
Explore how the introduction to chemical engineering blends chemistry, calculus, physics, and economics to solve real-world problems, from food processing to fertilizers, in an accessible course.
Learn unit concepts and conversions using the stepladder method, comparing cgs, British, and si systems, and convert cm to m and cm^3 to m^3 by cubing the conversion factor.
Explore units across the cgf and british systems, including pound-force and pound-mass, gravitational constant, psi, pascals, calories, btus, horsepower, viscosity, and heat capacity.
Explains how gravity converts mass to weight in si units and demonstrates converting a 70 kg mass to pounds in British units, yielding pound-mass and pound-force equivalents.
Explains dimensional consistency by equating left and right units in an equation and adding only like units. Uses the Reynolds number as a unitless example where units cancel.
Explain molecular mass with hydrogen, define mass fraction and mole fraction using a two-gas cylinder, and state the convention: gases use mole fraction, solids and liquids use mass fraction.
Calculate the average molecular mass of a gas mixture in a cylinder using mole fractions of components A and B, summing each component's mole fraction times its molecular mass.
Density measures mass per volume, denoted by rho. It compares objects with the same volume but different masses and is commonly expressed in grams per cubic meter.
Calculate the SG by dividing the material density by the density of water at 4 degrees, yielding about 1.3 (1300 kg/m^3). Note that the bulk density is 0.9 kg/L.
Examine concentration measures such as ppm, molarity, molality, and normality. Define each by its basis: solute per liter for molarity and normality, or per kilogram of solvent for molality.
Relate temperature scales by teaching how changes in Celsius equal changes in Kelvin, and how Fahrenheit changes are 1.8 times the Celsius changes, with practical conversions and reference points.
Convert 50 degrees Celsius to degrees Fahrenheit using the 1.8 factor above the freezing point. It yields 122 degrees Fahrenheit.
Analyze how gauge pressure and absolute pressure arise from liquid height, density, and gravity, including atmospheric references and vacuum scenarios.
Calculate hydrostatic pressure in a two-tank system using a gauge reading, liquid density, and vertical heights to determine P2 and P3 relative to atmosphere.
Explain normality through gram equivalents in neutralization, where one gram equivalent neutralizes one gram of base and one gram mole can equal one to four gram equivalents for compounds.
Explore buoyancy through a wood block example, showing how objects displace a mass of water equal to their weight, and how density—when a block is less dense than water—affects displacement.
Use buoyancy: a 1 m^3 cube of 400 kg displaces 0.4 m^3 of water, so the submerged height on a 1 m^2 area is 0.4 m.
Explore the empirical formula, treating constants A, B, and C with defined units, and apply dimensional consistency to determine unit relationships for X and convert units accordingly.
convert the empirical formula a = 1.537 x / y^0.71 from pounds per cubic foot and foot-hour degree fahrenheit to the ice system, deriving units and final expression.
Multiply the given value by conversion factors to convert units, handling exponents, and derive the empirical formula A = 0.4703 * X / Y^2 in SI units.
Measure flow rate through a pipe. Use inner diameter to compute cross-sectional area A = πr^2, then determine linear velocity v = volumetric flow rate / A.
Explain material balances at steady state with no reactions, showing mass and mole conservation across input streams a and b and output c. Illustrate saturated solutions and factors affecting solubility.
Apply material balances to a three-component oil–water–solid stream, use a separator to remove oil, compute feed and outlet rates, and convert the water outlet to barrels per hour.
Learn to estimate a y value by linear interpolation between two known points, then apply the same method to extrapolation beyond the given range.
Explore percentage yield and selectivity, and apply the in plus generated minus consumed equals out principle with a table method to solve material balances in chemical reactions.
In the third reactor, burn a carbon compound with oxygen to form carbon dioxide and water, balance the reaction, and apply 40% excess to obtain 840 kmol of oxygen.
Define conversion in the reactor and the process using system boundaries and mole-based formulas, with streams, feeds, outputs, and recycle.
Use the ideal gas law PV=nRT to calculate moles, apply mass balances, and relate gas densities via specific gravity to a reference gas like air, using partial pressures.
Apply the ideal gas law to a simple gas system with no reaction to compute the outgoing pressure from inlet conditions, flow rates, and temperatures, yielding 222.2 pascals.
Explore material balances with recycle bypass and purge streams, using a reactor–separator system diagram to relate feed, recycle and purge masses, compositions, and conversions via simultaneous equations.
Analyze a recycle, purge, bypass reactor-separator system with a feed of gas, water, methanol, and butanol, using 20 percent conversion to predict CO and H2 outputs.
Determine the mole fraction of methanol in stream c as 0.2272 by dividing the methanol amount by the total in stream c, which includes methanol and water.
Explain how to compute methanol flow rates in a recycle purge bypass setup by relating fractions in streams A, f, and P and the upstream-to-total stream ratio.
Explore coal composition and the proximate and ultimate analyses. Learn how moisture, free water, volatile matter, fixed carbon, ash, and key elements (C, H, S, N) are reported as percentages.
Analyze coal using proximate and ultimate analyses to determine fixed carbon, moisture, ash, hydrogen balance, sulfur, and nitrogen, and compute carbon in the volatile matter and its composition.
Explore combustion calculations, including percentage excess oxygen and oxygen required for combustion. Learn how hydrogen burns completely while carbon progresses from carbon monoxide to carbon dioxide, emphasizing 100 percent completion.
We burn a carbon compound with oxygen to form carbon dioxide and water, balance the equation, and compute the required oxygen with 40 percent excess from given flow rates.
