For the reaction system: 2NO(g) + O2(g) ? 2NO2(g) volume is suddenly reduce to half its value by increas- ing the pressure on it. If the reaction is of first order with respect to O2 and second order with respect to NO, the rate of reaction will

2NO(g) + O2(g) …............> 2NO2(g)
ratewe is given as: r=k[NO]^x * [O2]^y
where rate with respect to No=x(=2,given)
and with O2, it is=y(=1,given)
Rate of reaction is given as overall sum of the order with ndividual components,
so orderof reaction=x+y=1+2=3
so r=k[NO]²* [O2]
After decreasing the volume, the concentration of the species will increase in same proportion
r’=k{2*[NO]}² *2*[O2]=r*8
so it will be inceased by 8 times of the previous rate.