A certain reaction `A+B rarr C` is first order with respect to each reactant with `k=1.0xx10^(-3)` L `s^(-1)` If initial concentrations of A and B are `0.100` M and `0.200` M the concentration of A after 100 s is

Options

A. `0.098` M
B. `0.199` M
C. `0.019` M
D. None of these

Answer

A

Explanation

`{:(A,+,B,rarr,C),("0.100 M",,"0.200 M",,),("(0.100-x)M",,"(0.200-x)M",,"xM"):}`
`(dx)/(dt)=k.[A][B]`
`(dx)/(dt)=(1.0xx10^(-3)"mol L"^(-1)s^(-1))xx(0.100-x)(0.200-x)`
`(dx)/((0.100-x)(0.200-x))=1.0xx10^(-3)dt`
Integrating `int(dx)/((0.100-x)(0.200-x))`
`=1.0 xx 10^(-3) int dt`
`"log"_(e)(0.200-x)/(0.100-x)-"log"_(e)(0.200)/(0.100)`
`=1.0xx10^(-3)xx100(becauset=100s)`
`"log"_(e)(0.200-x)/(0.100-1)-log_(e)2=1.0xx10^(-1)`
`"log"_(e)=(0.200-x)/(0.100-x)=1.0xx10^(-1)+0.693`
`[:. l n2=0.693]`
`=x=0.002 M`
After `100s,[A]=(0.100-x)M`
`=(0.100-0.002)M=0.098 M`.