​In a typical experiment, 15 mL of an aqueous solution containing an unknown quantity of acetylcholine had a pH of 7.65. When the solution is incubated with acetylcholinesterase, the pH of the solution decreased to 6.87. Assuming that there was no buffer in the reaction mixture, determine the number of moles of acetylcholine in the 15 mL solution.​

Correct option is A

The correct option is (a)

EXPLANATION-

Step 1: Understand pH and [H⁺] relationship
pH is defined as:

​$$pH = -\log{[H^+]}$$

where  [H⁺]   is the concentration of hydrogen ions in moles per liter (M).

Using this formula, we calculate the initial and final hydrogen ion concentrations.

​​Step 2: Calculate initial  [H⁺]  concentration

 Given initial pH = 7.65

                            $$[H^+]_{\text{initial}} = 10^{-7.65}$$

Using a calculator

                        $$[H^+]_{\text{initial}} = 2.24 \times 10^{-8} \text{ M}$$

Step 3: Calculate final [H⁺]  concentration
Given final pH = 6.87​​

                         $$[H^{+}]_{\text{final}} = 10^{-6.87}$$

Using a calculator

                         $$[H^{+}]_{\text{final}} = 1.35 \times 10^{-7} \text{ M}$$

Step 4: Calculate the change in [H⁺] ​

​$$\Delta [H^+] = [H^+]_{\text{final}} - [H^+]_{\text{initial}}$$  $$= 1.35 \times 10^{-7} - 2.24 \times 10^{-8} = 1.13 \times 10^{-7} \, \text{M}$$

This increase in hydrogen ion concentration corresponds to the number of moles of acetylcholine hydrolyzed.
Step 5: Calculate the number of moles of acetylcholine in 15 mL
Convert 15 mL to liters:

                    $$15 \text{ mL} = 0.015 \text{ L}$$

Number of moles of  [H⁺]  (or acetylcholine hydrolyzed) in solution:

$$n = \Delta [H^+] \times \text{Volume (L)}$$$$=1.13 \times 10^{-7} \times 0.015 = 1.695 \times 10^{-9} \text{ mol}$$

Step 6: Compare with options
The calculated value $$1.695 \times 10^{-9}$$mol lies between

                  $$1.65 \times 10^{-9} \text{ mol to } 1.75 \times 10^{-9} \text{ mol}$$​​
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