Define the Residence Time Distribution (RTD) function $E(t)$ and its normalization.

$E(t)$ is the exit-age distribution: the fraction of fluid leaving with age between $t$ and $t+dt$ is $E(t)\,dt$. It is normalized so that $\displaystyle\int_0^{\infty} E(t)\,dt = 1$.

How is $E(t)$ obtained from a pulse (delta) tracer experiment?

$E(t) = \dfrac{C(t)}{\displaystyle\int_0^{\infty} C(t)\,dt}$, where $C(t)$ is the measured exit tracer concentration following an instantaneous pulse input.

Relate the step-response cumulative function $F(t)$ to $E(t)$.

$F(t) = \displaystyle\int_0^{t} E(t)\,dt$ and $E(t) = \dfrac{dF(t)}{dt}$; $F$ is the fraction of exit stream younger than age $t$.

Give the mean residence time and variance from the RTD.

Mean: $\bar{t} = \displaystyle\int_0^{\infty} t\,E(t)\,dt$. Variance: $\sigma^2 = \displaystyle\int_0^{\infty} (t-\bar{t})^2 E(t)\,dt = \int_0^{\infty} t^2 E(t)\,dt - \bar{t}^{\,2}$.

Write the RTD function $E(t)$ for an ideal CSTR (mixed flow reactor).

$E(t) = \dfrac{1}{\tau}e^{-t/\tau}$, where $\tau = V/v_0$ is the mean residence time; equivalently $E_\theta(\theta) = e^{-\theta}$ with $\theta = t/\tau$.

What is the RTD for an ideal plug flow reactor (PFR)?

A Dirac delta: $E(t) = \delta(t - \tau)$; all fluid elements have exactly the same residence time $\tau$, and the variance is zero.

What is the dimensionless variance $\sigma_\theta^2$ and its values for ideal PFR and CSTR?

$\sigma_\theta^2 = \dfrac{\sigma^2}{\bar{t}^{\,2}}$. For an ideal PFR $\sigma_\theta^2 = 0$; for an ideal CSTR $\sigma_\theta^2 = 1$.

Name the two common single-parameter models used to characterize non-ideal flow.

(1) The dispersion (axial dispersion) model, characterized by the vessel dispersion number $D/uL$; and (2) the tanks-in-series model, characterized by the number of equal-size CSTRs $N$.

In the tanks-in-series model, how is $N$ related to the dimensionless variance?

$N = \dfrac{1}{\sigma_\theta^2} = \dfrac{\bar{t}^{\,2}}{\sigma^2}$; large $N$ approaches PFR behavior, $N=1$ is a single CSTR.

Write the RTD for $N$ equal CSTRs in series (tanks-in-series model).

$E(t) = \dfrac{t^{N-1}}{(N-1)!\,\tau_i^{N}}e^{-t/\tau_i}$, where $\tau_i$ is the residence time of one tank and total $\tau = N\tau_i$.

🇮🇳 GATE Chemical Engineering · flashcards

GATE Chemical Engineering Chemical Reaction Engineering Flashcards

51 question-and-answer cards covering Chemical Reaction Engineering as it is examined in GATE Chemical Engineering. 24 of them are printed below, taken from across the deck — no signup, no paywall on the preview.

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24 sample cards from the Chemical Reaction Engineering deck

