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Chemical Kinetics

Question

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For a first order reaction, show that time required for 99% completion is twice the time required for the completion of 90% of reaction.

Solution

For space straight a space first space order space reaction comma space space space space space space space space space space space space space space space space space space space space space space straight A space space rightwards arrow space space space straight P straight T space equals 0 space space space space space space space space space space space space space space space straight a space space space space space space space space space 0 straight T equals straight t space space space space space space space space space space space space left parenthesis straight a minus straight x right parenthesis space space space space space space space straight x Case space 1 colon space If space apostrophe straight t apostrophe space is space the space time space required space for space 99 percent sign space completion space then space straight x space equals space 99 space percent sign space of space straight a space left parenthesis straight a minus straight x right parenthesis space equals 1 space percent sign space of space straight a space equals 1 over 100 space straight x space straight a space equals space straight a over 100 straight t equals space open parentheses fraction numerator 2.303 over denominator straight k end fraction close parentheses log space fraction numerator straight a space over denominator straight a minus straight x end fraction space equals space straight t equals space open parentheses fraction numerator 2.303 over denominator straight k end fraction close parentheses log space fraction numerator straight a space straight x 100 space over denominator straight a end fraction space equals fraction numerator 2.303 space over denominator straight k end fraction log space 10 squared Therefore space straight t equals space 2 open square brackets fraction numerator 2.303 over denominator straight k end fraction close square brackets Case space 2 space colon space space if space apostrophe straight t apostrophe space is space the space time space required space for space 90 percent sign space of space completion space then space straight x space equals space 90 percent sign space of space straight a space left parenthesis straight a minus straight x right parenthesis space space equals 10 percent sign space of space straight a space 10 over 100 space straight x space straight a space equals straight a over 10 straight t equals space open parentheses fraction numerator 2.303 over denominator straight k end fraction close parentheses space log space fraction numerator straight a over denominator straight a minus space straight x space end fraction equals space space open parentheses fraction numerator 2.303 over denominator straight k end fraction close parentheses space log space fraction numerator straight a space straight x space 10 over denominator straight a space end fraction straight t space equals fraction numerator 2.303 over denominator straight k end fraction Therefore comma space the space time space rquired space for space space 99 percent sign space completion space of space 1 to the power of st space order space reaction space is space twice space the space time space required space for space 90 percent sign space completion.

Some More Questions From Chemical Kinetics Chapter

The conversion of molecules X to Y follows second order kinetics. If concentration of X is increased to three times how will it affect the rate of formation of Y?

What will be the effect of temperature on rate constant?

A reaction is 50% complete in 2 hours and 75% complete in 4 hours. What is the order of the reaction.

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