Question
Derive integrated rate equation for zero order reaction and also explain how the rate constant can be determine with help of graph.
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Answer
$\rightarrow$ "Zero order reaction means that the rate of the reaction is proportional to zero power of the concentration of reactants."
$\rightarrow$ Consider the reaction.
$R \rightarrow P$
$\rightarrow$ Rate of reaction for this reaction can be expressed as
Rate $=-\frac{ d [ R ]}{ dt }= k [ R ]^0$
$\rightarrow$ As any quantity raised to power zero is units.
Rate $=-\frac{ d [ R ]}{ dt }= k \text { X I }$
$\rightarrow$ Thus, the rate of zero order reaction is independent from concentration of reactants.
$d [ R ]=- k\ dt$
$\rightarrow$ Integrating both sides
$[ R ]=- kt + I ...Eq. (1)$
Where, $I$ is the constant of integration
$\rightarrow$ At $t=0$, the concentration of the reactant
$R=[ R ]_0$, where $[ R ]_0$ is initial concentration of the reactant.
$\rightarrow$ Substituting in equation $(1)$
${[ R ]_0=- kx 0+ I }$
${[ R ]_0= I }$
$\rightarrow$ Substituting the value of $I$ in the equation $(1)$
$[ R ]=- kt +[ R ]_0 ......Eq. (2)$
$\rightarrow$ Further simplifying equation $(2)$
$k =\frac{[ R ]_0-[ R ]}{ t } ...... Eq. (3)$
$\rightarrow$ Comparing equation $(2)$ with equation of straight line, $y=m x+c$, if we plot $[R]$ against $t$ , we get a straight line with slope $=- k$ and intercept equal to $[ R ]_0$
$\rightarrow$ Consider the reaction.
$R \rightarrow P$
$\rightarrow$ Rate of reaction for this reaction can be expressed as
Rate $=-\frac{ d [ R ]}{ dt }= k [ R ]^0$
$\rightarrow$ As any quantity raised to power zero is units.
Rate $=-\frac{ d [ R ]}{ dt }= k \text { X I }$
$\rightarrow$ Thus, the rate of zero order reaction is independent from concentration of reactants.
$d [ R ]=- k\ dt$
$\rightarrow$ Integrating both sides
$[ R ]=- kt + I ...Eq. (1)$
Where, $I$ is the constant of integration
$\rightarrow$ At $t=0$, the concentration of the reactant
$R=[ R ]_0$, where $[ R ]_0$ is initial concentration of the reactant.
$\rightarrow$ Substituting in equation $(1)$
${[ R ]_0=- kx 0+ I }$
${[ R ]_0= I }$
$\rightarrow$ Substituting the value of $I$ in the equation $(1)$
$[ R ]=- kt +[ R ]_0 ......Eq. (2)$
$\rightarrow$ Further simplifying equation $(2)$
$k =\frac{[ R ]_0-[ R ]}{ t } ...... Eq. (3)$
$\rightarrow$ Comparing equation $(2)$ with equation of straight line, $y=m x+c$, if we plot $[R]$ against $t$ , we get a straight line with slope $=- k$ and intercept equal to $[ R ]_0$
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