Urea nitrate is usually synthesized by the direct combination of urea and nitric acid. However I decided to use another method that avoids the use of expensive (for me anyway) nitric acid.
To a 200ml conical flask, I added 27g of potassium nitrate and 16ml of water. With a bit of warming, most of the potassium nitrate dissolved, giving a milky solution. I then added in a solution of 15.85g of recrystallized urea in 20ml of water. The resulting solution was cloudy, probably due to small amounts of undissolved urea and potassium nitrate in suspension. I stirred the mixture well, then added 30ml of 33% hydrochloric acid in portions with frequent stirring. This took a few minutes. With the first addition, a little bit of fizzing occurred, but after this, the mixture became clear and the later additions had no visible effect. Next I heated the mixture up until it began to steam but not bubble, then let it cool to room temperature.
I then chilled the mixture to 0 C and a large amount of crystalline urea nitrate precipitated. I filtered off the urea nitrate crystals, pressed them on the filter to expel as much liquid as possible, then dried them. I was left with 22.8g of urea nitrate as colourless-white crystals. This is a 70% yield.
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