### Rate of Reactions - **Definition:** Change in concentration of reactants or products per unit time. - For a general reaction $aA + bB \rightarrow cC + dD$: $$ \text{Rate} = -\frac{1}{a}\frac{\Delta[A]}{\Delta t} = -\frac{1}{b}\frac{\Delta[B]}{\Delta t} = \frac{1}{c}\frac{\Delta[C]}{\Delta t} = \frac{1}{d}\frac{\Delta[D]}{\Delta t} $$ - **Units:** Usually mol L$^{-1}$ s$^{-1}$ or M s$^{-1}$. - **Types of Rates:** - **Average Rate:** Calculated over a time interval. - **Instantaneous Rate:** Rate at a specific point in time, determined by the slope of the tangent to the concentration vs. time curve. - **Initial Rate:** Instantaneous rate at $t=0$. ### Rate Law - **Definition:** An equation that relates the rate of reaction to the concentrations of reactants. - For a reaction $A + B \rightarrow Products$, the general rate law is: $$ \text{Rate} = k[A]^x[B]^y $$ - **Rate Constant ($k$):** Proportionality constant in the rate law. Its value depends on temperature and the specific reaction. - **Reaction Order:** - $x$ is the order with respect to reactant A. - $y$ is the order with respect to reactant B. - **Overall Reaction Order:** $x + y$. - **Determination:** Reaction orders ($x$ and $y$) **must be determined experimentally**; they are generally not related to the stoichiometric coefficients ($a$ and $b$) unless the reaction is elementary. ### Rate Constant ($k$) - **Definition:** The proportionality constant in the rate law. - **Factors Affecting $k$:** - **Temperature:** $k$ increases with temperature (Arrhenius equation). - **Activation Energy:** Lower activation energy leads to a larger $k$. - **Presence of Catalyst:** Catalysts increase $k$ by providing an alternative reaction pathway with lower activation energy. - **Units of $k$:** Depend on the overall reaction order. - **Zero Order (Rate = $k$):** mol L$^{-1}$ s$^{-1}$ (or M s$^{-1}$) - **First Order (Rate = $k[A]$):** s$^{-1}$ - **Second Order (Rate = $k[A]^2$ or $k[A][B]$):** L mol$^{-1}$ s$^{-1}$ (or M$^{-1}$ s$^{-1}$) - **General Units for $n^{th}$ order:** (concentration)$^{1-n}$ time$^{-1}$