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Define the Residence Time Distribution (RTD) function $E(t)$ and its normalization.
$E(t)$ is the exit-age distribution: the fraction of fluid leaving with age between $t$ and $t+dt$ is $E(t)\,dt$. It is normalized so that $\displaystyle\int_0^{\infty} E(t)\,dt = 1$.
How is $E(t)$ obtained from a pulse (delta) tracer experiment?
$E(t) = \dfrac{C(t)}{\displaystyle\int_0^{\infty} C(t)\,dt}$, where $C(t)$ is the measured exit tracer concentration following an instantaneous pulse input.
Relate the step-response cumulative function $F(t)$ to $E(t)$.
$F(t) = \displaystyle\int_0^{t} E(t)\,dt$ and $E(t) = \dfrac{dF(t)}{dt}$; $F$ is the fraction of exit stream younger than age $t$.
Give the mean residence time and variance from the RTD.
Mean: $\bar{t} = \displaystyle\int_0^{\infty} t\,E(t)\,dt$. Variance: $\sigma^2 = \displaystyle\int_0^{\infty} (t-\bar{t})^2 E(t)\,dt = \int_0^{\infty} t^2 E(t)\,dt - \bar{t}^{\,2}$.
Write the RTD function $E(t)$ for an ideal CSTR (mixed flow reactor).
$E(t) = \dfrac{1}{\tau}e^{-t/\tau}$, where $\tau = V/v_0$ is the mean residence time; equivalently $E_\theta(\theta) = e^{-\theta}$ with $\theta = t/\tau$.
What is the RTD for an ideal plug flow reactor (PFR)?
A Dirac delta: $E(t) = \delta(t - \tau)$; all fluid elements have exactly the same residence time $\tau$, and the variance is zero.
What is the dimensionless variance $\sigma_\theta^2$ and its values for ideal PFR and CSTR?
$\sigma_\theta^2 = \dfrac{\sigma^2}{\bar{t}^{\,2}}$. For an ideal PFR $\sigma_\theta^2 = 0$; for an ideal CSTR $\sigma_\theta^2 = 1$.
Name the two common single-parameter models used to characterize non-ideal flow.
(1) The dispersion (axial dispersion) model, characterized by the vessel dispersion number $D/uL$; and (2) the tanks-in-series model, characterized by the number of equal-size CSTRs $N$.
In the tanks-in-series model, how is $N$ related to the dimensionless variance?
$N = \dfrac{1}{\sigma_\theta^2} = \dfrac{\bar{t}^{\,2}}{\sigma^2}$; large $N$ approaches PFR behavior, $N=1$ is a single CSTR.
Write the RTD for $N$ equal CSTRs in series (tanks-in-series model).
$E(t) = \dfrac{t^{N-1}}{(N-1)!\,\tau_i^{N}}e^{-t/\tau_i}$, where $\tau_i$ is the residence time of one tank and total $\tau = N\tau_i$.
Define the vessel dispersion number and what its limits represent.
$\dfrac{D}{uL}$ where $D$ is the axial dispersion coefficient, $u$ velocity, $L$ length. $\dfrac{D}{uL}\to 0$ means negligible dispersion (plug flow); $\dfrac{D}{uL}\to\infty$ means large dispersion (mixed flow).
For small extents of dispersion, relate dimensionless variance to the dispersion number.
$\sigma_\theta^2 = 2\left(\dfrac{D}{uL}\right)$ for the small-dispersion (closed-closed, nearly plug flow) case.
What is the Bodenstein / Peclet number in the dispersion model?
The axial Peclet number $Pe = \dfrac{uL}{D}$, the reciprocal of the vessel dispersion number; large $Pe$ corresponds to plug flow, small $Pe$ to well-mixed flow.
Write the steady-state energy balance for an adiabatic reactor relating temperature and conversion.
$T = T_0 + \dfrac{(-\Delta H_R)\,C_{A0}X_A}{\sum \theta_i C_{p_i}\,\rho}$ (per mole fed); temperature rises linearly with conversion for an adiabatic exothermic reaction.
Define the adiabatic temperature rise for complete conversion.
$\Delta T_{ad} = \dfrac{(-\Delta H_R)\,C_{A0}}{\sum\theta_i C_{p_i}}$; it is the maximum temperature change attainable when all reactant converts with no heat exchange.
What characterizes multiple steady states in a non-isothermal CSTR?
The S-shaped heat-generation curve $Q_g(T)$ can intersect the linear heat-removal line $Q_r(T)$ at up to three points; the upper and lower are stable steady states and the middle one is unstable (ignition-extinction behavior).
State the stability criterion for a steady state in a non-isothermal CSTR.
