Question

For general reaction $X\to Y,$ the plot of concentration of X vs time is given in the figure. What is the order of the reaction and what is the units of rate constant.

• A.
  zero, $mol{L}^{-1}{s}^{-1}$
• B.
  First, $molL{s}^1$
• C.
  First, $s^{-1}$
• D.
  zero, $molLmol{s}^{-1}$

Answer 1

The correct option is A

zero, $mol{L}^{-1}{s}^{-1}$
For a zero order reaction, concentration versus time graph is a straight line with a negative slope.

Consider a zero ordeer reaction,

Rate, $R=K[A{]}^0-\frac{d\left[A\right]}{dt}=K[A{]}^0-\frac{d\left[A\right]}{dt}=K\times 1-d\left[A\right]=Kdt\text{Taking limit on both side}-{\int }_{|A{|}_0}^{|A{|}_t}d|A|=K{\int }_0^{t}dt$

When,
Time $=0,A=[A{]}_{0}time=t,A=[A{]}_t-[A{]}_{|A{|}_0}^{|A{|}_t}=K(t{)}_0^t[A{]}_0-[A{]}_t=Kt[A{]}_t=[A{]}_0-Kt\text{Its in y-= mx form.}$




Hence , Order of the given reaction is Zero Rate = Rate constant

$\frac{dx}{dt}unitsofK=mol{L}^{-1}{s}^1$