A first order reaction takes 40 minutes for 30 decomposition

Step-I: Calculation of rate constant: a=`100%, (a-x)=70%, t=40` min For first order reaction, `k=(2.303)/t log (a)/(a-x) =(2.303)/(40"min") log 100/70=(2.303 xx 0.1549)/(40"min") =0.0089 min^(-1)` Step-II Calculation of half life period `(t_(1//2))` `t_(1//2) = 0.693/k =(0.693)/(0.0089 min^(-1)) = 78 min`

Q. (a) A reaction is second order in A and first order in B. (i) Write the differential rate equation. (ii) How is the rate affected on increasing the concentration of A three times? (iii) How is the rate affected when the concentrations of both A and B are doubled? (b) A first order reaction 40 minutes for 30% decomposition. Calculate t 1 / 2 for this reaction. (Give log 1.428 = 0.1548)

`A->P` t=0 a 0 t=t (a-x) x Now, it takes 40 min for 30% decomposition i.e. reactant left after 40 min is 70% of its initial concentration. `So,(a-x)=70/100xxa=7/10xxa` `k=2.303/tlog(a/(a-x)) => k=2.303/40 log a/(7/10)a=2.303/40log1.428` `therefore k=0.00891 min ` `therefore t_(1/2)=0.693/k=0.693/0.008913=77.78 min`

\( \newcommand\) • • • • • • • • • • • A first-order reaction is a reaction that proceeds at a rate that depends linearly on only one reactant concentration. The Differential Representation Differential rate laws are generally used to describe what is occurring on a molecular level during a reaction, whereas integrated rate laws are used for determining the reaction order and the value of the rate constant from experimental measurements. The differential equation describing first-order kinetics is given below: \[ Rate = - \dfrac \] The "rate"is the reaction rate (in units of molar/time) and \(k\) is the reaction rate coefficient (in units of 1/time). However, the units of \(k\) vary for non-first-order reactions. These differential equations are The Integral Representation First, write the differential form of the rate law. \[ Rate = - \dfrac \] The integrated forms of the rate law can be used to find the population of reactant at any time after the start of the reaction. Plotting \(\ln[A]\) with respect to time for a first-order reaction gives a straight line with the slope of the line equal to \(-k\). More information can be found in the article on This general relationship, in which a quantity changes at a rate that depends on its instantaneous value, is said to follow an exponential law. Exponential relations are widespread in science and in many other fields. Consumption of a chemical reactant or the decay of a radioactive isotope follow the exponential decay law. Its...