Concentration of Reactant and Reaction Rates

Differential Rate Expressions and Stoichiometric Relationships

• Definition and Structure of Reaction Rates:

  • The rate of a chemical reaction measures the change in concentration of a reactant or product over a given period of time.

  • For a generic reactant $A$, the differential rate expression is written as:     $\text{Rate} = -\frac{1}{a} \frac{\Delta [A]}{\Delta t}$

  • Components of the rate expression:

  • $\Delta [A]$ represents the change in concentration of the chosen reactant $A$.

  • $\Delta t$ represents the change in time over which the reaction is measured.

  • $a$ represents the balanced coefficient, also referred to as the stoichiometric factor, derived from the balanced chemical equation for the reaction being measured.

• Sign Conventions for Reactants and Products:

  • Reactants: Assigned a negative sign ($-$) out front in the rate expression to indicate that reactant concentration decreases over time as it is consumed.

  • Products: Assigned a positive sign ($+$) out front in the rate expression because product concentration increases over time as it is generated.

• Stoichiometric Rearrangements and Calculations:

  • Stoichiometric factors relate the rates of consumption and formation of different chemical species in a reaction.

  • Rate equations can be algebraically rearranged by moving coefficient terms across the equality sign.

  • When dealing with balanced coefficients such as $4$ and $2$, expressing the ratio as $\frac{4}{2}$ allows direct calculation, such as multiplying a rate value of $5.61$ by $2$ to solve for a related rate.

Reaction Kinetics and Determination of Reaction Orders

• Zero-Order Reaction Characteristics:

  • In a zero-order reaction, changing the initial reactant concentration does not alter the overall rate of reaction.

  • Whether the starting reactant concentration $[A]$ begins at $0.2$ or $0.4$, the reaction rate remains constant.

• Method of Initial Rates for Order Determination:

  • To determine an unknown reaction order exponent (such as $x$ or $y$), initial rate data from separate experimental trials are simplified and divided by each other.

  • Step-by-Step Procedure for Exponent Calculation:

  • Identify initial reactant concentrations across trials: trial 3 has a concentration of $0.1$, while trial 2 has a concentration of $0.05$

  • Divide the concentrations to find the concentration ratio:       $\frac{0.1}{0.05} = 2$

  • Divide the corresponding initial rates for the two trials, which simplifies to a rate ratio of $8$

  • Set up the relationship where the concentration ratio raised to the unknown exponent $y$ equals the rate ratio:       $2^y = 8$

  • Solve the exponential equation for the unknown exponent $y$:       $y = 3$

  • The general analytical workflow involves setting up the ratio of two rates, simplifying the numerical values, taking the concentration ratio raised to the power of the exponent, and solving for the target exponent $y$

Questions & Discussion

• Mathematical Manipulation of Stoichiometric Ratios:

  • Question: Is it acceptable to use a ratio of coefficients like $\frac{4}{2}$ directly and simply multiply a given rate of $5.61$ by $2$?

  • Answer: Yes, rearranging the differential rate expression by moving the stoichiometric coefficient of $4$ to the opposite side of the equation yields a mathematically equivalent result.