The hypothetical reaction `A+B rarr C` is first order with respect to each reactant with `k=1.0xx10^(-2)` L `"mol"^(-1) s^(-1)` if initial concentration of each reactant is `0.100` M the concentration of A after 100s is

Options

A. `0.091` M
B. `1.0xx10^(-3)` M
C. `1.9xx10^(-3)` M
D. `9.1xx10^(-3)` M

Answer

A

Explanation

The change in concentration of water is just 0.81 %. Since the concentration of the two reactants start equal and remain equal throughout, the reaction can be treated as a simple second order reaction
`kt=(1)/([A])-(1)/([A]_(0))`
`(1)/([A])=kt+(1)/([A]_(0))`
`=(1.0xx10^(-2)"L mol"^(-1)s^(-1))xx(100s)+(1)/(0.100 "mol L"^(-1))=11 "L mol"^(-1)`
`:. [A]=(1)/(11)"mol L"^(-1)=0.091"mol L"^(-1)`
`=0.091 M`.