RCC Grade WC ratio and Min Cement

Reaction Rate

• Reaction rate refers to the change in reactant or product concentration over time.
• For a reaction $aA + bB \rightarrow cC + dD$, the rate can be expressed as: Rate $= -\frac{1}{a}\frac{d[A]}{dt} = -\frac{1}{b}\frac{d[B]}{dt} = \frac{1}{c}\frac{d[C]}{dt} = \frac{1}{d}\frac{d[D]}{dt}$.

Factors Affecting Reaction Rate

• Reactant concentration: Higher concentration usually leads to an increased reaction rate.
• Temperature: Higher temperatures generally increase the reaction rate.
• Surface area: For reactions involving solids, a larger surface area increases the reaction rate.
• Catalysts: Catalysts speed up the reaction rate without being used up in the reaction.
• Pressure: For gaseous reactions, higher pressure usually increases the reaction rate.

Rate Law

• Rate law expresses the relationship between the reaction rate and reactant concentrations.
• For a reaction $aA + bB \rightarrow cC + dD$, the rate law is Rate $= k[A]^m[B]^n$.
  • $k$ represents the rate constant.
  • $m$ and $n$ denote the reaction orders for reactants A and B, determined experimentally.
  • $m + n$ gives the overall reaction order.

Types of Rate Laws

• Zero-Order: Rate $= k$
• First-Order: Rate $= k[A]$
• Second-Order: Rate $= k[A]^2$ or Rate $= k[A][B]$

Methods for Determining Reaction Order

• Initial Rates Method: Reaction order is determined by varying reactant initial concentrations and measuring the initial reaction rate.
• Graphical Method: Reaction order is determined by plotting reactant concentration versus time, $\ln$[reactant] versus time, and 1/[reactant] versus time.
• Isolation Method: Keeping the concentration of all reactants except one in large excess helps determine the order with respect to one reactant.

Integrated Rate Laws

Zero-Order

• Rate $= -\frac{d[A]}{dt} = k$
• Integrated Rate Law: $[A]_t = -kt + [A]_0$
• Half-Life: $t_{1/2} = \frac{[A]_0}{2k}$

First-Order

• Rate $= -\frac{d[A]}{dt} = k[A]$
• Integrated Rate Law: $\ln[A]_t = -kt + \ln[A]_0$ or $[A]_t = [A]_0e^{-kt}$
• Half-Life: $t_{1/2} = \frac{0.693}{k}$

Second-Order

• Rate $= -\frac{d[A]}{dt} = k[A]^2$
• Integrated Rate Law: $\frac{1}{[A]_t} = kt + \frac{1}{[A]_0}$
• Half-Life: $t_{1/2} = \frac{1}{k[A]_0}$

Collision Theory

Postulates

• Reaction happens when reactant molecules collide.
• The collision must have sufficient energy to overcome the activation energy barrier.
• Molecules must collide with the proper orientation.

Activation Energy

• The minimum energy required for a reaction to occur is the Activation Energy ($E_a$).

Arrhenius Equation

Equation

• $k = Ae^{-E_a/RT}$
  • $k$ represents the rate constant.
  • $A$ is the frequency factor.
  • $E_a$ denotes the activation energy.
  • $R$ is the gas constant ($8.314 , \text{J/mol K}$).
  • $T$ is the temperature in Kelvin.

Determining $E_a$ Graphically

• $\ln k = -\frac{E_a}{R}\frac{1}{T} + \ln A$
• Plotting $\ln k$ versus $\frac{1}{T}$ results in a straight line.
  • Slope $= -\frac{E_a}{R}$
  • Intercept $= \ln A$

Reaction Mechanisms

Definition

• A reaction mechanism: a series of elementary steps describing the pathway of a reaction.

Elementary Step

• One single step in a reaction mechanism.

Rate-Determining Step

• The slowest step in a reaction mechanism that determines the overall reaction rate.

Catalyst

• A substance that increases reaction rate without being consumed.
  • Homogeneous Catalyst: Exists in the same phase as the reactants.
  • Heterogeneous Catalyst: Exists in a different phase than the reactants.

Intermediate

• A species is first produced and then consumed during the reaction, and is not present in the overall balanced equation.