Derive integrated rate equation for rate constant of a zero order reaction
Answers
We know that the rate law is the expression in which reaction rate is given in terms of molar concentration of reactants with each term raised to some power, which may or may not be equal to the stoichiometric coefficient of the reacting species in a balanced chemical equation.
Consider a general reaction, aA + bB → cC + dD where a, b, c, d are the stoichiometric coefficients of the reactants and products. Therefore, the rate law for this reaction is,
Rate ∝ [A]x [B]y
where x and y may or may not be equal to the stoichiometric coefficients of the reactants. Therefore, the rate of the reaction is equal to k [A]x [B]y, where k is the rate constant.
∴ -d[R]/dt = k [A]x [B]y
Order of Reaction
Order of a reaction is the sum of the powers of the concentrations of the reactants in the rate law expression. In the above general reaction, x and y are the powers. The sum of them will give the order of the reaction. Order of a reaction can be 0, 1, 2, 3 and even a fraction. A zero-order reaction means that the rate of the reaction is independent of the concentration of reactants.
Zero Order Reaction
So we already know that in a zero order reaction, the rate is independent of the concentration of the reactants. Thus, it means the sum of the powers of concentrations is zero. It can only be zero when the all the powers are zero. Consider a reaction, R → P. Therefore, the rate law of this reaction is,
Rate ∝ [R]0
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integrated rate equation for rate constant of a zero order reaction
