GATE Overflow for GATE ESE - Recent questions and answers in Kinetics and reactor design

GATE ES 2026 | Question: 6

Mon, 23 Feb 2026 13:15:38 +0000

In the reversible reaction shown below, $k_{f}$ is the forward reaction rate constant and $k_{r}$ is the reverse reaction rate constant.

The CORRECT expression representing the reaction equilibrium constant is $\_\_\_\_$.

$$A+B \underset{k_{r}}{\stackrel{k_{f}}{\rightleftharpoons}} C+D$$

$k_{f}+k_{r}$
$k_{f} \times k_{r}$
$\dfrac{k_{f}}{k_{r}}$
$\dfrac{k_{r}}{k_{f}}$

GATE ES 2026 | Question: 40

Mon, 23 Feb 2026 13:14:34 +0000

Reaction $\mathrm{A} \rightarrow \mathrm{B}$ follows first-order elementary kinetics and the reaction rate constant for $\text{A}$ is $0.01$ per min.

The time taken to reduce the concentration of $\text{A}$ from $100$ $\text{M}$ to $10$ $\text{M}$ in a batch reactor is $\_\_\_\_$ $\min$ (rounded off to one decimal place).

GATE ES 2026 | Question: 49

Mon, 23 Feb 2026 13:14:25 +0000

A continuous flow stirred tank reactor (CSTR) operates under a steady-state condition with a flow rate of $300$ $\text{L}$ per hour. The influent concentration of a substrate entering the reactor is $150 \mathrm{mg} / \mathrm{L}$.

To give a treatment efficiency of $76 \%$ for the substrate that decays according to halforder kinetics with a rate constant of $0.05(\mathrm{mg} / \mathrm{L})^{1 / 2}$ per hour, the required volume of the reactor is $\_\_\_\_$ $\mathrm{m}^{3}$ (answer in integer).

GATE ES 2025 | Question: 29

Thu, 06 Mar 2025 16:21:40 +0000

Consider the following figure of an activated sludge process (ASP), depicting the flow $(\mathbf{Q})$, substrate $(\mathbf{S})$, and microorganism concentration $(\mathbf{X})$ at various points in the system, where subscripts "$\mathbf{0}$ ", " $\mathbf{r}$ ", " $\mathbf{w}$ ", "$\mathbf{e}$", and " $\mathbf{i}$ " indicate influent, recycle line, wastage, effluent, and flow from aeration tank to settling tank, respectively. Note that influent to the ASP has microbes too. $\mathbf{V}$ is volume of aeration tank.

Choose the correct option for net rate of formation of microorganisms in the system at steady state, from the following

$\frac{\left(Q-Q_{W}\right) X_{e}+Q_{W} X_{r}-Q X_{0}}{V}$
$\frac{\left(Q-Q_{W}\right) X_{e}+Q_{W} X_{r}}{V}$
$\frac{\left(Q-Q_{W}\right) X_{e}+Q_{W} X_{r}}{V X}$
$\frac{\left(\mathrm{Q}+\mathrm{Q}_{\mathrm{r}}\right) \mathrm{X}_{\mathrm{i}}+\mathrm{Q}_{\mathrm{W}} \mathrm{X}_{\mathrm{r}}}{\mathrm{VX}}$

GATE ES 2025 | Question: 41

Thu, 06 Mar 2025 16:21:11 +0000

Aerobic biomass has yield coefficient value of $0.4$ for glucose (molecular weight $= 180 \mathrm{~g} / \mathrm{mole}$) substrate. Bacteria is represented as $\mathrm{C}_{5} \mathrm{H}_{7} \mathrm{O}_{2} \mathrm{N}$ (molecular weight $=113$ $\mathrm{g} / \mathrm{mole}$ ). Assume that no endogenous metabolism occurs. The percentage of carbon going into $\mathrm{CO}_{2}$ from $1 \mathrm{~mole} / \mathrm{L}$ glucose is $\_\_\_\_\_\_$ (rounded off to two decimal places)

GATE ES 2025 | Question: 47

Thu, 06 Mar 2025 16:21:03 +0000

You conducted a batch experiment in the lab for $10$ minutes to degrade a toxic compound, which follows first order kinetics. The compound degrades from $2 \times 10^{-3} \mathrm{M}$ to $2 \times 10^{-4} \mathrm{M}$. The information from the lab experiment will be used to design a plug flow reactor in field conditions.

