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 diluted
NaOH solution.
Answer in units of M

I didn't know what to do, so I just converted to moles for the first solution.

HCl + NaOH ==> NaCl + H2O

How many mols HCl used for the titration?
That's mols HCl = M x L = ?
How many mols for NaOH. That must be the same as mols HCl. So you have that many mols NaOH in 75 mL, and (NaOH) = mols/L = ?
All of that business about 350 mL, 6M, unknown amount of water added, etc etc is a red herring. You know the M and volume of the HCl, that gives you mols HCl, that must be the same as mols of the titrated NaOH, and that's what's in the 75 mL of the NaOH. It would have been interesting if the problem asked for the unknown amount of water added. In that case the 350 mL of 6 M would have been needed.

To determine the concentration of the diluted NaOH solution, we need to analyze the information provided step by step.

Step 1: Calculate the initial moles of NaOH in the 350 mL 6 M NaOH solution.
Molarity (M) is defined as moles of solute per liter of solution. Since we have the volume and concentration of the solution, we can calculate the moles of NaOH using the formula:

moles = volume (L) × concentration (M)

Given:
Volume = 350 mL = 350/1000 L = 0.35 L
Concentration = 6 M

Moles of NaOH in 350 mL solution = 0.35 L × 6 M = 2.1 moles NaOH

Step 2: Calculate the moles of NaOH in the 75 mL sample.
Since we know the volume and concentration of the initial solution, we can use the equation:

moles = volume (L) × concentration (M)

Given:
Volume = 75 mL = 75/1000 L = 0.075 L
Concentration = unknown (let's call it X M since that's what we are trying to find)

Moles of NaOH in 75 mL sample = 0.075 L × X M = 0.075X moles NaOH

Step 3: Use stoichiometry to relate the moles of NaOH and moles of HCl.
From the balanced equation:

NaOH + HCl → NaCl + H2O

we can see that the ratio of moles of NaOH to moles of HCl is 1:1. Therefore, the moles of NaOH in the 75 mL sample should be equal to the moles of HCl used for titration. We know that 52.5 mL of 6 M HCl was required for neutralization. Using the same logic as before:

Moles of HCl used for titration = 0.0525 L × 6 M = 0.315 moles HCl

Since the moles of NaOH and HCl are equal:

0.075X moles NaOH = 0.315 moles HCl

Step 4: Solve for the concentration of the diluted NaOH solution.
Rearranging the equation from the previous step:

X = (0.315 moles HCl) / (0.075 moles NaOH)

X = 4.2 M

Therefore, the concentration of the diluted NaOH solution is 4.2 M.

To solve this problem, you need to use the principles of stoichiometry and the concept of molarity. Let's break down the steps:

1. Start with the given information:
- Volume of the NaOH solution = 350 mL
- Concentration of the NaOH solution = 6 M
- Volume of the resulting solution = unknown
- Volume of the HCl used for titration = 52.5 mL
- Concentration of the HCl solution = 6 M

2. Convert the volume of NaOH solution to moles:
Moles = Volume (in liters) x Concentration
Volume of NaOH solution = 350 mL = 0.35 L
Moles of NaOH = 0.35 L x 6 mol/L = 2.1 moles

3. Since NaOH and HCl react in a 1:1 ratio, the moles of HCl used in titration are equal to the moles of NaOH in the sample solution.

4. Convert the volume of HCl used in titration to moles:
Moles of HCl = Volume (in liters) x Concentration
Volume of HCl used = 52.5 mL = 0.0525 L
Moles of HCl = 0.0525 L x 6 mol/L = 0.315 moles

5. Set up an equation based on the stoichiometry of the neutralization reaction:
Moles of NaOH = Moles of HCl

6. Solve for the volume of the diluted NaOH solution:
Since the moles of NaOH and HCl are equal, and the volume of the NaOH solution is unknown, we can write:
2.1 moles = Concentration x Volume of diluted NaOH solution (in liters)

Rearranging the equation, we have:
Volume of diluted NaOH solution (in liters) = 2.1 moles / Concentration

7. Convert the volume of diluted NaOH solution to milliliters:
The volume of the diluted NaOH solution is given in liters, but the answer needs to be in milliliters. Multiply the volume by 1000 to convert it:
Volume of diluted NaOH solution (in mL) = Volume (in L) x 1000

Now, you have all the information needed to calculate the concentration of the diluted NaOH solution.