Certainly! Let's go through the detailed calculations step-by-step, based on the given data.
### Step-by-Step Solution:
1. Determine Total Volume of the Reaction Mixture:
- Volume of iodide solution: [tex]\( 10.0 \, \text{mL} \)[/tex]
- Volume of thiosulfate solution: [tex]\( 1.0 \, \text{mL} \)[/tex]
- Volume of DI water: [tex]\( 2.5 \, \text{mL} \)[/tex]
- Volume of hydrogen peroxide solution: [tex]\( 7.5 \, \text{mL} \)[/tex]
Adding these together gives:
[tex]\[
\text{Total Volume} = 10.0 \, \text{mL} + 1.0 \, \text{mL} + 2.5 \, \text{mL} + 7.5 \, \text{mL} = 21.0 \, \text{mL}
\][/tex]
2. Calculate Molarity of Iodide in the Final Mixture:
- Initial concentration of iodide solution: [tex]\( 47.6 \, \text{mM} \)[/tex]
- Volume of iodide solution used: [tex]\( 10.0 \, \text{mL} \)[/tex]
The molarity in the final mixture can be calculated as:
[tex]\[
\text{Molarity}_{\text{iodide}} = \frac{(47.6 \, \text{mM} \times 10.0 \, \text{mL})}{21.0 \, \text{mL}} = 22.67 \, \text{mM}
\][/tex]
3. Calculate Molarity of Thiosulfate in the Final Mixture:
- Initial concentration of thiosulfate solution: [tex]\( 1.5 \, \text{mM} \)[/tex]
- Volume of thiosulfate solution used: [tex]\( 1.0 \, \text{mL} \)[/tex]
The molarity in the final mixture can be calculated as:
[tex]\[
\text{Molarity}_{\text{thiosulfate}} = \frac{(1.5 \, \text{mM} \times 1.0 \, \text{mL})}{21.0 \, \text{mL}} = 0.071 \, \text{mM}
\][/tex]
4. Calculate Molarity of Hydrogen Peroxide in the Final Mixture:
- Initial concentration of hydrogen peroxide solution: [tex]\( 63 \, \text{mM} \)[/tex]
- Volume of hydrogen peroxide solution used: [tex]\( 7.5 \, \text{mL} \)[/tex]
The molarity in the final mixture can be calculated as:
[tex]\[
\text{Molarity}_{\text{hydrogen peroxide}} = \frac{(63 \, \text{mM} \times 7.5 \, \text{mL})}{21.0 \, \text{mL}} = 22.5 \, \text{mM}
\][/tex]
5. Calculate the Initial Rate of the Reaction:
- Molarity of hydrogen peroxide in the final mixture: [tex]\( 22.5 \, \text{mM} \)[/tex]
- Time: [tex]\( 17.7 \, \text{s} \)[/tex]
The initial rate is calculated as:
[tex]\[
\text{Initial Rate} = \frac{\text{Molarity of Hydrogen Peroxide}}{\text{Time}} = \frac{22.5 \, \text{mM}}{17.7 \, \text{s}} = 1.271 \, \text{mM/s}
\][/tex]
### Summary of Calculations:
- Total Volume of the reaction mixture: [tex]\( 21.0 \, \text{mL} \)[/tex]
- Final Molarity of Iodide: [tex]\( 22.67 \, \text{mM} \)[/tex]
- Final Molarity of Thiosulfate: [tex]\( 0.071 \, \text{mM} \)[/tex]
- Final Molarity of Hydrogen Peroxide: [tex]\( 22.5 \, \text{mM} \)[/tex]
- Initial Reaction Rate: [tex]\( 1.271 \, \text{mM/s} \)[/tex]
These detailed calculations provide a comprehensive understanding of the concentrations and initial reaction rate for the given chemical reaction.
