Ethyl Chloride Reactor with Recycle: 23-Chem-A1 Process Balances and Chemical Thermodynamics, December 2014, Q3

Question 3: Ethyl Chloride Reactor with Recycle (Part B, 25 marks)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

Given. The separator sends unreacted $C_2H_6$ back as recycle $R$, delivers pure $C_2H_5Cl$ as product $P$, and rejects $Cl_2 + H_2$ as waste $W$. In the reactor feed the chlorine is 100% excess and the single-pass conversion of ethane is 60%.

Find. (a) reactor-feed composition; (b) $P/\,$(fresh ethane); (c) composition of $W$; (d) overall $Cl_2$ conversion.

Figure 2 — Fresh ethane + chlorine and recycled ethane feed the reactor; the separator returns unreacted ethane (R), ships pure ethyl chloride (P) and rejects Cl₂+H₂ as W.

Approach. Take a convenient basis of ethane into the reactor, fix the chlorine from the 100%-excess statement, run the 60% conversion, then close overall balances to reach the fresh-feed and waste streams.

Basis and chlorine feed. Let the ethane entering the reactor be $E_f = 100$ mol. Stoichiometry needs $\tfrac12 E_f = 50$ mol $Cl_2$; 100% excess doubles that, so $Cl_f = 100$ mol. The reactor feed is thus $$100\ \text{mol}\ C_2H_6 + 100\ \text{mol}\ Cl_2 \;\Rightarrow\; \boxed{50\ \text{mol\% }C_2H_6,\ 50\ \text{mol\% }Cl_2}.\quad\text{(a)}$$
Single-pass reaction (60% of ethane). Ethane reacted $=0.60(100)=60$ mol. From the stoichiometry ($2\,C_2H_6:1\,Cl_2:2\,C_2H_5Cl:1\,H_2$): $Cl_2$ consumed $=30$, $C_2H_5Cl$ formed $=60$, $H_2$ formed $=30$ mol.
Reactor outlet. Unreacted ethane $=100-60=40$ mol; unreacted chlorine $=100-30=70$ mol; plus 60 mol $C_2H_5Cl$ and 30 mol $H_2$.
Separator split ⇒ recycle, product, waste. $R = 40$ mol $C_2H_6$; $P = 60$ mol $C_2H_5Cl$; $W = 70\ Cl_2 + 30\ H_2$.
Fresh feed by overall balance. At steady state the recycle returns all unreacted ethane, so fresh ethane $=$ ethane consumed $=60$ mol (check: $60_{\text{fresh}}+40_{R}=100=E_f$ ✓). All chlorine is fresh (recycle is pure ethane), so fresh $Cl_2 = 100$ mol. $$\text{(b)}\quad \frac{P}{\text{fresh }C_2H_6} = \frac{60}{60} = \boxed{1.00}.$$
Waste composition (c). $W = 70+30 = 100$ mol: $$\boxed{70\ \text{mol\% }Cl_2,\ 30\ \text{mol\% }H_2}.$$
Overall chlorine conversion (d). Of the 100 mol fresh $Cl_2$, 30 mol react: $$X_{Cl_2,\text{overall}} = \frac{30}{100} = \boxed{30\%}.$$

Quantity	Result
(a) Reactor-feed composition	50 mol% C₂H₆ / 50 mol% Cl₂
(b) C₂H₅Cl produced : fresh ethane	1.00
(c) Waste stream $W$	70 mol% Cl₂ / 30 mol% H₂
(d) Overall Cl₂ conversion	30%

Concept & Theory

Topic. Reactor–separator–recycle system; single-pass versus overall conversion; percent excess reactant.

Key relations. % excess $=(\text{fed}-\text{stoich})/\text{stoich}$; single-pass conversion on the reactor feed; overall conversion on the fresh feed; steady-state overall balance (fresh in = products out).

Why this works. Because the recycle carries only unreacted ethane and the product is pure, the overall system consumes exactly the fresh ethane it is fed — so fresh ethane equals ethane reacted. The huge gap between the 60% single-pass and effectively 100% overall ethane conversion (versus only 30% for chlorine) is precisely what the recycle buys.

Common pitfall. Applying “100% excess” to the fresh chlorine rather than to the ethane in the reactor feed, or referencing the excess to the amount that actually reacts. Excess is always measured against the stoichiometric requirement of the limiting reactant present in the feed.

Source. Felder, Rousseau & Bullard, EPCP §4.6–4.7 (recycle and purge, multiple-unit balances; reactive systems).

Question 3 of 7: Ethyl Chloride Reactor with Recycle

Question 3: Ethyl Chloride Reactor with Recycle (Part B, 25 marks)