An unknown amount of water is mixed with
350 mL of a 6 M solution of NaOH solution.
A 75 mL sample of the resulting solution is
titrated to neutrality with 52.5 mL of 6 M
HCl. Calculate the concentration of the di-
luted NaOH solution.
Answer in units of M
M x mL = M x mL
M x 75 = 6 x 52.5
Solve for M.
To find the concentration of the diluted NaOH solution, we can use the concept of moles and the principle of conservation of moles. Here's how you can solve the problem step by step:
1. Determine the number of moles of HCl used in the titration.
- HCl is a strong acid and reacts with NaOH in a 1:1 ratio.
- Given that the concentration of HCl is 6 M and the volume used is 52.5 mL, we can calculate the moles of HCl:
Moles of HCl = concentration of HCl * volume of HCl (in liters)
= 6 M * 0.0525 L
= 0.315 moles of HCl
2. Calculate the number of moles of NaOH that reacted with HCl.
- Using the balanced chemical equation for the reaction of NaOH and HCl (1:1 ratio), we know that the number of moles of NaOH reacted is also 0.315 moles.
3. Determine the number of moles of NaOH in the 75 mL sample.
- Given that the sample obtained is 75 mL, we can calculate the moles of NaOH:
Moles of NaOH = Moles of HCl (or NaOH) reacted / Volume of the sample (in liters)
= 0.315 moles / 0.075 L
= 4.2 moles of NaOH
4. Find the total number of moles of NaOH in the original solution.
- Since the diluted NaOH solution was mixed with an unknown amount of water, the number of moles of NaOH remains the same after dilution.
- Therefore, the 75 mL sample contains the same number of moles as the original solution.
5. Calculate the initial volume of the NaOH solution.
- Assume the initial volume of the NaOH solution (V_initial) is unknown.
- The final volume of the solution after dilution (V_final) is given as 350 mL + V_initial.
- Based on the principle of conservation of moles, we can set up the equation:
Moles_initial = Moles_final
Concentration_initial * V_initial = Concentration_sample * (V_final - V_sample)
6 M * V_initial = 4.2 moles * (350 mL + V_initial - 75 mL)
6. Solve the equation for V_initial.
- Distribute and solve for V_initial:
6V_initial = 4.2 * (275 mL + V_initial)
6V_initial = 1155 + 4.2V_initial
1.8V_initial = 1155
V_initial = 642.5 mL
7. Calculate the concentration of the diluted NaOH solution.
- The concentration of the NaOH solution is given by the total number of moles of NaOH divided by the final volume of the solution:
Concentration_initial = Moles_initial / V_initial
= 4.2 moles / 0.6425 L
= 6.53 M
Therefore, the concentration of the diluted NaOH solution is 6.53 M.