Acids, such as those in vinegar, not only tenderize meat (just as in a marinade) and encourage the meat to release more delicious juices, but also encourages the breakdown of collagen into gelatin(1). Many recipes call for apple cider vinegar, particularly the Braggs brand with probiotics. Be mindful that if you use a ‘live’ vinegar such as an apple cider vinegar with the mother included, any probiotic benefit will be destroyed during the heat of cooking. You likely won’t be able to taste a few tablespoons of vinegar by the end of cooking, though a small number of supertasters can.
I tend to skip white vinegar, because I clean my bathroom with it – and don’t want that smell anywhere near my food! Consider the level of acidity as you choose your acid. You want an acid in at least the 5 to 6% acidity range. The percent acidity is listed on the label. Braggs apple cider vinegar is 5% acidity. I have a white wine vinegar that is 6% and a champagne vinegar at 7%. Pick a vinegar whose flavor you enjoy. Though many like to add wine to broth, wine only offers a 1% acidity.
Some like to add half a lemon with the rind included. The rind contains pectin, which adds to the body of your broth. Lemon juice has 7% acidity.
As long as you are cooking your bone broth for at least 24 hours, you don’t have to use any acidity to achieve a great broth, though.
(1)Krasnow, M., Bunch, T., Shoemaker, C. and Loss, C. R. (2012), Effects of Cooking Temperatures on the Physicochemical Properties and Consumer Acceptance of Chicken Stock. Journal of Food Science, 77: S19–S23.