For analysis of equilibria concerning dissociation of electrolytes into ions like
${CH}_{3} COOH \underset{K_{- 1}}{\overset{K_{1}}{⇌}} {CH}_{3} {COO}^{-} + H^{+}$
A term relaxation time is defined as reciprocal of $(K_{1} + K_{- 1} \cdot X),$ where $K_{1}$ and $K_{- 1}$ are rate constant of forward and backward reaction respectively and X is equilibrium concentration of any product. Calculate relaxation time for above equilibria if the two rate constant (not in any specific order) are $10^{8} M^{- 1} \sec^{- 1}$ and $4 \times 10^{2} \sec^{- 1}$ and initial concentration of ${CH}_{3} COOH$ taken is 1M. [If the answer is $\times 10^{- 6} \sec$ then, find value of y].

Question

For analysis of equilibria concerning dissociation of electrolytes into ions like
${CH}_{3} COOH \underset{K_{- 1}}{\overset{K_{1}}{⇌}} {CH}_{3} {COO}^{-} + H^{+}$
A term relaxation time is defined as reciprocal of $(K_{1} + K_{- 1} \cdot X),$ where $K_{1}$ and $K_{- 1}$ are rate constant of forward and backward reaction respectively and X is equilibrium concentration of any product. Calculate relaxation time for above equilibria if the two rate constant (not in any specific order) are $10^{8} M^{- 1} \sec^{- 1}$ and $4 \times 10^{2} \sec^{- 1}$ and initial concentration of ${CH}_{3} COOH$ taken is 1M. [If the answer is $\times 10^{- 6} \sec$ then, find value of y].

Accepted Answer

The reaction process as follows,CH3COOH⇌K1K−1CH3COO−+H+1             −x                        xrf            =K1CH3COOHrb           =K−1CH3COO−H+K1=4×102;K−1=108x21−x=4×102108 ⇒x=2×10−3t=14×102+108×2×10−3=5×10−6

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