Answer :
The concentration of AB, in mol/dm³, after 6 minutes : 0.125
Further explanation
For first-order reaction :
[tex]\tt [A]=[A]oe^{-kt}\rightarrow t1/2=\dfrac{ln~2}{k}[/tex]
The half-life of the reaction is 2 minutes⇒t1/2=2 minutes
The concentration of AB, in mol dm, after 6 minutes ⇒ t=6 minutes
The rate constant (k) :
[tex]\tt k=\dfrac{ln~2}{t1/2}=\dfrac{0.693}{2}=0.3465[/tex]
The concentration after 6 minutes :
[tex]\tt [A]o=0.1~mol/100~cm^3=1~~mol/dm^3\\\\(A]=1\times e^{-0.3465\times 6}\\\\(A]=0.125[/tex]