Free FE Chemical Exam Flashcards

x(n+1) = x(n) - f(x(n))/f'(x(n)). Start from a guess near the root and iterate until the change is smaller than your tolerance; it fails or diverges if f'(x) is near zero or the guess is far from the true root.

L{e^(-at)} = 1/(s + a) for s > -a. Recognizing standard transform pairs like this lets you convert a linear ODE (e.g., a first-order transient) into an algebraic equation in s, solve it, then invert back to the time domain.

Accuracy measures how close a value is to the true/accepted value; precision measures how repeatable a set of measurements is, regardless of whether they're correct. A result can be precise but inaccurate (tightly clustered but off-target). Round final answers to match the least-precise input's significant figures.

P(x) = C(n,x) * p^x * (1-p)^(n-x), where p is the probability of success on a single trial and C(n,x) = n!/[x!(n-x)!]. It only applies when trials are independent with a fixed success probability.

mean +/- z*(s/sqrt(n)), where z is the critical value for the desired confidence level, s is the sample standard deviation, and n is the sample size. A larger n or a lower confidence level narrows the interval.

Ohm's law: V = IR (voltage = current x resistance). Kirchhoff's current law: the sum of currents entering a node equals the sum of currents leaving it (conservation of charge).

Work W = F*d (force times distance moved in the force's direction). Power P = W/t (work done per unit time). A larger force or a shorter time both increase the power delivered, even if total work is unchanged.

mpy = (534 x W) / (D x A x T), where W = weight loss in mg, D = metal density in g/cm3, A = exposed area in in2, and T = exposure time in hours. A higher mpy value means faster material loss and shorter service life.

A thermoplastic softens and can be repeatedly melted, reshaped, and recycled (a physical change). A thermoset cures through irreversible cross-linking, so reheating causes charring or decomposition rather than melting, and it cannot be reshaped or recycled the same way.

Molarity (M) = moles of solute / liters of solution. Unlike molality (moles per kg of solvent), molarity changes slightly with temperature because solution volume expands or contracts.

pH = -log10[H+]. At 25 degC, pH + pOH = 14. A pH below 7 is acidic, above 7 is basic, and each whole-number drop in pH represents a 10x increase in [H+].

One species loses electrons and its oxidation state increases (it is oxidized, acting as the reducing agent), while another gains electrons and its oxidation state decreases (it is reduced, acting as the oxidizing agent). Electrons lost by the oxidized species must equal electrons gained by the reduced species.

It models enzyme-catalyzed reaction rate versus substrate concentration: v = (Vmax [S]) / (Km + [S]). At low [S], rate rises almost linearly with concentration; as [S] increases, rate levels off and approaches the saturation value Vmax.

Re = (rho*v*D)/mu, the ratio of inertial to viscous forces. In a pipe, flow is generally laminar below Re ~2100 and turbulent above Re ~4000, with a transitional region in between.

P/(rho*g) + v^2/(2g) + z = constant. Pressure head, velocity head, and elevation head trade off against each other; the equation no longer applies once friction losses or a pump/turbine are added without correction terms.

hf = f*(L/D)*(v^2/(2g)), where f is the Darcy friction factor, L is pipe length, D is diameter, and v is velocity. Higher velocity has the biggest impact on losses since head loss scales with v^2.

NPSH (net positive suction head) available is the pressure margin above the fluid's vapor pressure at the pump inlet. If NPSH available drops below NPSH required, the fluid can flash to vapor at the impeller, causing cavitation that damages the pump and reduces performance.

delta U = Q - W, where Q is heat added to the system and W is work done by the system. Energy is conserved: the change in internal energy equals net heat in minus net work out.

Total entropy generation is always >= 0 for any real process and equals exactly 0 only for an ideal reversible process. This is why no real process (engine, heat exchanger, compressor) can be 100% efficient.

p_A = x_A * P_A^sat: the partial pressure of component A equals its liquid mole fraction times its pure-component vapor pressure. It's a good approximation for chemically similar components across the full concentration range, unlike Henry's law, which only holds for a dilute solute.

It models how a pure component's vapor pressure varies with temperature: log10(P^sat) = A - B/(T + C), where A, B, and C are component-specific empirical constants valid only over a defined temperature range.

Compute the degree of freedom: DOF = (number of unknowns) - (number of independent equations). DOF = 0 means the problem is exactly specified and solvable; DOF > 0 means more information is needed; DOF < 0 means the problem is over-specified.

Accumulation = In - Out + Generation - Consumption. At steady state, accumulation = 0, so In + Generation = Out + Consumption; there is no buildup or depletion of the balanced quantity inside the system over time.

A purge stream continuously bleeds off a small fraction of the recycle to prevent inert gases or non-reacting impurities from building up indefinitely inside the loop, which would otherwise dilute the reactive feed over time.

