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58] Two substances A and B are present such that[A°) = 4[Bº] and half life of A is 5 min and thatof B is 15 min. If they start decaying at the sametime following first order kinetics how much timelater will take if the concentration of both ofthem would be same?1) 15 min2) 50 min3) 35 min4) 62 min |
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Answer» Initial concentration of A = [Ao]Amount of A left inn1half lives =(12)n1[Ao] Initial concentration of B = [Bo]Amount of A left inn2half lives =(12)n2[Bo] According to the question, concentration of both will be same, [Ao]/2^n1=[Bo]/2n^24/2^n1=1/2^n2(SinceAo=4Bo)2^n1/2^n2=2^22(n1−n2)=2^2n1−n2=2n2=n1−2Also,t=n1×t(1/2A)t=n2×t(1/2B)Let the concentration of both become equal after time t n1×t1/2/n2×t1/2=n1×5/n2×15=1n1/n2=3n1=3n2Usingaboverelationinequationn2=n1−2n2=3n2−2n2=1Therefore,n1=3Puttingthisvaluein,t=n1×t1/(A)=3×5=15minutes |
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