It has been found that for a chemical reaction with rise in temperature by 9K the rate constant gets doubled. Assuming a reaction to be occurring at 300 K, the value of activation energy is found to be________ kJ mol^-1. (in nearest integer)

(Given: In 10 = 2.3, R = 8.3 JK-1 mol^-1, log2 = 0.30)

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Payal Gupta | Contributor-Level 10

3 months ago

Initial temperature ; T₁ = 300 K

Final temperature ; T₂ = 309 K

Rate constant gets doubled i.e K₂ = 2K₁

$U s i n g l o g_{10} \frac{k_{2}}{k_{1}} = \frac{E a}{2.3 R} [\frac{T_{2} - T_{1}}{T_{1} T_{2}}]$

$l o g 2 = \frac{E a}{2.3 \times 8.3} [\frac{9}{300 \times 309}]$

$E_{a} = \frac{2.3 \times 8.3 \times 300 \times 309 \times l o g 2}{9} J / m o l$

$E_{a} = 58.98 k J / m o l$

Initial temperature ; T1 = 300 KFinal temperature ; T2 = 309 KRate constant gets doubled i.e K2 = 2K1 <math> <mrow> <mi>U</mi> <mi>s</mi> <mi>i</mi> <mi>n</mi> <mi>g</mi> <mo></mo> <mtext> </mtext> <mtext> </mtext> <mi>l</mi> <mi>o</mi> <msub> <mrow> <mi>g</mi> </mrow> <mrow> <mn>1</mn> <mn>0</mn> </mrow> </msub> <mfrac> <mrow> <msub> <mrow> <mi>k</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msub> </mrow> <mrow> <msub> <mrow> <mi>k</mi> </mrow> <mrow> <mn>1</mn> </mrow> </msub> </mrow> </mfrac> <mo>=</mo> <mfrac> <mrow> <mi>E</mi> <mi>a</mi> </mrow> <mrow> <mn>2</mn> <mo>.</mo> <mn>3</mn> <mi>R</mi> </mrow> </mfrac> <mrow> <mo> [</mo> <mrow> <mfrac> <mrow> <msub> <mrow> <mi>T</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msub> <mo>−</mo> <msub> <mrow> <mi>T</mi> </mrow> <mrow> <mn>1</mn> </mrow> </msub> </mrow> <mrow> <msub> <mrow> <mi>T</mi> </mrow> <mrow> <mn>1</mn> </mrow> </msub> <msub> <mrow> <mi>T</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msub> </mrow> </mfrac> </mrow> <mo>]</mo> </mrow> </mrow> </math> <math> <mrow> <mi>l</mi> <mi>o</mi> <mi>g</mi> <mn>2</mn> <mo>=</mo> <mfrac> <mrow> <mi>E</mi> <mi>a</mi> </mrow> <mrow> <mn>2</mn> <mo>.</mo> <mn>3</mn> <mo>×</mo> <mn>8</mn> <mo>.</mo> <mn>3</mn> </mrow> </mfrac> <mrow> <mo> [</mo> <mrow> <mfrac> <mrow> <mn>9</mn> </mrow> <mrow> <mn>3</mn> <mn>0</mn> <mn>0</mn> <mo>×</mo> <mn>3</mn> <mn>0</mn> <mn>9</mn> </mrow> </mfrac> </mrow> <mo>]</mo> </mrow> </mrow> </math> <math> <mrow> <msub> <mrow> <mi>E</mi> </mrow> <mrow> <mi>a</mi> </mrow> </msub> <mo>=</mo> <mfrac> <mrow> <mn>2</mn> <mo>.</mo> <mn>3</mn> <mo>×</mo> <mn>8</mn> <mo>.</mo> <mn>3</mn> <mo>×</mo> <mn>3</mn> <mn>0</mn> <mn>0</mn> <mo>×</mo> <mn>3</mn> <mn>0</mn> <mn>9</mn> <mo>×</mo> <mi>l</mi> <mi>o</mi> <mi>g</mi> <mn>2</mn> </mrow> <mrow> <mn>9</mn> </mrow> </mfrac> <mi>J</mi> <mo>/</mo> <mi>m</mi> <mi>o</mi> <mi mathvariant="script">l</mi> </mrow> </math> <math> <mrow> <msub> <mrow> <mi>E</mi> </mrow> <mrow> <mi>a</mi> </mrow> </msub> <mo>=</mo> <mn>5</mn> <mn>8</mn> <mo>.</mo> <mn>9</mn> <mn>8</mn> <mi>k</mi> <mi>J</mi> <mo>/</mo> <mi>m</mi> <mi>o</mi> <mi>l</mi> </mrow> </math>    <!- [if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_i1027" DrawAspect="Content" ObjectID="_1813568717"> </o:OLEObject></xml><! [endif]->         <!- [if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_i1028" DrawAspect="Content" ObjectID="_1813568718"> </o:OLEObject></xml><! [endif]->

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It has been found that for a chemical reaction with rise in temperature by 9K the rate constant gets doubled. Assuming a reaction to be occurring at 300 K, the value of activation energy is found to be________ kJ mol^-1. (in nearest integer)

(Given: In 10 = 2.3, R = 8.3 JK-1 mol^-1, log2 = 0.30)

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It has been found that for a chemical reaction with rise in temperature by 9K the rate constant gets doubled. Assuming a reaction to be occurring at 300 K, the value of activation energy is found to be________ kJ mol-1. (in nearest integer) (Given: In 10 = 2.3, R = 8.3 JK-1 mol-1, log2 = 0.30)

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It has been found that for a chemical reaction with rise in temperature by 9K the rate constant gets doubled. Assuming a reaction to be occurring at 300 K, the value of activation energy is found to be________ kJ mol^-1. (in nearest integer)

(Given: In 10 = 2.3, R = 8.3 JK-1 mol^-1, log2 = 0.30)