Chemical Kinetics and Nuclear ChemistryHard

Question

For the parallel reactions $A\overset{\quad K_{1}\quad}{\rightarrow}B\text{ and }A\overset{\quad K_{2}\quad}{\rightarrow}C$, the initial concentration of ‘A’ is CAo and initially ‘B’ and ‘C’ are absent. Concentrations of A, B and C at any time ‘t’ is CA, CB and CC, respectively. The correct relation(s) is/are

Options

A.CA + CB + CC = CAo
B.$\frac{dC_{A}}{dt} + \frac{dC_{B}}{dt} + \frac{dC_{C}}{dt} = 0$
C.$\frac{C_{B}}{C_{C}} = \frac{K_{1}}{K_{2}}$
D.$\frac{C_{B}}{C_{Ao} - C_{A}} = \frac{K_{1}}{K_{1} + K_{2}}$

Solution

As mole is not changing, $C_{A} + C_{B} + C_{C} = C_{A_{0}}$

Now, $\frac{C_{B}}{C_{A_{0}} - C_{A}} = \frac{C_{B}}{C_{B} + C_{C}} = \frac{K_{1}}{K_{1} + K_{2}}$

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