Chemical Engineering Fundamentals and Applied Mathematics
This domain rewards disciplined unit handling and clean algebra more than raw calculation speed. You should be fluent in: dimensional analysis and unit conversion (SI, cgs, engineering units, lb-mol vs kg-mol); mass, mole and equivalent bases; logarithms and exponential decay/growth; linearization of nonlinear data; simple and partial differentiation; integration of rate expressions; and statistics (mean, standard deviation, propagation of error). Numerical tools - Newton-Raphson, trapezoidal/Simpson integration, and linear regression - appear conceptually.
Common traps: mixing mass and molar bases mid-problem; forgetting that gauge and absolute pressures differ by one atmosphere; treating a ratio of unlike units as dimensionless; rounding intermediate results too early; and confusing log base 10 with natural log in exponential fits. Watch for questions that give redundant data - identify which values are irrelevant rather than using all of them.
Worked example: convert 2.5 lb-mol/ft³ to kg-mol/m³. Use 1 lb-mol = 0.4536 kg-mol and 1 ft³ = 0.02832 m³. Then 2.5 × 0.4536 = 1.134 kg-mol per ft³, divided by 0.02832 gives ≈ 40.0 kg-mol/m³. Rule of thumb: carry units through every step and cancel them explicitly; if the units don't reduce to the target, the answer is wrong regardless of the arithmetic.