To determine the pH of a solution obtained by mixing an acid and a base, we can use the concept of neutralization and the equation for calculating pH.
Step 1: Determine moles of the acid and the base.
First, we need to calculate the number of moles of HCl and NaOH used. We can use the formula:
Moles = Concentration (M) x Volume (L)
For HCl:
Moles of HCl = 0.250 M x 0.025 L = 0.00625 moles
For NaOH:
Moles of NaOH = 0.125 M x 0.025 L = 0.003125 moles
Step 2: Identify the limiting reactant.
To determine the pH, we need to find which reactant is limiting. The limiting reactant is the one that is completely consumed and determines the amount of product formed. In this case, we have an equal volume of HCl and NaOH, so whichever has the lower amount of moles is the limiting reactant.
Comparing the moles, we see that NaOH has the lower amount: 0.003125 moles. Therefore, NaOH is the limiting reactant.
Step 3: Determine the excess reactant.
Since NaOH is the limiting reactant, HCl is in excess. The excess HCl will remain after the reaction is complete.
Step 4: Determine the amount of excess reactant remaining.
To calculate the amount of excess HCl remaining, we subtract the amount of HCl reacted with NaOH from the initial amount of HCl used:
Excess HCl remaining = Initial moles of HCl - moles of HCl reacted
= 0.00625 moles - 0.003125 moles
= 0.003125 moles
Step 5: Calculate the concentration of the resulting solution.
To find the concentration of the resulting solution, we divide the moles of the limiting reactant (NaOH) by the volume of the resulting solution (Total volume of HCl + NaOH):
Concentration of resulting solution = Moles of limiting reactant / Total volume (L)
The total volume is 25.00 ml + 25.00 ml = 0.050 L
Concentration of resulting solution = 0.003125 moles / 0.050 L
= 0.0625 M
Step 6: Calculate the pOH.
The pOH is calculated using the equation:
pOH = -log10(OH-) concentration
Since NaOH is a strong base, it completely dissociates in water molecules. Therefore, for every 1 mole of NaOH, we have 1 mole of OH- ions.
Concentration of OH- ions in the resulting solution is 0.0625 M.
pOH = -log10(0.0625)
= 1.204
Step 7: Calculate the pH.
pH is calculated using the formula:
pH = 14 - pOH
pH = 14 - 1.204
= 12.796
So, the pH of the resulting solution obtained by mixing 25.00 ml of 0.250 M HCl and 25.00 ml of 0.125 M NaOH is approximately 12.796.