As shown in this post, the freezing point of full-strength Muriatic Acid (31.45% Hydrochloric Acid) is -46.8 Celsius which is -52.2ºF so much colder than even the coldest winters in Maine.
Half-strength Muriatic Acid that is, say, 15-16% Hydrochloric Acid is 15.5 grams of HCl in 100 grams of solution so 100-15.5 = 84.5 grams of water. (15.5 g HCl / 36.46 g/mole HCl) / ((100-15.5) grams water / 1000 grams/kilogram) = 5.03 m. So, 5.03 m * (-1.86C/m) * 2 = -18.7 Celsius which is -1.7ºF so barely below freezing.
So this means that storing full-strength Muriatic Acid outdoor should be fine, but storing half-strength outdoors could freeze.
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