Class 3 Friday, August 27 th Which of the following cannot be linearized? (P is in mm Hg and T is in degrees Celsius, m, a, b and c are constants). The concentrations of [H 2 ], [Br 2 ], and [H 2 O] are in mol/l. a) 1/P = a(t 4) -b b) P = at b c) P 2 = exp(at 3 + b) d) P=m[H 2 ] a [Br 2 ] b [H 2 O] c a) 1/P = a(t 4) -b b) P = at b c) P 2 = exp(at 3 + b) d) P=m[H 2 ] a [Br 2 ] b [H 2 O] c Sections 3.1 to 3.3 Mass & Volume Flow Rate Chemical Composition 1
Definitions: Density (ρ) is mass/unit volume (kg/m 3 ; lb m /ft 3, etc.): Specific Volume, V s, is volume/unit mass and is the inverse of density Specific Gravity, SG, is the ratio of the density, ρ, of the substance to the density of a reference substance, ρ ref,at a specific condition: Flow Rate mass flow rate (mass/time): lb m /h, kg/s, g/min volumetric flow rate (volume/time): ft 3 /h, m 3 /s Density, mass, and volume are related: SG = ρ/ρ ref Substance A and substance B each have a density of 1.34 g/cm 3. Therefore 3 cm 3 of A a) Has the same mass as 3 cm 3 of B b) Has a greater mass than 3 cm 3 of B c) Has less mass than 3 cm 3 of B d) May or may not have the same mass as B Substance A and substance B each have a specific gravity of 1.34. Therefore 3 cm 3 of A a) Has the same mass as 3 cm 3 of B b) Has a greater mass than 3 cm 3 of B c) Has less mass than 3 cm 3 of B d) May or may not have the same mass as B 2
Gas flows through the cone-shaped pipe below. Which of the following is true? a) The mass flow at the inlet equals the mass flow at the outlet. b) The mass flow at the inlet > the mass flow at the outlet. c) The mass flow at the inlet < the mass flow at the outlet. d) You need to know the density in order to determine that. Gas at a constant density flows through the coneshaped pipe below. Which of the following is true? a) The volumetric flow at the inlet equals the volumetric b) The volumetric flow at the inlet > the volumetric c) The volumetric flow at the inlet < the volumetric d) You need to know the density in order to determine that. The density of the gas decreases from the outlet to the inlet. Which of the following is true? a) The volumetric flow at the inlet equals the volumetric b) The volumetric flow at the inlet > the volumetric c) The volumetric flow at the inlet < the volumetric d) You need to know the density in order to determine that. Chemical Composition Mole and Mass Fraction Mole Fraction: y i = moles i/total moles Mass Fraction: x i = mass i/total mass For gases, volumetric fraction or volumetric % is the same as mole fraction or mole %. 3
Basis of Calculation (Important!) To convert between mass fraction and mole fraction or between mass composition and mole composition, you MUST assume a basis of calculation which is either a total mass or total moles for the mixture. Selecting a value of 100 is usually good unless something is already specified to simplify the problem. For example, what are the mass fractions of O 2 and N 2 in air? (the mole fractions are.79 and.21 respectively). Calculation of an Average Molecular Weight total mass of a mixture sample M avg = m t /n t = -------------------------------------------- total number of all moles in sample or M avg = y 1 M 1 + y 2 M 2 + y 3 M 3 + where y 1 + y 2 + y 3 + = 1 or 1 x 1 x 2 x 3 ------ = ------ + ----- + ----- + M avg M 1 M 2 M 3 A mixture of methane and air is capable of being ignited only if the mole % of methane is between 5 and 15 %. A mixture containing 9 mole % methane in air flowing at a rate of r is to be diluted with pure air to reduce methane to the lower flammability limit. Without doing any calculations, which do you think is closest to the average molecular weight of the stream coming out? (Methane has a molar mass of 16 g/mol and air has a molar mass of 29 g/mol) a) 17 b) 20 c) 23 d) 28 where x 1 + x 2 + x 3 + = 1 4
A mixture of methane and air is capable of being ignited only if the mole % of methane is between 5 and 15 %. A mixture containing 9 mole % methane in air flowing at a rate of r is to be diluted with pure air to reduce methane to the lower flammability limit. Find the mole fraction of O 2 in the stream coming out, n 1. 95 % air 95 % air n 1 Plan: a) Find mass fractions of stream coming in, then mass of each component b) Mass of methane coming in = mass of methane coming out in stream n 1 c) Find moles of methane coming out in stream n1 = 5 % of n1 d) Can then solve for n 1, and solve for moles of air in n 1 e) Can solve for amount of pure air coming in but don t need to f) Find moles of oxygen in air then divide by total moles (n 1 ) 5
A mixture containing 9 mole % methane in air flowing at a rate of 700 kg/hr is to be diluted with pure air to reduce methane to the lower flammability limit. The density of methane is lower than that of air. Therefore the density of the stream coming out will be: a) Lower than that of the methane stream coming in b) Higher than that of the methane stream coming in c) The same because of conservation of mass 6