209201 Chemical Stoichiometry References : Basic Principles and Calculations in Chemical Engineering, 7 edition, David. M. Himmerblau and James B. Riggs. ปริมาณสัมพันธ์สำหรับงานอุตสาหกรรม เล่ม 1, รศ. ดร. อนันต์เสวก เห่วซึงเจริญ, ภาควิชาเคมีอุตสาหกรรม, คณะวิทยาศาสตร์, มหาวิทยาลัยเชียงใหม่.

Introduction

Dimensions, Units and Their Conversion Dimensions : basic concepts of measurement e.g. length, time, mass, temperature, etc.

Fundamental (Basic) Dimensions Dimensions that can be measured independently and are sufficient to describe essential physical quantities. Length, Time, Mass, Temperature, Molar amount

Derived Dimensions Dimensions that can be developed in terms of the fundamental dimensions. Velocity, Acceleration, Force, Pressure, Density, Heat Capacity, Energy, Power, etc. Important Note! “Fundamental” or “Derived” – depending also on dimension/unit systems. (ดูตาราง​ 1.1, AH)

Units Units : means of expressing dimensions Systems of Units Length; feet, meters Time; hours, seconds Systems of Units SI : Le Systeme Internationale d’Unites (International System) AE : American Engineering USCS : U.S. Conventional System Metric systems : CGS (centimeters, grams, seconds) English system (ดูตาราง​ 1.2, ตาราง 1.3 และภาคผนวก 1, AH)

SI Prefixes (Remember!) G, giga, 109 M, mega, 106 k, kilo, 103 h, hecto, 102 da, deka, 101 d, deci, 10-1 c, centi, 10-2 m, milli, 10-3 μ, micro, 10-6 n, nano, 10-9

Caution! camel’s hair brush : camel’s – hair brush or camel’s hair – brush? Written with confusion ms – milliseconds or meter seconds? cm2 – square centimeters or centi square meters? Written without confusion m.s or (m)(s) (cm)2

Operations with Units Addition, Substraction, Equality only they are the same 2 kg + 1 kg = 3 kg 5 kg + 3 J 10 kg + 5 g Multiplication and Division be canceled or merged if they are identical m2/m -> m (kg)(m)/(s) m2/cm Nonlinear Operations sin, log, exp, … for simplicity, transform or scale variables to be dimensionless before apply nonlinear operations log (r m) = log r + log m log (r m / R m) = log r + log m – log R – log m = log r – log R = log(r/R)

Conversion of Units and Conversion Factors Many sources – web sites, mobile applications, CD, handbooks, etc. – find a very good one and keep for your academic life and career. For conversion or calculation, be systematic in writing. Prefer format :

Caution! There are several “miles”, “pounds”, “gallon”, “oz”, and “barrel”. U.S. frequent-flier mile (nautical mile) -> 1.85 km U.S. mile -> 1.61 km Ancient Italian mile -> 37 modern U.S. miles

Special Attention : Mass and Force Newton’s Law F = ma or F = Cma F = force C = constant or conversion factor, whose numerical value and units depend on those selected for F, m and a m = mass a = acceleration

Special Attention : Mass and Force AE system Make the numerical value of the force and the mass be essentially the same at the earth’s surface. 1 lbf : the unit of force when 1 lbm is accelerated at g ft/s2 gc is a conversion factor (to cancel the numerical value of g).

Special Attention : Mass and Force 1 kgf : the unit of force when 1 kgm is accelerated at g m/s2 gc is a conversion factor (to cancel the numerical value of g).

Special Attention : Mass and Force SI system 1 Newton (N) : the unit of force when 1 kg is accelerated at 1 m/s2

Examples (P3, DMH) Determine the kinetic energy of one pound of fluid moving in a pipe at the speed of 3 feet per second. Ans. 0.14 (ft)(lbf)

Examples (P4, DMH) Convert the following from AE to SI units: 4 lbm/ft to kg/m 1.00 lbm/(ft3)(s) to kg/(m3)(s) Ans. (a) 5.96 kg/m; (b) 16.0 kg/(m3)(s)

Examples (P5, DMH) Convert 1.57x10-2 g/(cm)(s) to lbm/(ft)(s) Ans. 1.06x10-3 lbm/(ft)(s)

Dimensional Consistency (Homogeneity) Both terms must have the same unit as d. 0.021 must have the unit of time. This cannot be correct. The lefthand side has units of 1/x, but the righthand side has units of x2 (the product of ax).

Examples (P1, DMH) An orifice meter is used to measure the rate of flow of a fluid in pipes. The flow rate is related to the pressure drop by the following equation where u = fluid velocity ΔP = pressure drop (force per unit area) ρ = density of the flowing fluid c = constant Ans. c is dimensionless.

Examples (P2, DMH) The thermal conductivity k of a liquid metal is predicted via the empirical equation k = A exp (B/T) where k is in J/(s)(m)(K) and A and B are constants. What are the units of A and B? Ans. A has the same units as k; B has the units of T