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  •  A first order reaction has the rate constant, <img alt="=4.6 \times 10^{-3} \mathrm{~s}^{-1}" src="https://entrancecorner.oncodecogs.com/gif.latex?%3D4.6%20%5Ctimes%2010%5E%7B-3%7D%20%5Cmathr

 A first order reaction has the rate constant, =4.6 \times 10^{-3} \mathrm{~s}^{-1}. The number of correct statement/s  from the following is/are
Given: \log 3=0.48

A. Reaction completes in 1000 \mathrm{~s}.
B. The reaction has a half-life of 500 \mathrm{~s}.
C. The time required for 10 \% completion is 25 times the time required for 90 \% completion.
D. The degree of dissociation is equal to \left(1-\mathrm{e}^{-\mathrm{kt}}\right)
E. The rate and the rate constant have the same unit.

Option: 1

1


Option: 2

-


Option: 3

-


Option: 4

-


Answers (1)

best_answer

\mathrm{k}=4.6 \times 10^{-3} \mathrm{sec}^{-1}

for Ist order :-

\mathrm{t}^{1 / 2}=\frac{0.693}{\mathrm{k}}=\frac{0.693}{4.6 \times 10^{-3}}=150.65 \mathrm{sec} .
\mathrm{t}_{\text {completion }}=\infty

\text { Degree of dissociation }(\propto)= \frac{\mathrm{x}}{[\mathrm{A}]_0}=\frac{[\mathrm{A}]_0-[\mathrm{A}]_{\mathrm{t}}}{[\mathrm{A}]_0}
=\frac{[\mathrm{A}]_0-[\mathrm{A}]_0 \mathrm{e}^{-\mathrm{kt}}}{[\mathrm{A}]_0}=1-\mathrm{e}^{-\mathrm{kt}}

rate and rate constant have different units

\mathrm{t}_{10 \%}=\frac{1}{\mathrm{~K}} \ln \frac{100}{90}
\mathrm{t}_{90 \%}=\frac{1}{\mathrm{~K}} \ln \frac{100}{10}
\frac{\mathrm{t}_{10 \%}}{\mathrm{t}_{90 \%}}=\frac{\log 10-\log 9}{\log 10}=0.045
\mathrm{t}_{10 \%}=0.045 \mathrm{t}_{90 \%}

Posted by

Pankaj Sanodiya

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