Process Flow Diagrams & Composition Variables

Read process flow diagrams and switch compositions between mass and mole bases.

Material & Energy BalancesChemical Engineering Year 1Free preview

⏱️ About 16 min

Two engineers describe the same gas mixture — one by mass %, one by mol %. Why can their numbers disagree, and how do you reconcile them?

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The big idea: A PFD plus a clear composition basis (mass or mole) is the starting point for every material balance.

🎯 By the end, you'll be able to

Read a process flow diagram and identify streams, units, and labels
Define mass fraction and mole fraction
Convert a binary composition from mass fractions to mole fractions and back
Recognize when mass and mole fractions differ

📎 Helpful to know first

Units & Dimensional Analysis

What Is a Process Flow Diagram?

A process flow diagram (PFD) is the engineer's schematic of a process. It shows unit operations as blocks (or standardized symbols), connected by streams drawn as arrows. Each stream is labeled with its flow rate, composition, and any known conditions (temperature, pressure).

Conventions: streams flow left-to-right; inputs enter on the left, products leave on the right; recycle streams loop back. A clear PFD lets you set up material and energy balances without losing track of a stream.

A minimal PFD: two feed streams enter a mixer and leave as one product. Note that 100 + 50 = 150 kg/h, a first glimpse of mass conservation.

\[ x_i = \frac{m_i}{\sum_j m_j}, \qquad y_i = \frac{n_i}{\sum_j n_j} \]

Mass fraction x_i uses masses; mole fraction y_i uses moles. They coincide only when all components share the same molecular weight.

⚠️ Mass fraction is not mole fraction

Only when two components have identical molecular weights will their mass and mole fractions coincide. Always label which basis a composition is on.

Converting Between Mass and Mole Fractions

Composition can be expressed on a mass basis (mass fraction x_i = m_i / Σm) or a molar basis (mole fraction y_i = n_i / Σn). They are generally not equal because each component carries a different mass per mole.

To convert mass fractions to mole fractions: pick a basis (e.g. 100 g), read off each component's mass, divide by molecular weight to get moles, then divide by total moles. Reverse the steps to go from mole to mass fractions.

📝 Worked example: A gas mixture contains 30.0 mass % N2 (MW = 28.02) and 70.0 mass % O2 (MW = 32.00). Find the mole fraction of each component.

Basis: 100 g of mixture → 30.0 g N2 and 70.0 g O2
Moles: n(N2) = 30.0 / 28.02 = 1.071 mol; n(O2) = 70.0 / 32.00 = 2.188 mol
Total moles: 1.071 + 2.188 = 3.259 mol
y(N2) = 1.071 / 3.259 = 0.329; y(O2) = 2.188 / 3.259 = 0.671
Check: 0.329 + 0.671 = 1.000

✓ y(N2) = 0.329, y(O2) = 0.671

✏️ Practice: A binary gas mixture is 0.40 mole fraction N2 and 0.60 mole fraction O2 (MW: N2 = 28.02, O2 = 32.00). What is the mass fraction of N2?

Solution

Basis 1 mol: 0.40 mol N2 × 28.02 g/mol = 11.21 g; 0.60 mol O2 × 32.00 g/mol = 19.20 g; total = 30.41 g
Mass fraction N2 = 11.21 / 30.41 = 0.369

Check your understanding

1. Mass fraction and mole fraction of a component in a mixture are equal when:

If every component shares the same M, then m_i is proportional to n_i and mass fractions equal mole fractions.

2. On a standard PFD, what does a stream arrow entering a block from the left typically represent?

By convention, feed streams enter from the left; products leave from the right.

✅ Key takeaways

A PFD shows unit operations as blocks and streams as labeled arrows
Mass fraction x_i = m_i / Σm; mole fraction y_i = n_i / Σn
Mass and mole fractions are equal only when all components share the same MW
Convert by choosing a basis, computing moles (or masses), and renormalizing

➡️ With mass and mole fractions in hand, the next step is computing a single molecular weight for a whole mixture — the average MW.

Want to test yourself on this? Try the Chemical Aptitude test →