The answer is 9.99 μL
9.99 μL of HCL is to be added to the unbuffered solution to change the pH from 10.00 to 3.8
pH is the measure of acidity or basicity of the given solution due to presence of hydrogen and hydronium ions. As the solution is indicated as unbuffered the HCL added dissociates completely and increases the molarity of hydronium ions.
To calculate molarity of hydronium ions in the initial condition, pH=10.00
Initial hydronium ions= 10⁻¹⁰=1.0✕10--10 M
Final hydronium ions=10⁻3.8= 1.5✕10-4 M
Molarity is defined by the formula number moles divided by the volume of the solution, to find the number of moles of hydronium ions that multiply volume and molarity.
Initial moles of hydronium ions= 0.4✕1.0✕10--10 =4✕10--12 moles
Final moles of hydronium ions= 0.4✕1.5✕10-4 =6 x 10-5 moles
Change in hydronium ions=(6 x 10-5)-(4✕10--12 )= 5.99x10-5 moles
Volume of HCL required=5.99x10-5 ✕(1/6)= 9.99 μL
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