Reaction: 𝒂𝑨 + 𝒃𝑩 + 𝒄𝑪 → 𝒅𝑫 + 𝒆𝑬
Expt 1: Vary [A] while keeping all other conditions the same.
Use Excel to determine the reaction with respect to A. (See
prelab background and Excel video for assistance in
understanding this calculation.) Save your Excel file!
Reaction order with respect to 𝐴: ______________

Time (s) [A], M
10 0.166
18 0.144
26 0.122
34 0.0998
42 0.0760
50 0.0523
58 0.0304

To determine the reaction order with respect to \( A \) using the given data, we need to analyze how the concentration of \( A \) changes over time and compare this with a reaction order model.

### Steps to Determine the Reaction Order with Respect to \( A \):

1. **Logarithmic Data Plotting**:
   - First, plot \( \ln[A] \) vs. time in Excel.
   - If the plot is linear, the reaction is **first order** with respect to \( A \).
   - If the plot of \( 1/[A] \) vs. time is linear, the reaction is **second order** with respect to \( A \).
   - If a plot of \( [A] \) vs. time is linear, the reaction is **zero order** with respect to \( A \).

2. **Calculate Necessary Data**:
   - Calculate \( \ln[A] \) and \( 1/[A] \) for each time point to check for linearity in different plots.
   - Use the given concentrations of \( A \) at different times and the time values to fill in the new columns.

3. **Create the Plots**:
   - Plot \( [A] \) vs. time.
   - Plot \( \ln[A] \) vs. time.
   - Plot \( 1/[A] \) vs. time.

4. **Determine the Linear Fit**:
   - The graph that produces the best linear fit (i.e., the highest \( R^2 \) value) will indicate the reaction order with respect to \( A \).

### Example Calculations:

For each time, we can compute:
- \( \ln[A] \) (natural logarithm of \( [A] \)).
- \( 1/[A] \) (reciprocal of \( [A] \)).

| Time (s) | [A] (M) | \( \ln[A] \) | \( 1/[A] \) |
|----------|---------|--------------|-------------|
| 10       | 0.166   | -1.796       | 6.024       |
| 18       | 0.144   | -1.937       | 6.944       |
| 26       | 0.122   | -2.104       | 8.197       |
| 34       | 0.0998  | -2.308       | 10.02       |
| 42       | 0.0760  | -2.576       | 13.16       |
| 50       | 0.0523  | -2.950       | 19.12       |
| 58       | 0.0304  | -3.492       | 32.89       |

### What to Do in Excel:
1. Enter the data for time and \( [A] \).
2. Create new columns for \( \ln[A] \) and \( 1/[A] \).
3. Plot:
   - \( [A] \) vs. time
   - \( \ln[A] \) vs. time
   - \( 1/[A] \) vs. time
4. Check which plot shows the best straight-line fit.
5. The slope of the linear plot will give you the rate constant \( k \) and the linearity (R² value) will confirm the order of the reaction with respect to \( A \).

### Expected Results:
- If the \( \ln[A] \) vs. time plot is linear, the reaction is **first order**.
- If the \( 1/[A] \) vs. time plot is linear, the reaction is **second order**.
- If \( [A] \) vs. time is linear, the reaction is **zero order**.

Would you like a more detailed explanation on using Excel or analyzing the results?

---

### Related Questions:
1. How can you calculate the rate constant \( k \) from a first-order reaction graph?
2. What role does the reaction order play in determining the half-life of a reactant?
3. How would you use a method of initial rates to determine reaction order with respect to other reactants?
4. What is the integrated rate law for second-order reactions?
5. How does temperature affect the reaction rate and reaction order?

**Tip**: Always compare the R² values from different graphs to determine which reaction order fits best.

Reaction: 𝒂𝑨 + 𝒃𝑩 + 𝒄𝑪 → 𝒅𝑫 + 𝒆𝑬
Expt 1: Vary [A] while keeping all other conditions the same.
Use Excel to determine the reaction with respect to A. (See prelab background and Excel video for assistance in understanding this calculation.) Save your Excel file!
Reaction order with respect to 𝐴: ______________

Time (s) [A], M
10 0.166
18 0.144
26 0.122
34 0.0998
42 0.0760
50 0.0523
58 0.0304

Learn how to determine the reaction order with respect to reactant A using Excel. Analyze time vs. concentration data to identify if the reaction follows zero, first, or second order. Includes logarithmic and inverse plotting techniques for kinetic studies.

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