JEE MAIN - Chemistry (2010 - No. 18)
The time for half life period of a certain reaction A $$\to$$ products is 1 hour. When the initial
concentration of the reactant ‘A’, is 2.0 mol L–1, how much time does it take for its concentration to
come from 0.50 to 0.25 mol L–1 if it is a zero order reaction ?
4 h
0.5 h
0.25 h
1 h
Explanation
For the reaction
$$A\,\, \to \,\,$$ Product ; given $${t_{1/2}} = 1\,\,$$ hour
for a zero order reaction
$${t_{completion}}\,\, = {{\left[ {{A_0}} \right]} \over k} = {{initial\,\,conc.} \over {rate\,\,cons\tan t}}$$
$$\therefore$$ $$\,\,\,\,\,{t_{1/2}} = {{\left[ {{A_0}} \right]} \over {2K}}$$
or $$\,\,\,\,\,k = {{\left[ {{A_0}} \right]} \over {2{t_{1/2}}}} = {2 \over {2 \times 1}} = 1\,\,mol\,li{t^{ - 1}}\,h{r^{ - 1}}$$
Further for a zero order reaction
$$k = {{dx} \over {dt}} = {{change\,\,\,in\,\,\,concentration} \over {time}}$$
$$I = {{0.50 - 0.25} \over {time}}\,\,\,$$
$$\therefore$$ $$\,\,\,\,\,$$ time $$ = 0.25\,\,hr.$$
$$A\,\, \to \,\,$$ Product ; given $${t_{1/2}} = 1\,\,$$ hour
for a zero order reaction
$${t_{completion}}\,\, = {{\left[ {{A_0}} \right]} \over k} = {{initial\,\,conc.} \over {rate\,\,cons\tan t}}$$
$$\therefore$$ $$\,\,\,\,\,{t_{1/2}} = {{\left[ {{A_0}} \right]} \over {2K}}$$
or $$\,\,\,\,\,k = {{\left[ {{A_0}} \right]} \over {2{t_{1/2}}}} = {2 \over {2 \times 1}} = 1\,\,mol\,li{t^{ - 1}}\,h{r^{ - 1}}$$
Further for a zero order reaction
$$k = {{dx} \over {dt}} = {{change\,\,\,in\,\,\,concentration} \over {time}}$$
$$I = {{0.50 - 0.25} \over {time}}\,\,\,$$
$$\therefore$$ $$\,\,\,\,\,$$ time $$ = 0.25\,\,hr.$$