$\"\"$

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(a)

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The differential equation is $\"\"$ .

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Where $\"\"$ , $\"\"$ and $\"\"$ are the initial concentrations of hydrogen and bromine.

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Find $\"\"$ as a function of $\"\"$ in the case where $\"\"$ and $\"\"$ .

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Substitute $\"\"$ in $\"\"$ .

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$\"\"$

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$\"\"$

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Apply integration on each side.

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$\"\"$

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$\"\"$

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Let $\"\"$ , then $\"\"$ .

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$\"\"$

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Substitute $\"\"$ in the above equation.

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$\"\"$

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Since $\"\"$ , the value of $\"\"$ is zero.

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Substitute $\"\"$ and $\"\"$ in $\"\"$ .

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$\"\"$

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Substitute $\"\"$ in $\"\"$ .

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$\"\"$

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Therefore, $\"\"$ as a function of $\"\"$ is $\"\"$ .

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$\"\"$

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(b)

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The differential equation is $\"\"$ .

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$\"\"$

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$\"\"$

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Apply integration on each side.

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$\"\"$

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$\"\"$

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Let $\"\"$

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$\"\"$

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$\"\"$

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Substitute corresponding values in the above integral.

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$\"\"$

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$\"\"$

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Apply the formula $\"\"$ .

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$\"\"$

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Substitute $\"\"$ in the above equation.

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$\"\"$

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$\"\"$

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Find the constant $\"\"$ .

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Intially $\"\"$ .

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Substitute $\"\"$ and $\"\"$ in the above equation.

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$\"\"$

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Substitute $\"\"$ in $\"\"$ .

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$\"\"$

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$\"\"$

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(a) $\"\"$ as a function of $\"\"$ is $\"\"$ .

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(b) $\"\"$ .