Key Formulas & Equations
Van der Waals Equation: (P + a(n/V)²)(V - nb) = nRT
Compressibility Factor: Z = PV/nRT
Real Gas Law: PV = ZnRT
Steady-State: Input = Output
Conversion: X = (FA0 - FA)/FA0
Enthalpy: H = U + PV
First Law: ΔU = Q - W
Entropy Change: ΔS = Qrev/T
Rate Law: r = kCAaCBb
First-Order: ln(CA/CA0) = -kt
Half-Life (1st order): t½ = ln(2)/k
Henry's Law: PA = HAxA
Relative Volatility: α = (yA/yB)/(xA/xB)
Murphree Efficiency: EMV = (yn - yn+1)/(y*n - yn+1)
Core Concepts
Process Design
The creation of processes for manufacturing chemical products. Includes equipment selection, flow diagram development, safety analysis, and economic evaluation.
Thermodynamics
Study of energy transformations in chemical systems. Key laws: conservation of energy, entropy increase, and equilibrium conditions for chemical reactions and phase changes.
Reaction Kinetics
The study of rates of chemical reactions. Includes reaction mechanisms, rate laws, activation energy, and the effect of temperature and concentration on reaction rates.
Transport Phenomena
The study of momentum transfer (fluid flow), heat transfer, and mass transfer. These three processes are fundamental to all chemical engineering operations.
Separation Processes
Techniques for separating mixtures: distillation, absorption, extraction, filtration, and membrane processes. Essential for product purification and waste treatment.
Process Control
The regulation of process variables (temperature, pressure, flow, level) to maintain stable operation. Uses feedback control, PID controllers, and advanced process control.
Chemical Reactor Design
The design of vessels where chemical reactions occur. Includes batch, CSTR, and PFR reactors. Optimization involves temperature, pressure, and residence time.
Process Safety
The prevention of accidents in chemical plants. Includes hazard analysis, risk assessment, inherently safer design, and emergency response planning.
Worked Examples
Example 1: Ideal Gas Law
Problem: Calculate volume of 2 mol gas at 300 K and 100 kPa (R = 8.314 J/mol·K).
Solution:
V = nRT/P = 2 × 8.314 × 300/100,000 = 0.0499 m³ = 49.9 L
Example 2: First-Order Reaction
Problem: A reaction has k = 0.05 min⁻¹. Calculate time for 90% conversion.
Solution:
ln(CA/CA0) = -kt → ln(0.1) = -0.05t
-2.303 = -0.05t → t = 46.05 minutes
Example 3: Distillation
Problem: A binary mixture has α = 2.5. If liquid composition x = 0.4, calculate vapor composition y.
Solution:
y = αx/(1 + (α-1)x) = 2.5 × 0.4/(1 + 1.5 × 0.4) = 1.0/1.6 = 0.625
Practice Problems
Problem 1
Calculate Z for 1 mol gas at 300 K, 200 kPa occupying 10 L (R = 8.314).
Answer: Z = PV/nRT = 200,000 × 0.01/(1 × 8.314 × 300) = 0.802
Problem 2
A CSTR processes 100 mol/h of A (CA0 = 2 mol/L) with k = 0.1 min⁻¹. Find reactor volume for 80% conversion.
Answer: V = FA0X/(-rA) = 100 × 0.8/(0.1 × 2 × 0.2 × 60) = 33.3 L
Problem 3
Calculate half-life for a first-order reaction with k = 0.02 s⁻¹.
Answer: t½ = ln(2)/k = 0.693/0.02 = 34.65 s
Problem 4
Using Arrhenius equation, find k at 350 K if k = 0.01 at 300 K and Ea = 50 kJ/mol.
Answer: k = 0.01 × exp[(50000/8.314)(1/300 - 1/350)] = 0.071 s⁻¹
Problem 5
Calculate ΔU for a system absorbing 500 J heat and doing 200 J work.
Answer: ΔU = Q - W = 500 - 200 = 300 J
Problem 6
Calculate y in vapor for x = 0.3 and α = 3.0.
Answer: y = 3 × 0.3/(1 + 2 × 0.3) = 0.9/1.6 = 0.5625
Problem 7
A batch reactor has k = 0.05 min⁻¹. How long to reduce concentration from 1.0 to 0.1 mol/L?
Answer: t = ln(1.0/0.1)/0.05 = 2.303/0.05 = 46.05 min