a) What is pseudo first order reaction? Inversion of cane sugar is which type of reaction. Write it's chemical reaction?
b) Calculate the half life of the first order reaction whose rate constant is $5 \times 10^{- 14} s^{- 1}$ .
c) Plot a graph between ln K & 1/T on the basis of Arrhenius equation.

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Solution

a) Pseudo first order reaction:
For a second order reaction, when one of the reactants is present in large excess, its concentration remains practically unchanged over a period of reaction. Such reaction is called pseudo first order reaction as the rate of the reaction is proportional to the concentration of other reactant.
Inversion of cane sugar is pseudo first order reaction.
$C_{12} H_{22} O_{11} (a q) + H_{2} O (l) i n v e r t a s e - ---- \to C_{6} H_{12} O_{6} (a q) (glucose) + C_{6} H_{12} O_{6} (a q) (fructose)$
Here, water is in large excess and the rate of the reaction is proportional to the concentration of cane sugar.
b) The half life of the first order reaction whose rate constant is $5 \times 10^{- 14} s^{- 1}$ is $t_{1 / 2} = \frac{0.693}{k} = \frac{0.693}{5 \times 10^{- 14} s^{- 1}} = 1.38 \times 10^{13} s$
c) The plot of graph between ln K & 1/T on the basis of Arrhenius equation
$(l n k = l n A - \frac{E_{a}}{R T})$ is a straight line with negative slope.

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