Problem: From the following data for the first-order gas-phase isomerization of CH3 NC at 215 oC, calculate the first-order rate constant and half-life for the reaction:Time  (s) Pressure CH3NC (torr)050220003355000180800095.51200041.71500022.4

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A first order reaction is a reaction whose rate depends linearly on the concentration of only one reactant.

For a hypothetical reaction: A → B

The rate law is written as:


<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mo mathvariant="italic">&#xA0;</mo><mo mathvariant="italic">=</mo><mo mathvariant="italic">&#xA0;</mo><mi>k</mi><mfenced open="[" close="]"><mi mathvariant="italic">A</mi></mfenced><mspace linebreak="newline"></mspace><mi>w</mi><mi>h</mi><mi>e</mi><mi>r</mi><mi>e</mi><mo mathvariant="italic">,</mo><mo mathvariant="italic">&#xA0;</mo><mi>k</mi><mo mathvariant="italic">&#xA0;</mo><mo mathvariant="italic">=</mo><mo mathvariant="italic">&#xA0;</mo><mi>f</mi><mi>i</mi><mi>r</mi><mi>s</mi><mi>t</mi><mo mathvariant="italic">-</mo><mi>o</mi><mi>r</mi><mi>d</mi><mi>e</mi><mi>r</mi><mo mathvariant="italic">&#xA0;</mo><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mo mathvariant="italic">&#xA0;</mo><mi>c</mi><mi>o</mi><mi>n</mi><mi>s</mi><mi>t</mi><mi>a</mi><mi>n</mi><mi>t</mi><mspace linebreak="newline"></mspace><mfenced open="[" close="]"><mi mathvariant="italic">A</mi></mfenced><mo mathvariant="italic">&#xA0;</mo><mo mathvariant="italic">=</mo><mo mathvariant="italic">&#xA0;</mo><mi>c</mi><mi>o</mi><mi>n</mi><mi>c</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mo mathvariant="italic">&#xA0;</mo><mi>o</mi><mi>f</mi><mo mathvariant="italic">&#xA0;</mo><mi>r</mi><mi>e</mi><mi>a</mi><mi>c</mi><mi>t</mi><mi>a</mi><mi>n</mi><mi>t</mi><mo mathvariant="italic">&#xA0;</mo><mi>A</mi></math>


We will be needing the integrated rate law for a first-order reaction. The integrated rate law is:


<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ln</mi><msub><mfenced open="[" close="]"><mi>A</mi></mfenced><mi>t</mi></msub><mo>&#xA0;</mo><mo>=</mo><mo>&#xA0;</mo><mo>-</mo><mi>k</mi><mi>t</mi><mo>&#xA0;</mo><mo>+</mo><mo>&#xA0;</mo><mi>ln</mi><msub><mfenced open="[" close="]"><mi>A</mi></mfenced><mn>0</mn></msub><mspace linebreak="newline"></mspace><msub><mfenced open="[" close="]"><mi>A</mi></mfenced><mi>t</mi></msub><mo>&#xA0;</mo><mo>=</mo><mo>&#xA0;</mo><mi>c</mi><mi>o</mi><mi>n</mi><mi>c</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mo>&#xA0;</mo><mi>a</mi><mi>t</mi><mo>&#xA0;</mo><mi>t</mi><mi>i</mi><mi>m</mi><mi>e</mi><mo>&#xA0;</mo><mo>&quot;</mo><mi>t</mi><mo>&quot;</mo><mspace linebreak="newline"></mspace><msub><mfenced open="[" close="]"><mi>A</mi></mfenced><mn>0</mn></msub><mo>&#xA0;</mo><mo>=</mo><mo>&#xA0;</mo><mi>i</mi><mi>n</mi><mi>i</mi><mi>t</mi><mi>i</mi><mi>a</mi><mi>l</mi><mo>&#xA0;</mo><mi>c</mi><mi>o</mi><mi>n</mi><mi>c</mi><mi>e</mi><mi>n</mi><mi>t</mi><mi>r</mi><mi>a</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi></math>


Since we have been given a pressure of CH3NC, we will use the pressure values in our integrated rate law. We will also see how the units of k are derived.


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Problem Details

From the following data for the first-order gas-phase isomerization of CH3 NC at 215 oC, calculate the first-order rate constant and half-life for the reaction:



Time  (sPressure CH3NC (torr)
0502
2000335
5000180
800095.5
1200041.7
1500022.4


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