The reaction $2\mathrm{NO}\left(\mathrm{g}\right)+{\mathrm{O}}_2\left(\mathrm{g}\right)\rightleftharpoons 2{\mathrm{NO}}_2\left(\mathrm{g}\right)$ is of first order. If volume of reaction vessel is reduced to ⅓, the rate of reaction would be 

For following reaction, $2\mathrm{NO}\left(\mathrm{g}\right)+{\mathrm{O}}_2\left(\mathrm{g}\right)\to 2{\mathrm{NO}}_2\left(\mathrm{g}\right)$

When the volume of vessel change into $\frac{1}{3}$, then concentration of reactant become three times $(\because c\alpha \frac{1}{v})$

The rate of reaction for first order reaction $\propto$ concentration. 

So rate of reaction will increases three times.