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0.0210\text{ }M\text{ }solution\text{ }of\text{ }{{N}_{2}}{{O}_{5}}\,is\text{ }allowed\text{ }to\text{ }decompose\text{ }at\text{ }43{}^\circ C.\text{ }How\text{ }long\text{ } will\text{ }it\text{ }take\text{ }to\text{ }reduce\text{ }to\text{ }0.0150M\text{ }?\text{ }\left( Given\text{ }k\text{ }=\text{ }6.0\text{ }\times \text{ }{{10}^{-4}}se{{c}^{-1}} \right)
Chemistry | Chemistry | MHTCET
0.0210\text{ }M\text{ }solution\text{ }of\text{ }{{N}_{2}}{{O}_{5}}\,is\text{ }allowed\text{ }to\text{ }decompose\text{ }at\text{ }43{}^\circ C.\text{ }How\text{ }long\text{ } will\text{ }it\text{ }take\text{ }to\text{ }reduce\text{ }to\text{ }0.0150M\text{ }?\text{ }\left( Given\text{ }k\text{ }=\text{ }6.0\text{ }\times \text{ }{{10}^{-4}}se{{c}^{-1}} \right)

 

  1. 5600 sec
  2. 360.0 sec
  3. 560.0 sec
  4.  3364 sec

Solution: 560 sec

Given:

{{[R]}_{0}}=0.0210\,M~

[R]=0.0150\,M~

k=6\times {{10}^{-4}}\,{{\sec }^{-1}}

For\text{ }a\text{ }first\text{ }order\text{ }reaction~

k=\frac{2.303}{t}log\frac{[R]{{}_{0}}}{[R]}

~\therefore ~\,t=\frac{2.303}{6\times {{10}^{-4}}}log\frac{0.0210}{0.0150}

t=3838.333\times \log \frac{7}{5}

t=3838.333\times 0.146

t=560\,\sec ~

i

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