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CBSE Class 12 Chemistry 2024 All Sets Solved Paper

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Question : 8 of 16
Marks: +1, -0
The rate of a reaction increases sixteen times when the concentration of the reactant increases four times. The order of the reaction is
Solution:  
Let the reaction be A → products
Differential rate law is
Rate=k[A]x\text{Rate} = k[A]^x
Rate1=k[a]x\text{Rate}_1 = k[a]^x
Rate2=k[4a]x\text{Rate}_2 = k[4a]^x
Thus,   Rate2Rate1=(4aa)x\;\frac{\text{Rate}_2}{\text{Rate}_1} = \left( \frac{4a}{a} \right)^x
16=(4)x16 = (4)^x
Taking log of both sides
log⁡16=xlog⁡4\log 16 = x \log 4
log⁡24=xlog⁡22\log 2^4 = x \log 2^2
4log⁡2=2xlog⁡24\log 2 = 2x \log 2
x=  42=2x = \;\frac{4}{2} = 2
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