO4 = 18 gmol H = 24 gmol O • 100 gmoles of O2 = gms • = lbmoles O2

7. Density, Specific gravity, sp. Volume, mole fraction, mass fraction, volume fraction • = mass/unit vol sp volume= 1/ = in units ? •  it is volume/unit mass ( vol of one unit of mass of material. • sp. gravity = densityA/ densityref • Does change with Temp? YES

8.  We need to specify the temp used for A and for the ref. • Example • sp. gr = 0.73 20o What does this mean ? • 4o

9. In the Petroleum Industry • sp gr is measured in oAPI • oAPI = 141.5 . • sp gr 60o • 60o - 131.5 • EXAMPLE (mass fr. , mole fr and Average MWt ) • What is the avg MWt of a gas mixture that contains: • Mass, Kg • H2 3 • CH4 8 • C2H4 56 • Total 67

10. = 16.75 kg/kgmol DO YOU HAVE QUESTIONS ?

11. Concentrations of solutions, • mass/unit vol, PPM, molar, molal , etc • Concentration is : Qty of solute per specified amount of solvent or solution • How do we specify concentration? 1.Mass of solute per unit volume solution For example 0.10 kgNaCl/L soln .

12. 2.Moles of solute per unit volume solution.For example : 0.10 kgmolNaCl/L soln 3.Molarity (mol solute/L soln) 4.Molality (mol solute/Kg solvent) 5.For dilute soln : we use PPM (parts per million) .

13. Q1: 700 mg salt /m3 water is PPM 0.7 PPM . Note: total mass of solution = 1000 kg+ 700 mg  1000 kg

14. FLOW RATES • How do we measure the flow rate of liquid in the pipe ? • L/s (Volumetric flow rate) • Kg/s (Mass flow rate) • How do we change from one to the other? We use the density • How do we calc the velocity ? • Example: • 40% NaCl soln is flowing at 10L/min in a pipe. If the sp gr of the soln is 1.4, • calculate the concentration of NaCl in Kg/L • calculate the flow rate of soln in kgmol soln/min

15. How do we calc the velocity ? • Example: • 40% NaCl soln is flowing at 10L/min in a pipe. If the sp gr of the soln is 1.4, then • calculate the concentration of NaCl in Kg/L • calculate the flow rate of soln in kgmol soln/min Q = A . v

16. 0.56

17. Example A gas mixture contains : 40% N2, 45% O2 and 15%CH4.This mixture is hazardous, so to make it safe, it was diluted by adding equal amount of N2 to it. What is the analysis of the new safe mixture ?

18. 40 mol% N2 45 mol% O2 15 mol% CH4 ? mol% N2 ? mol% O2 ? mol% CH4 • +Equal amount • of N2 ? • How do we solve? • What should we start with?

19. BASIS: 1000 gmoles of starting gas mixture BASIS: 100 gmoles of starting gas mixture BASIS: 1 lbmole of starting gas mixture BASIS: 50 kgmoles of starting gas mixture

20. BASIS: 100 gmoles of starting gas mixture 40 gmol N2 45 gmol O2 15 gmol CH4 80 gmol N2 45 gmol O2 15 gmol CH4 140gmoles +40 gmol N2  % 80 gmol N2 57 45 gmol O2 32 15 gmol CH411 140gmoles 100%

21. SOLUTION How do we solve? What should we start with?

22. Basis: ? SOLUTION Basis 100 kg of the solution , thus kg NaCl 5 KCl 10 HCl 5 H2SO4 soln80 100 H2SO4 solution (water + acid ) How much H2SO4 and how much water in the solution ?

23. Let us change the molality to mass % H2SO4 Molality = mol H2SO4 /Kg water  If we have 1 Kg water, there is 1.5 gmol of H2SO4 Therefore, in 1 Kg water there is 1.5 gmol x 98g gmol = 147 g H2SO4 1.0 kg water 1.5 gmol acid Basis: ? fraction 1000 g water 0.128 147 g acid 0.872 1147 1.000

24. kg NaCl 5 KCl 10 HCl 5 H2SO4 soln80 100 H2SO4 80x 0.128 =10.24 kg H2O 80x 0.872 =69.76 kg 80.00 kg How much H2SO4 and how much water in the solution ?

25. THEREFORE,