Experiments Show That If the Chemical Reaction $\mathrm { N } _ { 2 } \mathrm { O } _ { 5 } \rightarrow 2 \mathrm { NO } _ { 2 } + \frac { 1 } { 2 } \mathrm { O } _ { 2 }$

Experiments show that if the chemical reaction $\mathrm { N } _ { 2 } \mathrm { O } _ { 5 } \rightarrow 2 \mathrm { NO } _ { 2 } + \frac { 1 } { 2 } \mathrm { O } _ { 2 }$ takes place at $45 ^ { \circ } \mathrm { C }$ , the rate of reaction of dinitrogen pentoxide is proportional to its concentration as follows : $- \frac { d \left[ \mathrm {~N} _ { 2 } \mathrm { O } _ { 5 } \right] } { d t } = 0.0007 \left[ \mathrm {~N} _ { 2 } \mathrm { O } _ { 5 } \right]$ How long will the reaction take to reduce the concentration of $\mathrm { N } _ { 2 } \mathrm { O } _ { 5 }$ to 50% of its original value?

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