Answer
See the answer below.
Work Step by Step
a) For second-order reactions:
$1/C-1/C_0=kt$
$1/0.100\ M-1/0.250\ M=k\times 1.76\ min$
$k=3.41\ L/mol.min$
b) In the first case $r=-\Delta [NO_2]/\Delta t$, now $r'=\Delta[O_2]/\Delta t=-1/2\dot{}\Delta [NO_2]/\Delta t=1/2\dot{}r$
So the new constant is $k'=1/2\dot{}k$
