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?

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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.