GATE-CH-1988-7-b-iv-cre-2mark

Liquid \(A\) decomposes by first order kinetics in an isothermal batch reactor. Fifty percent of \(A\) is converted in 300 seconds. The time required for a conversion of 75 percent is

• \(300 \times 0.75/0.25\) seconds

• \(300 \ln 1\) seconds

• \(300 \ln (0.5/0.25)\) seconds

• \(300 [\ln (0.25) / \ln (0.5)]\) seconds

GATE-CH-1989-7-i-b-cre-1mark

For the following reaction, the rate constant at 373 K is 0.5 per minute. \[ 0.5A + B \rightarrow C \] The overall order of the reaction is

• 0.5

• 1.0

• 1.5

• 0

GATE-CH-1992-2-c-cre-2mark

A gaseous reaction \(A\rightarrow 2B+C\) takes place isothermally in a constant pressure reactor. Starting with a gaseous mixture containing 50% \(A\) (rest inerts), the ratio of final to initial volume is found to be 1.6. The percentage conversion of \(A\) is

• 30

• 50

• 60

• 74

GATE-CH-1992-8-a-cre-2mark

The conversion of a reactant, undergoing a first order reaction, at a time equal to three times the half life of the reaction is

• 0.875

• 0.5

• 0.425

• not possible to calculate because of insufficient data

GATE-CH-1999-2-14-cre-2mark

Consider the n\(^{th}\) order irreversible liquid phase reaction \(A \rightarrow B\). Which one of the following plots involving half-life of the reaction \((t_{1/2})\) and the initial reactant concentration \((C_{A0})\) gives a straight line plot?

• \(C_{A0}\) vs. \(t_{1/2}\)

• \(\ln C_{A0}\) vs. \(t_{1/2}\)

• \(C_{A0}\) vs. \(\ln t_{1/2}\)

• \(\ln C_{A0}\) vs. \(\ln t_{1/2}\)

GATE-CH-2000-1-19-cre-1mark

The reaction \(A\rightarrow B\) is conducted in an isothermal batch reactor. If the conversion of \(A\) increases linearly with holding time, then the order of the reaction is

• 0

• 1

• 1.5

• 2

GATE-CH-2000-2-17-cre-2mark

The following half-life data are available for the irreversible liquid phase reaction, \[ A \rightarrow \text { Products} \] 

Initial concentration (kmol/m3)	Half-life (min)
2	2
8	1

The overall order of the reaction is

• 0.5

• 1

• 1.5

• 2

GATE-CH-2001-1-14-cre-1mark

The conversion for a second order, irreversible reaction (constant volume), \(A \stackrel {k_2}{\longrightarrow } B\), in batch mode is given by

• \(\displaystyle \frac {1}{1+k_2C_{A0}t}\)

• \(\displaystyle \frac {k_2C_{A0}t}{1+k_2C_{A0}t}\)

• \(\displaystyle \frac {(k_2C_{A0}t)^2}{1+k_2C_{A0}t}\)

• \(\displaystyle \frac {k_2C_{A0}t}{(1+k_2C_{A0}t)^2}\)

GATE-CH-2001-2-17-cre-2mark

The first-order, gas phase reaction \(A \stackrel {k_1}{\rightarrow } 2B\) is conducted isothermally in batch mode. The rate of change of conversion with time is given by

• \(\displaystyle dX_A/dt = k_1(1-X_A)^2(1+2X_A)\)

• \(\displaystyle dX_A/dt = k_1(1-X_A)(1+0.5X_A)\)

• \(\displaystyle dX_A/dt = k_1(1-X_A)\)

• \(\displaystyle dX_A/dt = k_1(1-X_A)/(1+X_A)\)

GATE-CH-2004-73-cre-2mark

For an isothermal second order aqueous phase reaction \(A \rightarrow B\), the ratio of the time required for 90% conversion to the time required for 45% conversion is

