A reactor-design tool for making the desired product efficiently. Switch between parallel and series reactions and adjust the rate constants and reaction time to see the conversion, selectivity and yield in real time — plus, for series reactions, the optimal reaction time that maximises the desired product.
Parameters
Reaction scheme
Choose a series or a parallel reaction
Rate constant of the desired reaction k₁
1/s
First-order rate constant of A→D
Rate constant of the side / series reaction k₂
1/s
Rate constant of D→U (series) or A→U (parallel)
Initial concentration of A, C_A0
mol/L
Reaction time (residence time) t
s
Batch reaction time, or residence time of a flow reactor
Results
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Conversion X (%)
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Desired product C_D (mol/L)
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Selectivity S (%)
—
Yield Y (%)
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By-product C_U (mol/L)
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Optimal reaction time t_opt (s)
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Concentration-vs-time profile — animation
A (reactant) falls while D (desired) and U (by-product) rise. The solid vertical line is the current reaction time, the dashed line the optimal time t_opt for series reactions. A marker sweeps along the time axis.
Concentration of the desired product D in a series reaction A→D→U, and the optimal reaction time t_opt that maximises D. When k₁≈k₂, use the limit forms C_D=C_{A0}k₁t·e^{−k₁t} and t_opt=1/k₁.
Selectivity S (D per A reacted), yield Y (D per A fed) and conversion X. The three are tied together by Y = S·X.
$$\text{Parallel:}\quad S=\frac{k_1}{k_1+k_2}\ (\text{constant in time})$$
For a parallel reaction A→D, A→U of equal order, the selectivity depends only on the ratio of rate constants and is independent of reaction time and conversion.
What is Reaction Selectivity?
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In a chemical reaction, doesn't all of the reactant you put in turn into the product you want? I've never heard the word "selectivity" before.
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No, reality is rarely that kind. When you feed reactant A into a reactor, you don't only get the desired product D — an unwanted by-product U forms alongside it. Selectivity S measures "of the A that reacted, how much became D". If you react 100 mol of A and get 60 mol of D, the selectivity is 60%. The other 40 mol become U, which costs you disposal and separation. That is why a chemical plant gains a lot of money from raising selectivity by even one percent.
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I see. So how is "yield" different? It sounds like the same thing.
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Good question. Selectivity uses "A that reacted" as the denominator; yield uses "A that you fed in". As formulas, S = C_D/(C_A0−C_A) and Y = C_D/C_A0, and with the conversion X = (C_A0−C_A)/C_A0 you get Y = S·X. So yield is "selectivity × conversion". Even at 90% selectivity, if only 10% of A reacted the yield is just 9%. Conversely, pushing conversion to 99% gains you nothing if selectivity drops. That tug-of-war is the heart of reactor design.
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When I pick "parallel reaction" on the left, the selectivity stays exactly constant no matter how I change the reaction time. Is that a bug?
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No, that's the correct behaviour. A parallel reaction is A→D and A→U competing at the same time. Both eat the same A with the same first-order kinetics, so at every instant the ratio of D to U formed is fixed at k₁:k₂. Integrate it and the selectivity stays constant at S = k₁/(k₁+k₂). For a parallel reaction, fiddling with reaction time to raise selectivity is useless — you have to change temperature to shift the k₁/k₂ ratio, or pick a catalyst that speeds only the desired reaction. The yield, on the other hand, does grow with reaction time because conversion rises.
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When I switch to "series reaction", the yield card goes up and then down with reaction time. Is that what the optimal reaction time is about?
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Exactly. A series reaction is A→D→U, where the desired D is an "intermediate". At first A→D builds D up fast. But as D accumulates, the over-reaction D→U kicks in, so at a certain time the D concentration peaks and then starts to fall. That peak time is the optimal reaction time, t_opt = ln(k₂/k₁)/(k₂−k₁). Keep it in the reactor longer and you "overcook" the D you made into U. Like cooking — leave it on the heat too long and you burn it.
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So in a real plant, do they stop the reaction exactly at that optimal time?
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That's the idea, but the field adds one more trick. For example "reactive separation", continuously withdrawing D from the reactor to cut off the over-reaction to U, or dropping the temperature partway through to halt D→U. With series reactions it is also standard practice to not push conversion all the way and to recycle unreacted A. Stopping at 70% conversion and recovering the unreacted A gives more total D than reacting to 99% and burning the D. Switch to series in this tool and move the reaction-time slider — you will feel the yield card rise and fall in an arc.
Frequently Asked Questions
Selectivity S is how many moles of desired product D were formed per mole of A that reacted; yield Y is how many moles of D were formed per mole of A fed. As formulas, S = C_D/(C_A0−C_A) and Y = C_D/C_A0, and using the conversion X = (C_A0−C_A)/C_A0 they are linked by Y = S·X. Selectivity expresses the quality of the reaction and yield the final amount harvested: a high selectivity does not give a high yield if conversion is low.
In a parallel reaction A→D (rate k₁·C_A) and A→U (rate k₂·C_A), both routes consume the same reactant A with the same order. At every instant the ratio of D and U formed is k₁:k₂, so when integrated the selectivity stays constant at S = k₁/(k₁+k₂). It does not move when you change time or conversion. To raise selectivity you must change the rate constants themselves — change temperature to shift the k₁/k₂ ratio, or choose a different catalyst.
