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The reaction $2X\to B$ is a zeroth order reaction. If the initial concentration of X is 0.2M, the half-life is 6h. When the initial concentration of X is 0.5M, the time required to reach its final concentration of 0.2M will be.
(A) 18.0 h
(B) 7.2 h
(C) 9.0 h
(D) 12.0 h


Answer
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Hint: Rate is defined as the speed at which a chemical reaction occurs. Rate is generally expressed in the terms of concentration of reactant which is consumed during the reaction in a unit of time or the concentration of product which is produced during the reaction in a unit of time. The order of the reaction is defined as the sum of the exponents of the terms expressing the concentration of the molecules or atoms in the expression of the rate of the reaction.

Complete step by step solution:
Given in the question:
Order of the reaction = zero
Reaction: $2X\to B$
Initial concentration of X i.e. ${{A}_{0}}$=0.2M
Half-life of X i.i t= 6h
For the zeroth order reaction, the formula to determine K is:
\[[{{A}_{0}}]-[{{A}_{1}}]=kt\]
Put the values in the above equation we get,
\[\begin{align}
  & 0.2-0.1=(k)(6) \\
 & k=\dfrac{1}{60}M/hr \\
\end{align}\]
Not it is given that
The initial concentration of X is 0.5M i.e. this will be ${{A}_{0}}$ this time
And we have to find the time required to reach its final concentration of 0.2M
Again using the same equation i.e.
\[[{{A}_{0}}]-[{{A}_{1}}]=kt\]
Put the values in the above equation we get,
\[0.5-0.2=(\dfrac{1}{60})(t)\]
The time required to reach its final concentration i.e. t = 18 h

Hence the correct answer is option (A) i.e. the time required to reach its final concentration is 18 h.

Note: If the reaction is a third order reaction, the unit for third order reaction is ${{M}^{-2}}h{{r}^{-1}}or\text{ mo}{{\text{l}}^{-2}}{{L}^{2}}h{{r}^{-1}}$. The negative and positive sign in the expression of the rate or reaction only means the change in concentration. A negative charge indicates that the concentration of the reactant is decreasing, similarly a positive charge means that the concentration of product is increasing.