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Rate of Reaction

In a 1st orde...

Question

In a 1st order reac. A-> products the conc. Of reactant decreases to 6.25% of its initial value in 80 min. What is 1) the k 2)R,100minafter the start if the initial conc. Is 0.2 mole/litre

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Solution

a)
Let the initial concentration be
For first order reaction
$k equals fraction numerator 2.303 over denominator t end fraction log R subscript 0 over R$
Here,
R = 6.25
$k equals fraction numerator 2.303 over denominator 80 end fraction log fraction numerator 100 R subscript 0 over denominator 625 R subscript 0 end fraction$
k=0.0288 log
k=0.03466
b)
$k equals fraction numerator 2.303 over denominator t end fraction log R subscript 0 over R$
0.03466 = $fraction numerator 2.303 over denominator 100 end fraction log fraction numerator 0.2 over denominator R end fraction$ $rightwards double arrow 0.03466 cross times fraction numerator 100 over denominator 2.303 end fraction equals log fraction numerator 0.2 over denominator R end fraction$
1.50499 $equals log fraction numerator 0.2 over denominator R end fraction$
$e to the power of 1.50499 end exponent equals fraction numerator 0.2 over denominator R end fraction$
4.09098 $equals fraction numerator 0.2 over denominator R end fraction$
R = 0.04888 $fraction numerator m o l e over denominator l i t e r end fraction$

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