In a series reaction A→D→U the desired product D is an intermediate. Early on, A→D builds D up, but once D accumulates the over-reaction D→U becomes significant, so at a certain time the D concentration reaches a maximum and then falls. That peak is the optimal reaction time, t_opt = ln(k₂/k₁)/(k₂−k₁). Running the reactor longer over-reacts D into the unwanted U, so conversion and yield become a trade-off.
In a parallel reaction the selectivity S in Y = S·X is fixed, so raising the conversion X (running longer) increases the yield. In a series reaction the most important thing is to match the reaction time to the optimal time t_opt. For both schemes it also helps to make the desired reaction's rate constant relatively larger through temperature or catalyst, and to suppress over-reaction. For series reactions, reactive separation that continuously withdraws D and cuts off the over-reaction to U is also used.
Real-World Applications
Petrochemicals and bulk chemicals: The synthesis of ethylene oxide by partial oxidation of ethylene, and of formaldehyde by oxidation of methanol, are classic series reactions in which the desired product is further over-oxidised to carbon dioxide. These plants deliberately hold conversion low, recycle unreacted feed and run to maximise selectivity for the desired product. The series mode of this tool visualises exactly that "stop before you overcook it" sense.
Pharmaceutical and fine-chemical synthesis: In multi-step synthesis, every step shows both competition with side reactions (parallel) and over-reaction of intermediates (series). For fine chemicals with expensive feedstock, a 1% difference in yield feeds straight into cost, so reaction time, temperature and catalyst are tuned in detail. Training yourself to separate selectivity from yield with this tool is a foundation for designing synthetic routes.
Choosing the reactor type: For a parallel reaction where the desired reaction has a higher order than the side reaction, a batch reactor or plug-flow reactor (PFR) that keeps reactant concentration high is favourable; if lower, a continuous stirred-tank reactor (CSTR) is favourable. For a series reaction, a PFR with concentration changing from inlet to outlet gives a higher intermediate-D yield than a well-mixed CSTR. The concentration profiles in this tool show the behaviour that is the starting point for such reactor selection.
Combustion and environmental processes: The carbon monoxide CO produced by incomplete combustion of fuel can be seen as the intermediate of the series oxidation CO→CO₂. In selective catalytic reduction (SCR) for flue-gas treatment, the desired reaction — NOx reduction — competes with the side reaction of ammonia oxidation. The concept of selectivity is shared not only by chemistry that makes products, but also by process design that reduces harmful substances.
Common Misconceptions and Pitfalls
The most common misconception is the belief that "raising conversion always raises yield". This is true for a parallel reaction but dangerous for a series one. If you extend the reaction time of a series reaction to push conversion towards 100%, the desired product D over-reacts to U and the yield actually falls. Move the reaction-time slider up in the series mode of this tool and you will see conversion rise monotonically while yield crests and declines. Treating "leftover unreacted feed is wasteful", giving up on recycle and being greedy with conversion loses you money on the whole.
Next is the error of "treating selectivity and yield as the same thing". Even when a paper or a catalogue says "yield 80%", it matters greatly whether that is a yield that includes conversion or a selectivity that looks only at what reacted. A reaction at 50% conversion and 90% selectivity (45% yield) and one at 95% conversion and 50% selectivity (48% yield) have nearly the same yield, but very different loads on feed recycle and separation/purification. When comparing numbers, always check conversion, selectivity and yield as a set of three.
Finally, do not forget the assumption that this tool's equations assume first-order kinetics, isothermal operation and constant volume. Real reactions can be second order or higher, can heat up exothermically so the rate constants change, or — in the gas phase — can change volume because the mole count changes. The constant selectivity of a parallel reaction holds only when the desired and side reactions are of the same order; with different orders, selectivity depends on concentration (and thus conversion). This tool is an educational tool for grasping the basic structure of reaction selectivity intuitively; designing a real plant requires measured rate equations and detailed simulation.
How to Use
Select reaction topology: parallel (A→D and A→U simultaneously) or series (A→D→U sequential)
Input rate constants k1 and k2 (units: s⁻¹ for first-order) using numeric entry or range sliders
Set initial concentration C_A0 (mol/L) and residence time t (seconds)
Observe real-time updates: conversion X, desired product concentration C_D, selectivity S, yield Y, unwanted byproduct C_U, and optimal reaction time t_opt
Iterate parameters to maximize selectivity or desired product formation
Worked Example
For a parallel reaction scheme producing fine chemical intermediate: k1=0.15 s⁻¹ (desired pathway), k2=0.08 s⁻¹ (byproduct pathway), C_A0=2.5 mol/L, residence time t=8 s. At t=8 s: conversion X=72%, C_D=1.44 mol/L, selectivity S=87%, yield Y=63%, C_U=0.22 mol/L, t_opt=6.8 s. Switching to series mode shows C_D peaks at t_opt=4.2 s (1.38 mol/L) before secondary decomposition reduces desirable product. Adjusting k1 to 0.22 s⁻¹ increases selectivity to 91% while maintaining similar conversion.
Practical Notes
For exothermic parallel reactions (pharmaceutical synthesis), minimize t and favor k1 selectivity ratio: target S>85% by keeping k2<0.5×k1
Series reactions require optimization at inflection point—use t_opt output to identify maximum C_D before consecutive degradation becomes significant
High C_A0 (>3 mol/L) may trigger diffusion limitations in real reactors; validate with pilot-scale experiments before scale-up
Selectivity inversely correlates with conversion in competitive parallel pathways—reactor residence time trade-offs demand economic cost-benefit analysis