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+1 vote
21.7k views
in Chemistry by (42.5k points)
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For the first order reaction A → 2B, 1 mole of reactant A gives 0.2 moles of B after 100 minutes. The half life of the reaction is ...... min. (Round off to the nearest integer). 

[Use : ln 2 = 0.69, ln 10 = 2.3 Properties of logarithms : ln xy = y ln x;

In \(\Big(\frac{x}{y}\Big)\) = In x - In y ]

(Round off to the nearest integer)

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1 Answer

+1 vote
by (4.0k points)

\(A\longrightarrow 2B\)

 t = 0  

A =1

t = 100 

A \(= 1 -0.1 = 0.9\)

\(=2\times0.01=0.2\)

\(k=\frac{1}{t}ln\frac{[A_0]}{[A_t]}\)

\(k=\frac{1}{t}\;ln\;\frac{1.0}{0.9}\) \(\bigg[k=\frac{0.693}{t_{1/2}}\bigg]\)

\(\frac{0.693}{t_{1/2}}=\frac{1}{t}\;[ln\;10-ln\;9]\)

\(0.693\times t=t_{1/2}[ln\;10-2\;ln\;3]\) \(\bigg[ln\;9\Rightarrow ln\;3^2=2\;ln\;3\bigg]\)

\(0.693\times t=t_{1/2}[2.3-2\times1.1]\)

\(0.693\times t=t_{1/2}[2.3-2.2]\)

\(0.693\times t=t_{1/2}[0.1]\)

\(t_{1/2}=\frac{0.693\times t}{0.1}\)

\(=\frac{0.693\times 100}{0.1}\)

\(t_{1/2}=693\;minute\)

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