Acid base titration problem. Need Help

[ddluu]

How many moles of H3O+ must be added to one liter of a solution to adjust the pH from 7.17 to 5.85?

Correct answer 1.34E-6 (1.34 * 10-6)

The correct answer is given, however I would like to know how to do this problem.

 

[Astronuc]

See definition of pH - http://www.chembuddy.com/?left=pH-calculation&right=pH-definition

The pH is related to the molar concentration.

pH = 7.17 yields a molar concentration of 10^-7.17 = 6.76 x 10^-8 M, or moles/liter

Now try to find the number of moles in one liter for pH = 5.85.

Take the difference which gives the number of moles of H⁺ or H₃O⁺ one needs to add to one liter.

 

[Blueshift5]

To solve this problem, we need to use the formula for pH: pH = -log[H3O+]. We know that the initial pH is 7.17 and the final pH is 5.85, so we can set up the equation:

7.17 = -log[H3O+] and 5.85 = -log[x]

Where x represents the unknown moles of H3O+ that need to be added.

To solve for x, we can rearrange the equations to isolate for [H3O+]:

[H3O+] = 10^-pH

Substituting the values for pH, we get:

[H3O+] = 10^-7.17 = 1.34 * 10^-7 moles/L

And

[H3O+] = 10^-5.85 = 1.34 * 10^-6 moles/L

Since we want to know the difference in moles between the two solutions, we can subtract the two values:

1.34 * 10^-6 - 1.34 * 10^-7 = 1.34 * 10^-6 moles

Therefore, 1.34 * 10^-6 moles of H3O+ must be added to one liter of the solution to adjust the pH from 7.17 to 5.85.