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For a reaction if its rate constant is 10–3 min–1 and initial concentration of reactant is 0.2 mol dm–3, then how much fraction of reactant will be converted into products in 200 min?

Asked by Atulcaald 15th May 2018, 1:00 PM
Answered by Expert
Answer:
Rate space constant space comma space straight k equals space 10 to the power of negative 3 end exponent space min to the power of negative 1 end exponent
It space is space straight a space first space order space reaction.

Initial space rate space equals space straight k left square bracket straight A right square bracket space equals space 10 to the power of negative 3 end exponent space min to the power of negative 1 end exponent cross times 0.2 space mol space dm to the power of negative 3 end exponent

space space space space space space space space space space space space space space space space space space space space space space space space space space equals space 2 cross times 10 to the power of negative 4 end exponent space space space mol space dm to the power of negative 3 end exponent space min to the power of negative 1 end exponent

For space first space order space reaction colon

straight k equals space fraction numerator 2.303 over denominator straight t end fraction log space fraction numerator straight a over denominator open parentheses straight a minus straight x close parentheses end fraction

log space fraction numerator straight a over denominator open parentheses straight a minus straight x close parentheses end fraction equals space fraction numerator kt over denominator 2.303 end fraction


space space space space space space space space space space space space space space space space space space equals fraction numerator space space 10 to the power of negative 3 end exponent cross times 200 over denominator 2.303 end fraction

space log space fraction numerator straight a over denominator open parentheses straight a minus straight x close parentheses end fraction space space equals space 8.68 cross times 10 to the power of negative 2 end exponent

Taking space antilog

space fraction numerator straight a over denominator open parentheses straight a minus straight x close parentheses end fraction equals space 1.22

straight a equals space 1.22 straight a minus 1.22 straight x

1.22 straight x equals space 1.22 straight a minus straight a

space space space space space space straight x equals fraction numerator 0.22 straight a over denominator 1.22 end fraction

space space space space space space straight x equals space 0.181 straight a

therefore space space fraction numerator 0.181 straight a over denominator straight a end fraction cross times 100

equals 18.1 percent sign
Answered by Expert 16th May 2018, 6:11 PM
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