How many moles of NaOH must be added to 1.00L of this solution to increase the PH to 9.25?

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To determine how many moles of NaOH must be added to the solution, we need to use the concept of pH and the dissociation of NaOH in water.

Step 1: Determine the concentration of OH- ions needed to achieve a pH of 9.25.
Since the solution is in water, we can use the equation: pH + pOH = 14.
pOH = 14 - pH = 14 - 9.25 = 4.75

Step 2: Convert pOH to OH- concentration.
pOH is defined as the negative logarithm (base 10) of the molar concentration of OH- ions.
We can use the formula: pOH = -log[OH-], where [OH-] is the concentration of OH- ions.
To find [OH-], we need to take the antilog of pOH.
[OH-] = 10^(-pOH) = 10^(-4.75)

Step 3: Determine the volume of the solution.
The given information states that the volume is 1.00 L.

Step 4: Calculate the moles of NaOH needed.
Since NaOH is a strong base, it completely dissociates in water.
The stoichiometry between NaOH and OH- is 1:1, meaning one mole of NaOH produces one mole of OH- ions.
To calculate the moles of NaOH, we can multiply the volume of the solution (in liters) by the concentration of OH- ions (in moles per liter).
Moles of NaOH = volume of solution (in liters) * [OH-] (in moles per liter)

Putting it all together:
Moles of NaOH = 1.00 L * 10^(-4.75)