what is the pH solution in which 15 mL of 0.10 M NaOH has been added to 25 mL of 0.10 M HCl
HCl + NaOH ==> NaCl + H2O
millimols NaOH = 15 x 0.1 = 1.5
mmols HCl = 25 x 0.1 = 2.5
Excess HCl = 2.5-1.5 = 1
(HCl) = (H^+) = 1 mmol/40 mL = ?
Convert to pH.
To find the pH of the solution, we can use the concept of neutralization. When a strong acid reacts with a strong base, they completely neutralize each other, resulting in a solution with a pH close to 7 (neutral pH).
Here's how you can find the pH:
Step 1: Determine the mole ratio between the acid (HCl) and the base (NaOH) based on their balanced equation.
The balanced equation for the reaction between HCl and NaOH is:
HCl + NaOH → NaCl + H2O
From the equation, we can see that one mole of HCl reacts with one mole of NaOH.
Step 2: Convert the volume of the solution to moles.
Given:
Volume of NaOH solution (VNaOH) = 15 mL = 0.015 L
Concentration of NaOH (CNaOH) = 0.10 M
Moles of NaOH = VNaOH × CNaOH
= 0.015 L × 0.10 M
= 0.0015 moles
Step 3: Determine the limiting reactant.
Since the mole ratio between HCl and NaOH is 1:1, the limiting reactant is the one with the lesser number of moles. In this case, both HCl and NaOH have the same number of moles, so neither is a limiting reactant.
Step 4: Calculate the resulting moles and concentration of each ion in the solution.
Since NaOH and HCl react in a 1:1 mole ratio, the resulting solution will have equal moles of Na+ and Cl- ions.
Moles of Na+ = 0.0015 moles
Moles of Cl- = 0.0015 moles
Using the volume of the solution, we can calculate their concentrations:
Volume of the resulting solution (Vresult) = VNaOH + VHCl = 0.015 L + 0.025 L = 0.04 L
Concentration of Na+ = Moles of Na+ / Vresult
= 0.0015 moles / 0.04 L
= 0.0375 M
Concentration of Cl- = Moles of Cl- / Vresult
= 0.0015 moles / 0.04 L
= 0.0375 M
Step 5: Find the pH of the resulting solution.
Since the initial solutions of HCl and NaOH are both at the same concentration of 0.10 M and they neutralize each other, the concentration of H+ ions in the resulting solution will be zero.
The concentration of OH- ions can be found from the concentration of Na+ ions, since one mole of NaOH produces one mole of OH-. Therefore, the concentration of OH- ions is also 0.0375 M.
Since the concentration of H+ ions is zero and the concentration of OH- ions is 0.0375 M, the solution is basic. The pH of a basic solution can be calculated using the pOH, which is given by the formula:
pOH = -log10(OH- concentration)
pOH = -log10(0.0375)
= 1.42
Since pH + pOH = 14 (for an aqueous solution at 25°C), we can find the pH using:
pH = 14 - pOH
= 14 - 1.42
= 12.58
Therefore, the pH of the resulting solution is approximately 12.58.