This givesformula_36Thus it is found that a sucrose solution is inverted once at least formula_37 of the sucrose has been hydrolyzed into glucose and fructose. Holding a sucrose solution at temperatures of hydrolyzes no more than about 85% of its sucrose. Finding formula_1 when r = 0.85 shows that the optical rotation of the solution after hydrolysis is done is –12.7° this reaction is said to invert the sugar because its final optical rotation is less than zero. A polarimeter can be used to figure out when the inversion is done by detecting whether the optical rotation of the solution at an earlier time in its hydrolysis reaction equals –12.7°. Common sugar can be inverted quickly by mixing sugar and citric acid or cream of tartar at a ratio of about 1000:1 by weight and adding water. If lemon juice which is about five percent citric acid by weight is used instead then the ratio becomes 50:1. Such a mixture, heated to  and added to another food, prevents crystallization without tasting sour. Inverted sugar syrup can be made without acids or enzymes by heating it up alone: two parts granulated sugar and one part water, simmered for five to seven minutes, will be partly inverted. Commercially prepared enzyme-catalyzed solutions are inverted at . The optimum pH for inversion is 5.0. Invertase is added at a rate of about 0.15% of the syrup's weight, and inversion time will be about 8 hours. When completed the syrup temperature is raised to inactivate the invertase, but the syrup is concentrated in a vacuum evaporator to preserve color. Commercially prepared hydrochloric-acid catalyzed solutions may be inverted at the relatively low temperature of . The optimum pH for acid-catalyzed inversion is 2.15. As the inversion temperature is increased, the inversion time decreases. They are neutralized when the desired level of inversion is reached. In confectionery and candy making, cream of tartar is commonly used as the acidulant, with typical amounts in the range of 0.15-0.25% of the sugar's weight. The use of cream of tartar imparts a honey-like flavor to the syrup. After the inversion is completed, it may be neutralized with baking soda using a weight of 45% of the cream of tartar's weight. The amount of water can be increased to increase the time it takes to reach the desired final temperature, and increasing the time increases the amount of inversion that occurs.