Integrated rate equations and half-life (zero and first order)
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See all →- If the rate constant of a reaction is 0.03 s^-1, how much time does it take for 7.2 mol L^-1 concentration of the reactant to get reduced to 0.9 mol L^-1?(Given: log 2 = 0.301) Answer: 1. 69.3 s Key idea: the unit mathrms⁻¹ means first order: t=2.303/klog[A]₀/[A] . 7.2/0.9=8 , log8=3×0.301=0.903 . t=2.303×0.903/0.03... 1
- If the half-life (t_1/2) for a first order reaction is 1 minute, then the time required for 99.9% completion of the reaction is closest to : Answer: 4. 10 minutes Key idea: first order: k=frac0.693t_(1/2) and t=2.303/kloga/a-x . k=0.693\ mathrmmin⁻¹ . 99.9% complete: a/a-x=1000 ,... 1
- For a first order reaction A → Products, initial concentration of A is 0.1 M, which becomes 0.001 M after 5 minutes. Rate constant for the reaction in min^-1 is Answer: 3. 0.9212 Key idea: for a first order reaction k=2.303/tlog[A]₀/[A] . k=2.303/5log0.1/0.001=2.303/5×2=0.9212\ mathrmmin⁻¹ . 1
- The given graph is a representation of kinetics of a reaction.[Graph: y versus x at constant temperature T]The y and x axes for zero and first order reactions, respectively are Answer: 4. zero order ( y = rate and x = concentration), first order ( y = t_(1/2) and x = concenration) Key idea: a horizontal line means y... 1
- The rate constant for a first order reaction is 4.606×10^-3 s^-1. The time required to reduce 2.0 g of the reactant to 0.2 g is : Answer: 3. 500 s For a first-order reaction t=2.303/klog[A]₀/[A] . t=frac2.3034.606×10⁻³log2.0/0.2=frac2.3034.606×10⁻³×1=500\ s Answer: opti... 1
- If the rate constant for a first order reaction is k, the time (t) required for the completion of 99% of the reaction is given by : Answer: 3. t = 4.606/k For a first order reaction t = 2.303/klog[A]₀/[A] . When 99% is complete, [A] = 0.01[A]₀ , so t = 2.303/klog 100 = 2.... 1