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.

Lecture 1. Introduction

1.1 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 – 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, 10 9 M, mega, 10 6 k, kilo, 10 3 h, hecto, 10 2 da, deka, 10 1 d, deci, c, centi, m, milli, μ, micro, 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? – cm 2 – square centimeters or centi square meters? Written without confusion – m.s or (m)(s) – (cm) 2

1.2 Operations with Units 1.Addition, Substraction, Equality – only they are the same – 2 kg + 1 kg = 3 kg – 5 kg + 3 J – 10 kg + 5 g 2.Multiplication and Division – be canceled or merged if they are identical – m 2 /m -> m – (kg)(m)/(s) – m 2 /cm 3.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)

1.3 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 lb f : the unit of force when 1 lb m is accelerated at g ft/s 2 – g c is a conversion factor (to cancel the numerical value of g).

Special Attention : Mass and Force – 1 kg f : the unit of force when 1 kg m is accelerated at g m/s 2 – g c 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/s 2

Examples Lecture 1.3 (P3, DMH) Determine the kinetic energy of one pound of fluid moving in a pipe at the speed of 3 feet per second. Ans (ft)(lb f )

Examples Lecture 1.3 (P4, DMH) Convert the following from AE to SI units: a.4 lb m /ft to kg/m b.1.00 lb m /(ft 3 )(s) to kg/(m 3 )(s) Ans. (a) 5.96 kg/m; (b) 16.0 kg/(m 3 )(s)

Examples Lecture 1.3 (P5, DMH) Convert 1.57x10 -2 g/(cm)(s) to lb m /(ft)(s) Ans. 1.06x10 -3 lb m /(ft)(s)

1.4 Dimensional Consistency (Homogeneity) -Both terms must have the same unit as d 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 x 2 (the product of ax).

Examples Lecture 1.4 (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 Lecture 1.4 (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

Significant Figures 1.43 – 1.43 ± 0.005, between and – 1.43 ± 0.01, between 1.44 and 1.42 Engineering Calculation – Cost of inaccuracy is high, knowledge of the uncertainty is vital, and vice versa.

1.5 Significant Figures Decision criteria 1.Common Sense 2.Absolute Error 3.Relative Error 4.Statistical Analysis

Absolute Error Numbers with a decimal point – the last significant figure in a number represents the associated uncertainty. – > 4 significant figures – > normally 6 significant figures since there usually was a reason for displaying the trailing zeros e.g. rounding to – 100. ? -> 3 significant figures

Absolute Error Numbers without a decimal point – assume that the trailing zeros do not imply any additional accuracy – 458,300 -> 4 significant figures – 0.23 or or > 2 significant figures

Absolute Error Multiplying or Dividing – the lowest number of significant figures retained. – (1.47)(3.0926) -> > 4.55 Adding or Subtracting – final significant figures determined by the error interval of the largest number – > > 110.3

Relative Error 1.01/1.09 -> > (absolute error) – Uncertainty by absolute error (0.001/0.927)100 -> 0.1% – Uncertainty of original numbers (0.01/1.09)100 -> 1% Should the answer be truncated to 0.93, rather than 0.927? -> The decision is yours.

Statistical Analysis more rigorous and complicated concept of confidence limits

What criterion would be chosen? Most answers are based on “absolute error”. In examples and problems, common sense should often be used. Precision of measurement in practice and relation of accuracy as compared to other values in the examples or problems should be considered. – 10 kg without a decimal point Accuracy is not trivial -> less significant figures Accuracy is trivial -> more significant figures since mass can be accurately measure to a level of mg. – 2/3 can be treated as in relation to the accuracy of other values in the samples or problems.

Examples Lecture 1.5 A)If 20,100 kg is subtracted from 22,400 kg, is the answer of 2,300 kg good to 4 significant figures? -If note that 22,400, 20,100, and 2,300 have no decimal point, -22,400 -> 3 significant figures -20,100 -> 3 significant figures Scientific Notation will help. -> 2 significant figures (by absolute error)

Examples Section 1.5 (E1.8, DMH) If 20,100 kg is subtracted from 22,400 kg, is the answer of 2,300 kg good to 4 significant figures? -If a decimal point point were placed in each number thus 22,400. and 20,100., -22,400. -> 5 significant figures -20,100. -> 5 significant figures 22,400. – 20,100. = 2,300. Relative Error – (1/224)(100), about 0.5% – (1/201)(100), about 0.5% – (1/23)(100), about 5% – (1/230)(100), about 0.5% -> 4 significant figures (by absolute error) -> 3 significant figures (by relative error) -> x 10 4 ? No. -> 230. x 10

Examples Lecture 1.5 (E1.9, DMH) If the DNA is stretched out, and a cut made with a width of 3 μm, how many base pairs (bp) should be reported in the fragment? Note : 1 kb = 1000 base pairs, 3 kb = 1 μm Precision in the 9000 value is determined by that of 3 μm, e.g. 3.0 or 3.00 μm.

1.6 Validation/Verification of Problem Solutions 1.Repeat the calculations, possibly in a different order. 2.Start with the answer and perform the calculations in reverse order. 3.Review your assumptions and procedures. Make sure two errors do not cancel each other. 4.Compare numerical values with experimental data or data in a database (handbooks, Internet, textbooks) 5.Examine the behavior of the calculation procedure. For example, use another starting value and check that the result changed appropriately. 6.Assess whether the answer is reasonable given what you know about the problem and its background.

Problems : Chapter 1 P1.4* P1.11** P1.12** P1.20** P1.21*** P1.30* P1.33*