Analyze exhaust gas composition using Orsat data, determine nitrogen by difference, and apply dry and sulfur-free or water-free bases with imaginary separators to perform mass balances.
Examine number types from integers to real numbers, noting ranges and no fractional parts, and distinguish rational from irrational numbers with examples like 1/3 and pi.
Learn the fundamentals of notation, including set notation such that x is an element of the reals and interval notation with open and closed brackets, plus union and intersection.
Explore rules for solving inequalities, including addition and multiplication by positives or negatives and reciprocal behavior, then factor a rational expression to locate zeros and undefined points.
Explore the absolute value concept as the distance from the origin, review its piecewise definition, and apply rules such as |A|=A for A≥0 and |A|=-A for A<0.
Examine the piecewise form of the absolute value function |x+2|, yielding f(x)=x+2 for x≥-2 and f(x)=-x-2 for x<-2, resulting in a V-shaped graph with positive outputs.
Explore how even functions, like a parabola, satisfy f(x)=f(-x), yielding identical y-values for x and -x. Note that odd functions satisfy f(-x) = -f(x), with x and y signs swapped.
Explore radian measure by relating arc length, radius, and angle through s = r theta, and convert between degrees and radians, noting 360° = 2π radians and 180° = π.
Explore composite functions like f(g(x)) where the input to a function becomes another function. Analyze how the range of g determines the domain of f and the notation behind f(g(x)).
Examine conditions for continuity by ensuring a lies in the domain, the limit as x approaches a exists, and this limit equals f(a), while identifying removable, infinite, and jump discontinuities.
Explore the intermediate value theorem: for any continuous function on a closed interval [a, b], every value between f(a) and f(b) is attained by f(x) for some x.
Explain horizontal and vertical asymptotes using limits as x approaches infinity and finite points, with examples from arctan and hyperbola, and distinguish end behavior from unbounded growth.
Explore derivatives and rates of change, including tangent lines and gradients, defined as limits. Learn first principles to derive f'(x) and apply to x^2 for instantaneous rate of change.
Derivatives give the gradient of the tangent line at a point; they require continuity, but not all continuous functions are differentiable, e.g., sharp corners and vertical tangents.
Explore why differentiability implies continuity, outlining a proof that the derivative at a point exists only if the function is continuous at that point, using the limit definition.
The lecture proves the power rule using the limit definition. It shows that the derivative of x^n is n x^{n-1}, with examples for positive and negative exponents.
Explore the product rule for derivatives, deriving the product of two functions as (ab)' = a b' + b a', and extend to three functions.
Derive the quotient rule for h(x)=f(x)/g(x) by using limits to obtain h'(x) = [g(x)f'(x) − f(x)g'(x)] / [g(x)]^2.
Prove the derivative of sin(x) from first principles using limits, expanding sin(x+h) and applying the limits of sin h over h and cos h, to arrive at cos(x).
Derive the derivative of cos x from first principles by evaluating the limit as h tends to zero with cos h and sin h, arriving at -sin x.
Apply the quotient rule to tan x, written as sin x over cos x, using derivatives of sine and cosine to show the derivative equals sec^2 x.
Show a geometric proof that the limit of sin theta over theta equals one as theta tends to zero. It uses triangle inequalities, arc length, and the squeeze theorem.
This lecture proves the limit as theta approaches zero of (cos theta minus one) over theta equals zero, by writing cos theta as one minus sin squared theta and simplifying.
Demonstrate, via conjugate manipulation, that the limit as theta approaches zero of (cos theta minus 1)/theta equals zero, using the sine limit sin theta/theta = 1.
Explore the chain rule for differentiable composite functions, deriving the outer and inner derivatives to compute f(g(x)), with an example using the square root of x cubed minus 4.
Explore explicit versus implicit differentiation, how the chain rule yields y' when y cannot be isolated, and why two versus one solutions arise.
Learn the derivative of arcsin(x) through implicit differentiation, deriving y' = 1 / sqrt(1 − x^2) with x in [−1, 1] and y in [−π/2, π/2].
Derive the derivative of arccos x using the chain rule, yielding y' = -1/√(1−x²) by using cos y = x and 1−cos²y = sin²y.
Derive the derivative of arctan x using the chain rule, establishing y = arctan x and dy/dx = 1/(1+x^2), with the identity tan y = x.
Explore the derivative of ln(x) and show why it equals 1/x, using the relationship between natural logs and exponentials.
Identify absolute max and absolute min as highest and lowest on a function’s graph within its domain, and local maxima and minima as high and low points, called global extrema.
Chemical Engineering Calculations Made Easy!
This course includes video and text explanations of the fundamentals in chemical engineering, and it includes more than 40 worked through examples with easy-to-understand explanations. 'Introduction to Chemical Engineering' is organized into two main sections:
And here’s what you get inside of every lesson:
Videos: Watch over my shoulder as I solve chemical engineering problems from start to finish. We start from the beginning... First I teach the theory. Then I do an example problem. I explain the problem, the steps I take and why I take them, how to work through the yucky, fuzzy middle parts, and how to simplify the answer when you get it.
Notes: The notes section of each theory lesson is where you find the most important things to remember. The notes include tips and tricks on how to study as well as how to save time in tests and exams. Ultimately, I cover everything you need to know to pass your class and nothing you don’t.
One-On-One Assistance: You can ask me for chemical engineering help in the Q&A section any day, any time, whether it's related to the video content or another problem you're struggling with at home. Either way, I'm here to help you pass and do the best you possibly can!