作业帮一道GRE数学题,请详解
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一道GRE数学题,请详解
The rate of a certain chemical reaction is directly proportional to the square of the concentration of chemical A present and inversely proportional to the concentration of chemical B present.If the concentration of chemical B is increased by 100 percent,which of the following is closest to the percent change in the concentration of chemical A required to keep the reaction rate unchanged?
(A) 100% decrease
(B) 50% decrease
(C) 40% decrease
(D) 40% increase
(E) 50% increase
The rate of a certain chemical reaction is directly proportional to the square of the concentration of chemical A present and inversely proportional to the concentration of chemical B present.If the concentration of chemical B is increased by 100 percent,which of the following is closest to the percent change in the concentration of chemical A required to keep the reaction rate unchanged?
(A) 100% decrease
(B) 50% decrease
(C) 40% decrease
(D) 40% increase
(E) 50% increase
关键词：
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%
所以选择（C）
希望对你有所帮助 还望采纳~~~
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%
所以选择（C）
希望对你有所帮助 还望采纳~~~