请教一道prep数学

toneere

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%, 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

 

correct answer: d

 

我没弄明白题干，请大家指点一下，万分感谢！

taoyeye

 一个化学量同A浓度平方成正比，同B浓度成反比，若B翻倍，要原来的反应速率不变，A浓度当如何？应该变成根号2倍，增加40%左右

antiquarks

化学反映的速率跟A物质的浓度的平方成正比，跟B物质的浓度成反比，现在B的浓度增长了100%，问A的浓度增长多上才能保证反映速率不变。

设原来速率为r,原来B的浓度为b,原来A的浓度为a，所求A的浓度为A,那么列出方程：
r=k(a^2)/(tb)=k(A^2)/(t2b)，其中k和t为自设定的比率，常数。

解方程得：A=(根号2)*a，所以选D

toneere

谢谢~~~