Given field conditions:

Flow rate of contaminated water to be treated: $1 \mathrm{~m}^{3} /$ hour
Concentration of toxic compound in contaminated water: $5 \times 10^{-1} \mathrm{M}$
Target concentration of toxic compound in treated water: $1 \times 10^{-4} \mathrm{M}$
Temperature is same in lab and field conditions.

The required volume of the plug flow reactor is $\_\_\_\_\_\_\_ \: \mathrm{m}^{3}$. (rounded off to two decimal places)

GATE ES 2024 | Question: 29

Mon, 19 Feb 2024 10:24:09 +0000

Consider second order kinetics $\left(r_{c}=-k C^{2}\right)$ under steady state condition. The ratio of volume of a complete mixed reactor (CMR) to that of a plug flow reactor (PFR) to achieve $90 \%$ reduction in the concentration is ________.

Inlet concentrations in both the reactors are same.

$10.0$
$1.0$
$0.1$
$2.3$

GATE ES 2023 | Question: 45

Tue, 23 May 2023 03:11:54 +0000

A biological reactor is getting wastewater containing 1 mole/L acetate ions as carbon source. The following reaction takes place in the bio-reactor:
\[
\begin{array}{l}
0.125 \mathrm{CH}_{3} \mathrm{COO}^{-}+0.0295 \mathrm{NH}_{4}^{+}+0.103 \mathrm{O}_{2} \rightarrow 0.0295 \mathrm{C}_{5} \mathrm{H}_{7} \mathrm{O}_{2} \mathrm{~N}+0.0955 \mathrm{H}_{2} \mathrm{O}+ \\
0.095 \mathrm{HCO}_{3}^{-}+0.007 \mathrm{CO}_{2}
\end{array}
\]
Assume that all acetate ions are consumed and ammonia serves as a nutrient source. Given that $1 \mathrm{~g}$ acetate exerts $1.07 \mathrm{~g}$ COD; 1 mole bacteria $=113 \mathrm{~g}$ VSS; 1 mole acetate ion $=59 \mathrm{~g}$. Value of observed yield is ____________ (in $\mathrm{g} \mathrm{VSS} / \mathrm{g}$ COD, $\text{rounded off to two decimal places).}$

GATE ES 2021 | Question: 30

Tue, 14 Mar 2023 03:44:21 +0000

An ideal PFR or an ideal CFSTR may be used to degrade a pollutant with first order reaction kinetics. Both the reactors are fed with the same inlet concentration and the same volumetric flow rate, and are designed to achieve the same outlet concentration. Which of the following statements is true when comparing PFR with CFSTR?
PFR is Plug Flow Reactor.
CFSTR is Continuous Flow Stirred Tank Reactor $\text{(also referred to as CSTR)}$.

PFR will always require less reactor volume than CFSTR.
PFR will require the same reactor volume as CFSTR.
CFSTR will always require less reactor volume than PFR.
CFSTR can sometimes require less reactor volume than PFR.

GATE ES 2022 | Question: 30

Fri, 17 Feb 2023 07:05:50 +0000

Which one of the following statements is NOT correct with respect to a batch reactor?

No reactant is added after the reactor has started operation.
No product is withdrawn during the course of the reactor operation.
The reactor operates under steady state.
The reactor operation is carried out for a pre-specified duration.

GATE ES 2022 | Question: 36

Fri, 17 Feb 2023 07:05:46 +0000

Which of the following statement(s) is/are NOT correct while comparing continuously stirred tank reactor (CSTR) and plug flow reactor (PFR)?

CSTR and PFR are normally operated under steady state condition.
There is complete homogeneity in the CSTR while there are concentration variations within the PFR.
The overall reaction carried out in a PFR is always higher than that in a CSTR for same total volume.
Reaction kinetics do not play any role in choosing between a CSTR and PFR.