## Reaction Kinetics

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

1988-7-b-iv-cre

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

1989-7-i-b-cre

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

1992-2-c-cre

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

1992-8-a-cre

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

1999-2-14-cre

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. $$\ln t_{1/2}$$

[Index]

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

2000-1-19-cre

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

2000-2-17-cre

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

2001-1-14-cre

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

2001-2-17-cre

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

2004-73-cre

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

[Index]

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

2005-26-cre

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

2006-16-cre

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

2009-14-cre

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

2012-19-cre

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

2015-18-cre

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

[Index]

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

2015-19-cre

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

2007-58-cre

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

2014-37-cre

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.

$$t$$ (s) 0 30 60 90 120 150 180
$$C_A$$ (kmol/m$$^3$$) 1.00 0.92 0.89 0.81 0.76 0.72 0.70

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$$^{-1}$$

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

BT-2016-48-cre

Decimal reduction of bacterial spores is 23 min at 121oC and the death kinetics follow first order. One litre medium containing $$10^5$$ spores per mL was sterilized for 10 min at 121oC 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 ____________$$\times 10^7$$.

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

BT-2018-48-cre

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) ____________

### 0700-3-cre-2mark

0700-3-cre

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.

Run No. $$C_{A0}$$ (mol/litre) $$C_{B0}$$ (mol/litre) Initial rate (mol/litre.s)
1 0.10 0.10 1.01
2 0.15 0.10 1.51
3 0.10 0.20 2.01

[Index]