Material and Energy Balances Tutoring

Material and energy balances is usually the first chemical engineering course, and it goes by several names: Chemical Process Principles, Stoichiometry, or Introduction to Chemical Engineering. The problems read like short stories. A stream enters, a reactor converts part of it, a separator splits the rest, and you are asked for a flow rate nobody gave you. Many students freeze at the first line. STEM Tutor 360 teaches one routine that fits every problem in the course: draw and label the flowchart, choose a basis, count degrees of freedom, write the balances, and solve.

Sessions start with single units and build to multiple units, then to reactions with extent of reaction and atomic balances. From there we cover recycle, bypass, and purge, then gases, vapor pressure, and humidity, and finally energy balances with sensible heat, phase changes, and heats of reaction. We work from your own text, whether that is Felder and Rousseau, Himmelblau and Riggs, or Reklaitis, and from any old exams you have.

A typical material balance problem, worked

Pure A is fed at 100 mol/h. In the reactor, A converts to B, and 40% of the A entering the reactor reacts. A separator sends all the B out as product and returns all the unreacted A to the reactor feed. Find the reactor feed rate, the recycle rate, and the product rate.

Draw five streams: fresh feed, reactor feed, reactor effluent, product, and recycle. Count degrees of freedom on the overall process first. The unknowns are the product rate and the extent of reaction, and there are two balances (A and B), so the overall system solves on its own. A balance: $0 = 100 - \text{extent}$, so the extent is 100 mol/h. B balance: $\text{product} = 0 + 100 = 100\ \text{mol/h}$.

Now the reactor. It must consume 100 mol/h of A and it converts 40% of what enters, so the reactor feed is $\tfrac{100}{0.40} = 250\ \text{mol/h}$. At the mixing point, 100 of fresh feed plus the recycle makes 250, so the recycle is 150 mol/h.

Check the separator. The reactor effluent holds 150 mol/h of A and 100 mol/h of B, 250 in total. The B leaves as product and the 150 of A goes back. Overall conversion is 100% even though single-pass conversion is only 40%, and that gap is the reason plants use recycle.

Where students usually get stuck

• Mixing up single-pass conversion and overall conversion in recycle problems.
• Skipping the basis, then not knowing what to scale at the end.
• Using mass fractions in a mole balance, or the reverse.
• Miscounting degrees of freedom, often by forgetting that the mole fractions in a stream add to one.
• In energy balances, changing reference states midway or mixing kJ and J.