The rate constant for a first order reaction is given by the following equation Ink = 33.24 - $\frac{2.0\times 10^{4}K}{T}$  

The activation energy for the reaction is given by ___________kJ mol^-1 (In nearest integer) (Given: R = 8.3JK^-1mol^-1)

<p>According to Arrhenius equation ;</p><p><span contenteditable="false"> <math> <mrow> <mi>I</mi> <mi>n</mi> <mi>k</mi> <mo>=</mo> <mi>l</mi> <mi>n</mi> <mi>A</mi> <mo>−</mo> <mfrac> <mrow> <mi>E</mi> <mi>a</mi> </mrow> <mrow> <mi>R</mi> <mi>T</mi> </mrow> </mfrac> </mrow> </math> </span> &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&lt;!- [if gte mso 9]>&lt;xml&gt; <o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_i1025" DrawAspect="Content" ObjectID="_1815380885"> </o:OLEObject>&lt;/xml&gt;&lt;! [endif]-&gt;&nbsp;</p><p>Here lnk = 33.24&nbsp;<span contenteditable="false"> <math> <mrow> <mo>−</mo> <mfrac> <mrow> <mn>2</mn> <mo>.</mo> <mn>0</mn> <mo>×</mo> <mn>1</mn> <msup> <mrow> <mn>0</mn> </mrow> <mrow> <mn>4</mn> </mrow> </msup> </mrow> <mrow> <mi>T</mi> </mrow> </mfrac> </mrow> </math> </span>&lt;!- [if gte mso 9]>&lt;xml&gt; <o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_i1026" DrawAspect="Content" ObjectID="_1815380886"> </o:OLEObject>&lt;/xml&gt;&lt;! [endif]-&gt;&nbsp;</p><p><span contenteditable="false"> <math> <mrow> <mo>∴</mo> <mfrac> <mrow> <mi>E</mi> <mi>a</mi> </mrow> <mrow> <mi>R</mi> </mrow> </mfrac> <mo>=</mo> <mn>2</mn> <mo>.</mo> <mn>0</mn> <mo>×</mo> <mn>1</mn> <msup> <mrow> <mn>0</mn> </mrow> <mrow> <mn>4</mn> </mrow> </msup> </mrow> </math> </span> &nbsp; &nbsp;&lt;!- [if gte mso 9]>&lt;xml&gt; <o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_i1027" DrawAspect="Content" ObjectID="_1815380887"> </o:OLEObject>&lt;/xml&gt;&lt;! [endif]-&gt;&nbsp;</p><p><span contenteditable="false"> <math> <mrow> <mi>a</mi> <mi>n</mi> <mi>d</mi> <mtext> </mtext> <mtext> </mtext> <msub> <mrow> <mi>E</mi> </mrow> <mrow> <mi>a</mi> </mrow> </msub> <mo>=</mo> <mn>2</mn> <mo>.</mo> <mn>0</mn> <mo>×</mo> <mn>1</mn> <msup> <mrow> <mn>0</mn> </mrow> <mrow> <mn>4</mn> </mrow> </msup> <mo>×</mo> <mi>R</mi> <mo>=</mo> <mn>2</mn> <mo>.</mo> <mn>0</mn> <mo>×</mo> <mn>1</mn> <msup> <mrow> <mn>0</mn> </mrow> <mrow> <mn>4</mn> </mrow> </msup> <mo>×</mo> <mn>8</mn> <mo>.</mo> <mn>3</mn> <mo>=</mo> <mn>1</mn> <mn>6</mn> <mo>.</mo> <mn>6</mn> <mo>×</mo> <mn>1</mn> <msup> <mrow> <mn>0</mn> </mrow> <mrow> <mn>4</mn> </mrow> </msup> <mi>J</mi> <mo>=</mo> <mn>1</mn> <mn>6</mn> <mn>6</mn> <mi>k</mi> <mi>J</mi> </mrow> </math> </span> &nbsp; &nbsp; &lt;!- [if gte mso 9]>&lt;xml&gt; <o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_i1028" DrawAspect="Content" ObjectID="_1815380888"> </o:OLEObject>&lt;/xml&gt;&lt;! [endif]-&gt;&nbsp;</p>

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