FE Chemical flashcards

32 cards. Read the term and the definition here. The deck at the top of this page is optional.

Conversion in a reactor

Fraction of the limiting reactant fed that has reacted. For a single reaction A to products, moles remaining equal initial moles times one minus conversion, and extent equals initial moles times conversion.

CSTR design equation

Volume equals molar feed rate of A times conversion divided by the rate of reaction of A evaluated at outlet conditions. Because the CSTR operates at outlet composition, it requires the largest volume for positive-order kinetics.

PFR design equation

Volume equals the molar feed rate of A times the integral from zero to conversion of dX divided by negative rate of A. Concentration varies along the length, so the PFR is more efficient than a CSTR for positive-order reactions.

Arrhenius rate constant

Rate constant equals pre-exponential factor times exponential of negative activation energy divided by gas constant times absolute temperature. A plot of natural log of rate constant versus inverse temperature is linear with slope negative activation energy over gas constant.

Equilibrium constant from Gibbs energy

Standard Gibbs free energy change equals negative gas constant times temperature times natural log of the equilibrium constant. The constant depends only on temperature for ideal gases, and negative standard Gibbs energy means products are favored.

Van't Hoff equation

Derivative of natural log of equilibrium constant with respect to temperature equals standard enthalpy of reaction divided by gas constant times temperature squared. Exothermic reactions have decreasing equilibrium constant as temperature rises.

Le Chatelier pressure rule

At constant temperature, increasing pressure shifts a gas-phase equilibrium toward the side with fewer moles of gas. Adding an inert at constant pressure shifts equilibrium toward the side with more gas moles.

Raoult's law

Partial pressure of a component in an ideal liquid mixture equals its liquid mole fraction times its pure-component vapor pressure at the same temperature. Summing partial pressures gives total pressure for bubble-point calculation.

Relative volatility

Ratio of the vapor-liquid equilibrium K values of two components, equal to the ratio of their pure vapor pressures for ideal mixtures. Values near one make distillation difficult and require many stages and high reflux.

Fenske minimum stages

Minimum theoretical stages at total reflux equals natural log of the product of the light-key ratios in distillate and bottoms divided by natural log of relative volatility. It assumes constant relative volatility and total reflux.

Underwood minimum reflux

Two equations using a parameter theta solve for minimum reflux ratio. The first uses feed composition and feed quality; the second uses distillate composition and gives minimum reflux plus one.

Kremser absorption equation

Number of stages equals natural log of a term involving the absorption factor and inlet and outlet ratios divided by natural log of the absorption factor. The absorption factor equals liquid rate divided by equilibrium slope times vapor rate.

Azeotrope behavior

A mixture whose vapor and liquid compositions are identical at equilibrium, so the equilibrium curve crosses the diagonal. Simple distillation cannot pass the azeotropic composition; pressure-swing or extractive distillation is needed.

Fick's first law

Molar flux of a species equals negative diffusivity times the concentration gradient. Steady diffusion of A through a stagnant, insoluble film includes a log-mean correction for the inert component's mole fraction.

Two-film mass transfer

Overall mass transfer resistance equals the sum of gas-film and liquid-film resistances, with the liquid term scaled by the Henry constant. The slower film controls the overall rate.

Height of a transfer unit

Packed column height equals height of an overall transfer unit times number of transfer units. The height equals gas molar flux divided by the overall gas-phase mass transfer coefficient times interfacial area per volume.

Henry's law

Partial pressure of a dilute dissolved gas equals the Henry constant times its liquid mole fraction. Large Henry constant means low solubility, and the partition ratio equals Henry constant divided by total pressure.

Reynolds number in a pipe

Density times velocity times diameter divided by viscosity. Flow is laminar below about 2100, transitional to 4000, and turbulent above 4000 for circular pipes.

Darcy-Weisbach friction loss

Head loss equals friction factor times length over diameter times velocity squared over twice gravitational acceleration. Laminar friction factor equals 64 divided by Reynolds number.

Bernoulli mechanical energy balance

Pressure head plus velocity head plus elevation head is constant along a streamline for frictionless incompressible flow; real flow adds a friction loss term. Pump work adds energy to the fluid.

Pump power requirement

Fluid power equals density times gravity times head times volumetric flow rate; shaft power equals fluid power divided by pump efficiency. Total head includes static lift, pressure difference, and friction losses.

NPSH and cavitation

Net positive suction head available equals suction pressure head plus static head minus vapor pressure head minus suction friction loss. Cavitation occurs when available NPSH falls below the pump's required NPSH.

Ergun packed-bed equation

Pressure drop per bed length equals a viscous term proportional to viscosity times velocity times one minus void fraction squared over void fraction cubed times particle diameter squared, plus an inertial term proportional to density times velocity squared.

Overall heat transfer coefficient

Reciprocal of overall coefficient times area equals the sum of inside convection, wall conduction, and outside convection resistances. The largest resistance controls the overall rate.

Log-mean temperature difference

Temperature difference equals the difference of the two terminal differences divided by the natural log of their ratio. It applies to counterflow and, with a correction factor, to multipass and crossflow exchangers.

Heat exchanger effectiveness

Effectiveness equals actual heat transfer divided by the maximum possible, which is minimum heat capacity rate times inlet temperature difference. It depends on number of transfer units and capacity ratio.

Biot and Fourier numbers

Biot number equals convection coefficient times length divided by thermal conductivity and compares internal to external resistance. Fourier number equals diffusivity times time divided by length squared and measures transient progress.

Stefan-Boltzmann radiation

Net radiative heat transfer between a gray surface and surroundings equals emissivity times Stefan-Boltzmann constant times area times the difference of absolute temperatures to the fourth power. The constant is 5.67 times ten to the negative eighth watt per square meter kelvin fourth.

PID controller equation

Controller output equals gain times error plus gain over integral time times the error integral plus gain times derivative time times the error derivative. Proportional band equals one hundred divided by controller gain in percent.

First-order process response

Transfer function equals gain divided by time constant times Laplace variable plus one. A step reaches 63.2 percent of final value at one time constant and 95 percent at three time constants.

Ziegler-Nichols ultimate gain tuning

From the ultimate gain and ultimate period at the stability limit, proportional gain equals 0.6 times ultimate gain, integral time equals half the ultimate period, and derivative time equals one eighth the ultimate period.

Present worth and annuity factors

Present worth of a future amount equals that amount divided by one plus interest rate raised to the number of periods. Annuity present worth equals payment times the capital recovery factor reciprocal.