A first order reaction has a rate constant $$1.15 \times {10^{ - 3}}\,{s^{ - 1}}.$$   How long will $$5\,g$$  of this reactant take to reduce to $$3\,g?$$

Solution :
$$\eqalign{ & t = \frac{{2.303}}{k}\log \frac{{\left[ {{R_0}} \right]}}{{\left[ R \right]}} \cr & \,\,\, = \frac{{2.303}}{{1.15 \times {{10}^{ - 3}}}}\log \frac{5}{3} \cr & \,\,\, = 2.00 \times {10^3}\,\log \,1.667 \cr & \,\,\, = 2 \times {10^3} \times 0.2219 \cr & \,\,\, = 444\,s \cr} $$