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Using oxalic acid dihydrate as a primary standard just seems really odd to me. I'd expect a primary standard to be oven dried. It just seems weird that a hydrate would be used.

Granted, I saw numerous references to using oxalic acid dihydrate on the web to standardize $ce{NaOH}$. I assume that for high school and freshman labs that it is "good enough." Using student grade burettes and open air pan balances would greatly limit the possible precision.

Also I'd guess that "good enough purity" oxalic acid dihydrate can be purchased much more cheaply than potassium hydrogen phthalate (KHP), which would be my choice.

The analytical method as I remember from nearly 50 years ago...

Prepare a concentrated stock solution (4 molar?) of $ce{NaOH}$ using distilled water. That went in a jug with a spout just above the bottom. It was capped with a dedicator tube filled with $ce{NaOH}$ to absorb $ce{CO2}$ from the atmosphere. It sat for a couple of days to allow sodium carbonate to settle out. ($ce{NaOH}$ will have some carbonate.)

Dried KHP in an oven at $pu{120 ^{circ}C}$ for four hours and then put that in a desiccator to cool.

Boiled distilled water to remove dissolved $ce{CO2}$ and stoppered that to cool.

Using the cooled boiled distilled water made an approximately $pu{0.1 M}$ solution of $ce{NaOH}$ by diluting the concentrated stock solution.

Using an analytical balance, weigh out 3 samples of KHP to nearest $pu{0.0001 g}$ into flasks and carefully dissolved the KHP in the cooled boiled distilled water with swirling to minimize introducing bubbles into the solution.

Then using $ce{NaOH}$ as the titrant, phenolphthalein was used as the indicator. Again careful to swirl solution, not shake, to prevent bubbles.

Using class 1 50-mL burette which was marked to $pu{0.1 mL}$s but read to $pu{0.01 mL}$.

At first glance, use of oxalic acid dihydrate ($ce{H2C2O4.2H2O}$ or simply OADH) as a primary standard seems really odd to anybody including me (although I'm not a analytical chemist). I'd also expect a primary standard to be oven dried and cool it in desiccator before use as we all did in our college analytical lab using potassium hydrogen phthalate (KHP). Yet, there is a good reason why these chemist use OADH continuously.

When it comes to be a good primary standard, Low hygroscopicity is one of the features in consideration, in order to minimize weight changes due to humidity. Oxalic acid dihydrate (OADH) and potassium hydrogen phthalate (KHP) are the most accessible acids for standardization, because of their low cost and their hardly changing content per a unit (of measurement). Specifically, OADH in the crystalline solid state, represents an interesting species that is still producing many surprises since 1920s. Although there are two extra water molecules in OADH (thich is hard to loose), the alternating acid and these water molecules act both as hydrogen-bond donors and acceptors [Ref.1]. The conclusion of that reference states that:

The trends both in the metric and electronic parameters exhibited by the model clusters with increasing the number of participating oxalic acid and water molecules (Figure 1) shows clearly that the cooperative effect is the major factor in the shortening of H-bonds. This is particularly well pronounced in the optimized $R_{ce{O··O}}$ of the carboxylic hydroxyl group bonded to the water molecules. One of the most eloquent steps in the reduction of $R_{ce{O··O}}$ is between the hydrated single molecule and the circular model consisting of two acid and two water molecules, indicating that it is the circular motif that primarily supports cooperativity. However, both the polarization evoked by the hydration of the carbonyl groups as well as the crystal field effect also contribute notably to the shortening.

This strong H-bonding make it so stable that two water molecule won't loose in ambient conditions. That's a good reason to use it as a primary standard.

Reference:

1. J. Stare, D. Hadži, “Cooperativity Assisted Shortening of Hydrogen Bonds in Crystalline Oxalic Acid Dihydrate: DFT and NBO Model Studies,” J. Chem. Theory Comput. 2014, 10(4), 1817–1823 (DOI: 10.1021/ct500167n).

Jander-Blasius (14. Ed., 1995) uses nonhygroscopic sodium oxalate, dried at 230-250°C (it decomposes above 250 according to wikipedia), to standardise permanganate titer solution against. They give no other recommended standard for manganometry, so I assume this is it.

I have no idea why anybody would want to use (or recommend using) the free acid instead, except perhaps to insult his first-year students' intelligence. Can't imagine it's much cheaper, in analytical grade.

For NaOH titer solution, Jander recommends using a secondary standard, e.g. HCl solution. HCl itself is standardised against freshly precipitated and dried sodium carbonate, or HgO ($ce{+ 4 KI + H2O -> K2[HgI4] + 2 KOH}$) dried over conc. sulfuric acid.