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题库 / Prep2007E1-PS-142
The rate of a certainchemical reaction is directly proportional to the square of the concentrationof chemical A present and inversely proportional to the concentration ofchemical B present. If the concentrationof chemical B is increased by 100 percent, which of the following is closest tothe percent change in the concentration of chemical A required to keep thereaction rate unchanged?
100% decrease
50% decrease
40% decrease
40% increase
50% increase
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反应速率r＝k*(A^2)*(1/B)
B上升100%后，B'＝（1+100%）B＝2B
要反应速度不变，需要k*(A^2)*(1/B)＝k*(A'^2)*(1/B')
k约掉，B'代入，(A^2)*(1/B)＝(A'^2)*(1/2B)
B约掉，A’^2=2*(A^2)
两边开根号，A'=根号2*A
根号2＝1.414，故上涨40%
rate速度，proportional成比例的，concentration浓度，inversely相反地
解题过程：
反应速率＝k*(A^2)*(1/B)
B上升100%后，B'＝（1+100%）B＝2B
要反应速度不变，需要k*(A^2)*(1/B)＝k*(A'^2)*(1/B')
k约掉，B'代入，(A^2)*(1/B)＝(A'^2)*(1/2B)
B约掉，A’^2=2*(A^2)
两边开根号，A'=根号2*A
根号2＝1.414，故上涨40%
directly proportional是正比，inversely proportional是反比，b乘以2，则r除以2，r除以2，a方也除以2，才能保持正反比关系
square of the concentrationof chemical A
分子A平方 分母B
初始公式：r = kA^2 / B, Bdouble后 r = kA^2 / 2B， 维持不变， A也要乘以2才能上下抵消，平方1.4=1.96, 平方1.5=2.25， 明显1.4更接近2