JEE MAIN - Chemistry (2016 - 9th April Morning Slot - No. 15)
The reaction of ozone with oxygen atoms in the presence of chlorine atoms can occur
by a two step process shown below :
O3(g) + Cl$${^ \bullet }$$ (g) $$ \to $$ O2(g) + ClO$${^ \bullet }$$ (g) . . . . . .(i)
ki = 5.2 × 109 L mol−1 s−1
ClO$${^ \bullet }$$(g) + O$${^ \bullet }$$(g) $$ \to $$ O2(g) + Cl$${^ \bullet }$$ (g) . . . . . . (ii)
kii = 2.6 × 1010 L mol−1 s−1
The closest rate constant for the overall reaction O3(g) + O$${^ \bullet }$$ (g) $$ \to $$ 2 O2(g) is :
O3(g) + Cl$${^ \bullet }$$ (g) $$ \to $$ O2(g) + ClO$${^ \bullet }$$ (g) . . . . . .(i)
ki = 5.2 × 109 L mol−1 s−1
ClO$${^ \bullet }$$(g) + O$${^ \bullet }$$(g) $$ \to $$ O2(g) + Cl$${^ \bullet }$$ (g) . . . . . . (ii)
kii = 2.6 × 1010 L mol−1 s−1
The closest rate constant for the overall reaction O3(g) + O$${^ \bullet }$$ (g) $$ \to $$ 2 O2(g) is :
5.2 × 109 L mol−1 s−1
2.6 × 1010 L mol−1 s−1
3.1 × 1010 L mol−1 s−1
1.4 × 1020 L mol−1 s−1
Explanation
We have
$${O_3}(g) + C{l^ \bullet }(g) \to {O_2}(g) + Cl{O^ \bullet }(g)$$ ...... (1)
$$Cl{O^ \bullet }(g) + {O^ \bullet }(g) \to {O_2}(g) + C{l^ \bullet }(g)$$ ...... (2)
On adding Eq. (1) and Eq. (2), we get the required equation for overall reaction
$${O_3}(g) + {O^ \bullet }(g) \to 2{O_2}(g)$$
Therefore,
$${k_{overall}} = {k_1} \times {k_2}$$
$$ = 5.2 \times {10^9} \times 2.6 \times {10^{10}}$$
$$ = 1.4 \times {10^{20}}$$ L mol$$-$$1 s$$-$$1
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