A steady state is stable when the slope of the heat-removal line exceeds the slope of the heat-generation curve at the operating point: $\dfrac{dQ_r}{dT} > \dfrac{dQ_g}{dT}$.
Distinguish exothermic and endothermic reactions in terms of optimum temperature progression.
For an irreversible reaction, use the highest allowable temperature. For a reversible exothermic reaction, decrease temperature as conversion proceeds (locus of maximum rates). For a reversible endothermic reaction, use the highest allowable temperature throughout.
Define the Thiele modulus and what it measures in catalysis.
For a first-order reaction in a sphere, $\phi = R\sqrt{\dfrac{k}{D_e}}$ (general $M_T = L\sqrt{k C_A^{n-1}/D_e}$). It is the ratio of surface (intrinsic) reaction rate to intraparticle diffusion rate.
Define the internal effectiveness factor $\eta$ and its limiting forms.
$\eta = \dfrac{\text{actual rate with diffusion}}{\text{rate if entire interior were at surface concentration}}$. When $\phi \ll 1$ (kinetics control) $\eta \to 1$; when $\phi \gg 1$ (strong diffusion limitation) $\eta \approx 1/\phi$.
For strong pore-diffusion resistance, how do the observed reaction order and activation energy compare with the true values?
The observed order becomes $\dfrac{n+1}{2}$ (so first order appears first order, second order appears 1.5 order) and the observed activation energy is about half the true value, $E_{obs}\approx \tfrac{1}{2}E_{true}$.
What is the Weisz-Prater criterion and its use?
$C_{WP} = \eta\phi^2 = \dfrac{(-r_A')_{obs}\,\rho_c R^2}{D_e C_{As}}$, computed from observable quantities. $C_{WP} \ll 1$ means no internal diffusion limitation; $C_{WP} \gg 1$ means severe internal diffusion control.
Classify the mechanisms of catalyst deactivation.
(1) Sintering/aging - loss of active surface area by thermal agglomeration; (2) Fouling/coking - deposition of carbon or material blocking sites; (3) Poisoning - chemisorption of impurities on active sites. They may be parallel, series, side-by-side, or independent with respect to the main reaction.
Write a general rate expression for catalyst deactivation in terms of an activity term.
$-r_A' = a(t)\,k\,f(C_A)$ with deactivation rate $-\dfrac{da}{dt} = k_d\,a^{\,d}\,h(C_{poison})$, where activity $a(t)=\dfrac{-r_A'(t)}{-r_A'(t=0)}$ ranges from 1 (fresh) to 0 (fully deactivated) and $d$ is the deactivation order.

What this deck covers

The Chemical Reaction Engineering deck follows the GATE Chemical Engineering Chemical Reaction Engineering syllabus — 4 chapters and 7 topics — so questions land on material that is genuinely examinable rather than trivia around it. That works out to roughly 12.8 cards per chapter.

Answers are written to be recallable, not just readable — averaging about 184 characters, which is long enough to carry the reasoning and short enough to say out loud.

A deck like this earns its keep on the second and third pass. Read the syllabus first so you know the shape of the subject, then use the cards to find the specific facts that have not stuck.

Chemical Reaction Engineering flashcards FAQ

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51 cards. This page previews 24 of them, sampled evenly across the deck so you can judge the difficulty before installing anything.

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Yes. The preview here is free to read with no signup, and the full 51-card deck is free inside the Examius app.

What do the Chemical Reaction Engineering cards cover?

They follow the GATE Chemical Engineering Chemical Reaction Engineering syllabus — 4 chapters and 7 topics — so the questions track what is actually examinable.

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Read the syllabus first so you know the shape of the subject, then drill the deck. Examius schedules each card with spaced repetition, so cards you keep missing come back sooner and ones you know drift further apart.