Question

In the following reaction : xA$\longrightarrow$Yb

$\log\left\lbrack - \frac{d\lbrack A\rbrack}{dt} \right\rbrack = \log\left\lbrack - \frac{d\lbrack B\rbrack}{dt} \right\rbrack + 0.3$where –ve sign

indicates rate of disappearance of the reactant. Thus, x : y is :

• A. 1 : 2
• B. 2 : 1
• C. 3 : 1
• D. 3 : 10

Answer 1

Answer: (B)

2 : 1

Answer 2

$xA\overset{\quad\quad}{\rightarrow}YB$

$\frac{- 1}{x}\frac{d}{dt}\lbrack A\rbrack = \frac{1}{y}\frac{d}{dt}\lbrack B\rbrack \Rightarrow \frac{- d}{dt}\lbrack A\rbrack = \frac{x}{y}\frac{d}{\text{dt}}\lbrack B\rbrack$

$\log\left( \frac{- d\lbrack A\rbrack}{dt} \right) = \log\left( \frac{x}{y} \right)\left( \frac{+ d\lbrack B\rbrack}{dt} \right)\log\frac{- d}{dt}\lbrack A\rbrack = \log\frac{- d}{dt}\lbrack B\rbrack + \log\left( \frac{x}{y} \right)$

$\log\left( \frac{x}{y} \right) = 0.3 \Rightarrow \frac{x}{y} = \frac{2}{1} \Rightarrow x:y2:1$