What will be the final pH value if you mix 50ml HCl (aqueous solution, pH=0.5) and 40ml NaOH (aqueous solution, pH=12). Hint: convert pH value to concentration of acids/base, then consider the neutralization reaction, then find out the resulting pH value. Please show me your calculations.
To find the final pH value, we need to consider the neutralization reaction between HCl and NaOH.
First, let's convert the pH values to concentration of acids/base using the formula:
[H+] = 10^(-pH)
For HCl with pH = 0.5:
[HCl] = 10^(-0.5)
For NaOH with pH = 12:
[NaOH] = 10^(-12)
Next, let's calculate the concentrations of the acids/base:
[HCl] = 10^(-0.5) = 0.316 M
[NaOH] = 10^(-12) = 1 × 10^(-12) M
Now, we can determine the stoichiometry of the neutralization reaction:
HCl + NaOH -> NaCl + H2O
From the balanced equation, we can see that one mole of HCl reacts with one mole of NaOH to form one mole of NaCl and one mole of water. Therefore, the moles of HCl are equal to the moles of NaOH in the reaction.
Next, let's calculate the total volume of the solution:
Total volume = volume of HCl + volume of NaOH = 50 ml + 40 ml = 90 ml
To find the molar concentration (M) of the final solution, we divide the number of moles by the total volume in liters:
[HCl] = [NaOH] = (moles of HCl/total volume) = (moles of NaOH/total volume)
Let's calculate the moles of HCl:
moles of HCl = [HCl] × volume of HCl (in liters) = 0.316 M × 0.050 L = 0.0158 moles
Similarly, let's calculate the moles of NaOH:
moles of NaOH = [NaOH] × volume of NaOH (in liters) = 1 × 10^(-12) M × 0.040 L = 4 × 10^(-14) moles
Since the moles of HCl and NaOH are equal, we can use either value to calculate the final concentration:
[HCl] = [NaOH] = (moles of reactant/total volume) = (0.0158 moles/0.090 L) ≈ 0.176 M
Now, we can calculate the resulting pH value using the formula:
pH = -log10([H+])
pH = -log10(0.176) ≈ 0.754
Therefore, the final pH value will be approximately 0.754.