% excess air = [(air supplied - theoretical air) / theoretical air] x 100. Theoretical (stoichiometric) air is the exact amount needed to completely combust the fuel; excess air is added to ensure complete combustion but lowers flame temperature and efficiency.

n_i = n_i,0 + nu_i * xi, where nu_i is the stoichiometric coefficient of species i (negative for reactants, positive for products) and xi is a single extent-of-reaction variable shared by every species in that reaction.

q/A = -k(dT/dx), where k is thermal conductivity. Heat flux is proportional to the temperature gradient and flows from hot to cold (the negative sign), independent of any fluid motion.

q = hA*deltaT, where h is the convective heat transfer coefficient, A is surface area, and deltaT is the temperature difference between the surface and the surrounding fluid. h is much larger for forced convection than for natural convection.

deltaT_lm = (deltaT1 - deltaT2) / ln(deltaT1/deltaT2), using the temperature differences at each end of the exchanger. Use LMTD for sizing problems where all four terminal temperatures (both inlets and both outlets) are already known.

1/(UA) equals the sum of all thermal resistances in series: inside-fluid convection, wall conduction, outside-fluid convection, and fouling resistance on each surface. Fouling buildup over time lowers U and reduces exchanger performance.

J = -D(dC/dx), where D is the diffusion coefficient. Molar flux is proportional to the concentration gradient and flows from high to low concentration, analogous to Fourier's law for heat.

It's a graphical stage-by-stage method that steps between the equilibrium curve and the operating lines (rectifying and stripping sections) to find the number of theoretical trays needed for a specified separation, given the reflux ratio and feed condition.

alpha_AB = (y_A/x_A)/(y_B/x_B), comparing how much more volatile component A is than B at equilibrium. Higher relative volatility means an easier separation (fewer trays needed); a value near 1 signals a difficult separation, sometimes requiring an azeotropic or extractive method.

R = L/D, the ratio of liquid returned to the column over distillate withdrawn. Increasing R improves separation (fewer trays needed for a given purity) but increases reboiler and condenser duty and required column diameter, raising both energy and capital cost.

It's the steepest angle from horizontal at which a poured pile of the material remains stable without sliding. A larger angle of repose signals a more cohesive, poorer-flowing solid that is more prone to bridging or rat-holing in bins and hoppers.

k = A * exp(-Ea/(RT)), where A is the pre-exponential (frequency) factor, Ea is activation energy, R is the gas constant, and T is absolute temperature. The rate constant k rises rapidly with temperature since Ea/(RT) sits in the exponent.

For rate = k[A]^m[B]^n, the overall reaction order is m + n. These exponents must be found experimentally from rate data - they generally do NOT equal the stoichiometric coefficients in the balanced chemical equation, except for elementary reactions.

V = F_A0 * X / (-r_A). A CSTR is perfectly mixed, so composition (and thus reaction rate) inside the tank is uniform and equal to the exit-stream composition - there's only one rate value to apply across the whole reactor volume.

V = F_A0 * (integral from 0 to X of dX/(-r_A)). In a PFR, concentration and rate change continuously along the reactor's length as conversion increases, so the volume must be found by integrating over the whole conversion range rather than using a single rate value.

P = F * (1+i)^(-n), where F is the future amount, i is the interest rate per period, and n is the number of periods. This single-payment present-worth factor (P/F, i, n) discounts a future value back to today.

D = (Cost - Salvage Value) / Useful Life (years), giving the same depreciation expense every year over the asset's life. It's the simplest depreciation method and is often used for quick economic screening even when accelerated methods apply for tax purposes.

A process flow diagram (PFD) shows major equipment, overall stream flows, compositions, and operating conditions at a high level. A piping and instrumentation diagram (P&ID) adds every pipe, valve, instrument, and control loop needed to actually build and operate the unit.

Minimize (use smaller quantities of hazardous material), Substitute (use a less hazardous material or route), Moderate (use less severe conditions, e.g., lower pressure, temperature, or dilution), and Simplify (reduce complexity so less can go wrong) - reducing hazard at the design stage instead of only adding protective layers afterward.

Mixing, heat transfer, and mass transfer don't scale the same way as reaction rate or volume - surface-area-to-volume ratio shrinks as vessels get larger, changing heat removal and mixing time. This is why pilot testing and dimensionless scale-up criteria are used before committing to full plant-scale design.

It finds the pinch point - the minimum-approach-temperature location that splits the process into a heat-surplus region (above the pinch) and a heat-deficit region (below it). No heat should be transferred across the pinch; utilities are added only above it (heating) or below it (cooling) to minimize energy use.

Proportional (P) responds to the current error; Integral (I) accumulates past error over time to eliminate steady-state offset; Derivative (D) responds to the rate of change of error to reduce overshoot, though it can amplify measurement noise.

Feedback control measures the controlled variable (the output) and corrects it only after a deviation from setpoint has already occurred. Feedforward control measures a disturbance directly and adjusts the manipulated variable before that disturbance can affect the output.

LFL (lower flammable limit) and UFL (upper flammable limit) bound the flammable range as % vapor in air. Below LFL the mixture is too lean (fuel-starved) to ignite; above UFL it's too rich (oxygen-starved); only concentrations between LFL and UFL can burn or explode if ignited.

HAZOP is a qualitative, team-based review that systematically applies guide words (more, less, no, reverse, etc.) to process deviations to identify hazard scenarios. LOPA follows up on specific HAZOP-identified scenarios with a semi-quantitative check of whether existing independent protection layers reduce the risk to a tolerable frequency.

Engineers must hold paramount the safety, health, and welfare of the public in performing their professional duties - this obligation outranks duties to an employer or client whenever they conflict, and it's the ethical foundation behind the FE exam's ethics questions.