• 2

• 4

• 11

• 22

GATE-CH-2005-26-cre-1mark

For the liquid phase reaction \(A \rightarrow P\), in a series of experiments in a batch reactor, the half-life \(t_{1/2}\) was found to be inversely proportional to the square root of the initial concentration of \(A\). The order of the reaction is

• \(3/2\)

• \(1\)

• \(+1/2\)

• \(-1/2\)

GATE-CH-2006-16-cre-1mark

A first order reversible reaction \(A\xrightleftharpoons [k_2]{k_1} B\) occurs in a batch reactor. The exponential decay of the concentration of \(A\) has the time constant

• \(\dfrac {1}{k_1}\)

• \(\dfrac {1}{k_2}\)

• \(\dfrac {1}{k_1-k_2}\)

• \(\dfrac {1}{k_1+k_2}\)

GATE-CH-2009-14-cre-1mark

The half-life of a first order liquid phase reaction is 30 seconds. Then the rate constant, in min^-1, is

• 0.0231

• 0.602

• 1.386

• 2.0

GATE-CH-2012-19-cre-1mark

The half-life of an \(n^{\text {th}}\) order reaction in a batch reactor depends on

• only the rate constant

• only the rate constant and the order of the reaction

• only the rate constant and the initial reactant concentration

• the rate constant, initial reactant concentration, and the order of the reaction

GATE-CH-2015-18-cre-1mark

For which reaction order, the half-life of the reactant is half of the full lifetime (time for 100% conversion) of the reactant?

• Zero order

• Half order

• First order

• Second order

GATE-CH-2015-19-cre-1mark

An irreversible, homogeneous reaction \(A\rightarrow \text {products}\), has the rate expression: \[ \text {Rate} = \frac {2C_A^2+0.1C_A}{1+50C_A}, \qquad \text {where \(C_A\) is the concentration of \(A\).} \] \(C_A\) varies in the range 0.5 - 50 mol/m³.
For very high concentrations of \(A\), the reaction order tends to:

• 0

• 1

• 1.5

• 2

GATE-CH-2007-58-cre-2mark

The following rate-concentration data are calculated from experiment. Find the activation energy temperature (\(E/R\)) of the first order reaction.

\(d_p\)	\(C_A\)	\(-r_A\)	\(T\)
1	20	1	480
2	40	2	480
2	40	3	500

• 2432.8

• 4865.6

• 9731.2

• 13183.3

GATE-CH-2014-37-cre-2mark

A homogeneous reaction (\(R\rightarrow P\)) occurs in a batch reactor. The conversion of the reactant \(R\) is 67% after 10 minutes and 80% after 20 minutes. The rate equation for this reaction is

• \(-r_R=k\)

• \(-r_R=kC_R^2\)

• \(-r_R=kC_R^3\)

• \(-r_R=kC_R^{0.5}\)

GATE-CH-2001-14-cre-5mark

The concentration versus batch time data for a constant volume, isothermal batch reactor is given in the table below.

Assuming the reaction to be first order in \(A\), the best value of \(k\) by least squares regression is found to be = _______________ \(\times 10^{-3}\) s\(^{-1}\)

• Answer

GATE-CH-BT-2016-48-cre-2mark

Decimal reduction of bacterial spores is 23 min at 121^oC and the death kinetics follow first order. One litre medium containing \(10^5\) spores per mL was sterilized for 10 min at 121^oC in a batch sterilizer. The number of spores in the medium after sterilization (assuming destruction of spores in heating and cooling period is negligible) will be ____________\(\times 10^7\).

• Answer

GATE-CH-BT-2018-48-cre-2mark

Mammalian cells in active growth phase were seeded at a density of \(1\times 10^5\) cells/mL. After 72 hours, \(1\times 10^6\) cells/mL were obtained. The population double time of the cells in hours is (up to two decimal places) ____________

• Answer

0700-3-cre-2mark

Consider the reaction \(A+2B\rightarrow R\). This reaction was carried out and the following initial-rate data were reported. Determine the overall order of reaction and the reaction rate constant.

• Answer