In this experiment NaOH is standardized to titrate it with vinegar so thtat the percent by mass of the acetic acid can be determined.

How does dissolved CO2 in distilled water affect the accuracy of the determination of a NaOH solution's concentration? How is the term acid anhydride applied here?

Is the answer that the added CO2 reacts with NaOH to form Na2CO3 when titrated and the NaOH and the Na2CO3 is also titrated, so there is no difference?

Or is there a difference? high determination of a NaOH solution's concentration? low? How does the CO2 affect the determination of a NaOH solution's concentration?

You can find other answers to the CO2 question and some analytical chemists don't agree with this but I think it may or may not make a difference. When CO2 reacts with NaOH it forms Na2CO3.

CO2 + 2NaOH ==> Na2CO3 + H2O. For every mole CO2 added we form 1 mol Na2CO3 and use up 2 mols NaOH. No one disagrees on that step. I think that when titrating the NaOH, IF we use methyl red as an indicator we titrate CO3^2- all the way (meaning CO3^2- + 2H^+ ==> H2CO3 ==> CO2 + H2O). In this way all of the CO3^2- formed by the reaction with 2NaOH is titrated so there is no difference in the M NaOH this way vs no dissolved CO2. If, however, we use phenolphthalein as an indicator, only one of H is added (H^+ + CO3^2- ==> HCO3^-) and there IS a difference. Less HCl is used in the titration step which makes mols NaOH present less than it should be which makes M NaOH too low. When standardizing NaOH I ALWAYS use methyl red or another appropriate indicator to avoid this problem.

The presence of dissolved carbon dioxide (CO2) in distilled water can indeed affect the accuracy of determining the concentration of a NaOH solution. When CO2 dissolves in water, it forms carbonic acid (H2CO3) through the following reaction: CO2 + H2O ↔ H2CO3.

During the titration process, the NaOH solution is added to the vinegar, which contains acetic acid (CH3COOH). If there is dissolved CO2 in the distilled water used to prepare the NaOH solution, it will react with NaOH to form sodium carbonate (Na2CO3) according to the following reaction: 2NaOH + CO2 → Na2CO3 + H2O.

This reaction between NaOH and CO2 uses up some of the NaOH that would otherwise be available for reacting with the acetic acid in the vinegar. Consequently, the amount of NaOH required to neutralize the acetic acid will be underestimated, leading to a lower determination of the NaOH solution's concentration.

Regarding the term "acid anhydride," it is not directly applicable in this experiment. Acid anhydrides are compounds that are formed by removing a water molecule from a pair of carboxylic acids. In the context of the titration between NaOH and acetic acid, acetic acid itself is not an acid anhydride. However, the reaction with CO2 can indirectly affect the accuracy of determining the NaOH concentration by reducing the amount of NaOH available for reacting with the acetic acid.

In summary, the presence of dissolved CO2 in distilled water can lead to a lower determination of a NaOH solution's concentration when titrated with vinegar. This is because the CO2 reacts with NaOH, forming sodium carbonate, and thereby reducing the available NaOH for neutralizing the acetic acid.