5.2.7 Rate-Concentration Graphs

Rate-concentration graphs help determine the order of a reaction with respect to each reactant by plotting the reaction rate against the concentration of that reactant. Understanding these graphs is essential for deriving the rate equation and deducing reaction mechanisms.

Initial Rate Monitoring Method

Initial rate monitoring involves measuring the rate at the very start of the reaction when concentrations are known and remains nearly constant. The initial rate is typically determined by measuring a property that changes as the reaction progresses.

Examples include:

• Gas Production: Measured using a gas syringe to track the volume produced.
• Colour Change: Tracked using a colourimeter if a coloured reactant or product is involved.
• pH Change: Monitored with a pH meter if hydrogen ions ($H⁺$) or hydroxide ions ($OH⁻$) are produced or consumed.

Method to Determine Reaction Order Using Initial Rate

Step 1: Select a Reactant

• Choose one reactant whose concentration will be varied to determine its effect on the reaction rate. Step 2: Run Experiments at Different Concentrations

• Measure the change in a measurable property (e.g., gas volume, pH, or colour change) over time. Step 3: Plot a Concentration-Time Graph

• For each concentration, plot the measurable quantity against time. Step 4: Draw Tangents at $t = 0$

• For each concentration-time graph, draw a tangent at t = 0 and calculate its gradient, which represents the initial rate. Step 5: Plot Rate-Concentration Graph:

• Graph the initial rate of reaction against the concentration of the reactant varied.

• The resulting shape of this graph indicates the order of the reaction concerning the reactant.

Continuous Rate Monitoring Method

In continuous rate monitoring, the concentration of a reactant or product is tracked directly over time, without needing to measure just the initial rate.

Suitable methods include:

• Direct pH Measurement: When a reactant involves hydrogen or hydroxide ions, pH changes can be monitored continuously.
• colourimetric Measurement: When a reactant or product has a colour, a colourimeter and calibration curve can provide concentration data throughout the reaction.
• Titration of Samples: Reactant concentrations can also be measured by periodically quenching the reaction (e.g., by cooling or diluting) and titrating the reactant of interest.

Interpreting Rate-Concentration Graphs

The shape of a rate-concentration graph reveals the order of the reaction for a particular reactant:

• Zero Order: A horizontal line indicates a zero-order reaction concerning that reactant, meaning the rate does not change as concentration changes.
• First Order: A straight line through the origin shows a first-order reaction, where the rate is directly proportional to the concentration.
• Second Order: A curve with an increasing slope indicates a second-order reaction, where the rate is proportional to the square of the concentration.

Deriving the Rate Equation

Once the order of reaction with respect to each reactant is identified, the rate equation can be written as:

$$\text{Rate} = k[A]^m[B]^n$$

Where:

• k is the rate constant,
• $[A]$ and $[B]$ are the concentrations of the reactants,
• $m$ and $n$ are the orders of the reaction with respect to reactants $A$ and $B$, respectively.

Example: Iodine Clock Reaction

The iodine clock reaction is a well-known experiment used to determine the order of reaction with respect to iodide ions.

In this reaction, the iodide ($\text{I}^-$) ions react with peroxydisulfate ions ($\text{S}_2\text{O}_8^{2-}$), producing iodine ($\text{I}_2$), which forms a blue-black colour with starch, signalling the reaction's endpoint.

Steps to Determine Reaction Order

Step 1: Set Up the Reaction Mixtures

• Prepare several reaction mixtures with different concentrations of potassium iodide ($\text{KI}$) while keeping potassium peroxydisulfate ($\text{K}_2\text{S}_2\text{O}_8$) concentration constant.

• Add starch as an indicator. Step 2: Start the Reaction and Timer

• Combine the reactants, start a timer immediately, and note the time taken for the blue-black colour to appear, indicating the endpoint. Step 3: Calculate Initial Rate

• For each concentration of iodide, calculate the initial rate of reaction using the formula:

$$\text{Rate} = \frac{1}{\text{time taken for colour change}}$$

Step 4: Plot Rate-Concentration Graph

• Plot the initial rate against the concentration of iodide ions.

• The graph's shape indicates the order of reaction:

  • Zero Order: Horizontal line (rate is constant).
  • First Order: Straight line through the origin (rate ∝ $[ \text{I}^- ]$).
  • Second Order: Upward curve (rate ∝ $[ \text{I}^- ]^2$). Step 5: Derive the Rate Equation

• Using the order found from the graph, write the rate equation.

• For example, if first-order with respect to iodide:

$$\text{Rate} = k [ \text{I}^- ] [ \text{S}_2\text{O}_8^{2-} ]$$

Step 6: Calculate the Rate Constant $k$

• Rearrange the rate equation to solve for $k$, using your calculated rates and concentrations.

Key Points

• Temperature Control: Ensure constant temperature for accuracy.
• Consistent Mixing: Stir solutions well for reliable measurements. The iodine clock reaction, with its clear colour change, provides an accessible way to determine reaction order and understand reaction kinetics.