Why is distilled water used to wash the conical flask during titration and why does adding water here not affect the titration results?

No, at least if it doesn't contain something he's titrating. Too much can influence the sudden change at the end point, so no indicator will 'see' it.

Updated July 21, 2017

By Serm Murmson

In a typical titration, you add a known quantity of a reagent called a titrant to an analyte. The analyte is a solution of unknown concentration. As you slowly add the titrant, you can monitor for signs that a reaction is taking place. Water is necessary to create the solutions in titrations. Additionally, if you add water to a solution, you change the concentration of the solution. You must incorporate these changes into your calculations.

Adding water to a titrant or analyte will change the concentration of that solution. Each solution has a molarity, which is equal to the number of moles of a solvent per liter of solution. When you add water to a solution, the number of moles of the solvent stays the same while the volume increases. Therefore, the molarity decreases; the solution is diluted.

When you add water to the analyte, you dilute a solution of unknown molarity. This dilution ultimately does not affect the experimental results. The concentration of the analyte is still unknown. As long as your volume measurements are accurate, you can calculate the moles of the unknown compound after the titration is complete.

When you add water to the titrant, you dilute a solution of known molarity. This is important to factor into your calculations at the end of the titration; you must know the number of moles of the titrant used in the titration. As long as you incorporate the added water into your calculations, your results should be accurate. Also, because you dilute the titrant, it will take a larger amount of titrant to cause a change in the analyte. Therefore, the entire titration process will take longer.

Most titrations depend on precise pH measurements. Water has pH of seven, which is neutral. When you add it to an acid or base, it dilutes that solution and brings the pH closer to seven. As long as you account for this dilution in your titration calculations, the addition of water should not cause errors in your results.

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Considering a direct titration:

You will probably use a volumetric pipette to pass the acid solution to the erlenmeyer used on the titration, so the volume of acid is known (the exactly volume of the pipette).

Any distilled water you add to this erlenmeyer will change its volume, but won't change the amount of substance of acid inside it, neither the initial volume you added of the acid solution. Sometimes it's even recommended that you add some water to make the color change more visible.

The objective of the titration is to find the volume of the base (of known concentration) necessary to neutralize the acid, and therefore, since you know the volume of acid added in the erlenmeyer (the pipette volume), calculate the concentration of the acid solution.

Water in the glass of the buret can cause variations in the concentration of the base being used, reason why we rinse it with the base, so we have a good precision titration. The erlenmeyer can be rinsed only with distilled water, since the volume of acid solution used for the calculation is constant.

You will have a equation that looks like this:

$$V(\text{base}) \cdot c(\text{base}) = V(\text{acid}) \cdot c(\text{acid}) \cdot f$$

Where $V(\text{base})$ is the volume of base consumed in the titration, $c(\text{base})$ is the concentration of the base (which is known), $V(\text{acid})$ is the volume of the solution of acid added to the erlenmeyer (the volume of the pipette), $c(\text{acid})$ is the estimated concentration of the acid and $f$ is the correction coefficient (so the real acid concentration is $c(\text{acid}) \cdot f$).