# The Science of Sweet Tea

Sweet tea is a popular beverage in the South, but Yankees and Communists seem to be content dropping some sugar into cold, iced tea and calling that sweet tea. Newsflash: adding sugar to cold tea does not make it sweet tea! If you have ever made sweetened iced tea, you will have taken advantage of the characteristics of a supersaturated solution.  By adding sugar to hot tea, you were able to dissolve much more sugar into the water than you would have been able to dissolve into cold tea.  When the tea cooled, the additional sugar remained dissolved in the tea as a supersaturated solution.  If you tried to add more sugar to the cooled tea, however, the excess solute would drop out of solution and the tea would become less sweet.

A solution is a homogeneous mixture (a mixture that is the same throughout) of two or more substances. The two types of substances making up a solution are called a solute and a solvent. The substance being dissolved (separated into parts and spread throughout) is called the solute, and the substance doing the dissolving is called the solvent. A solution can exist in any state of matter. The substance present in the smaller amount is usually considered the solute. Solutions in which water is the solvent are called aqueous solutions and are the most common kind of solutions.

The strength of a solution is referred to as its concentration (the amount of solute in a specific amount of solvent). The more solute that is dissolved in a solvent, the greater the concentration of the solution. For example, in a glass of water, the more instant tea added to the water, the greater the concentration of tea in the solution. A glass of tea with a small amount of tea in it is said to be dilute (has a low concentration) in comparison to the more concentrated solution with more tea. If the solute has a color, the darker the color, the more concentrated the solution.

There is a limit to the amount of solute that will dissolve in a given amount of solvent. For example, when you add sugar to a glass of iced tea, it is a waste to keep adding the sugar once it starts settling to the bottom of the glass. No matter how much you stir, the extra sugar will not dissolve. When no more sugar will dissolve in the tea, a saturated solution is produced. A saturated solution is one in which the maximum amount of solute is dissolved in a solvent at a given temperature (a measure of how hot or cold a material is). When less than the maximum amount of solute is dissolved, the mixture is called an unsaturated solution.

What effects do temperature and pressure have on the amount of solute needed to prepare a saturated solution? Why is it that (sugar + tea) != sweet tea? First, let us look at a sample problem.

Given: 4 g sugar cube ($C_{12} H_{22} O_{11}$) is dissolved in a 350 ml teacup of 80 °C water. Density of water at 80° = 0.975 g/ml. Density of water at 20° = 1.000 g/ml. Solubility of sucrose @ 20° C is 179 g/ 100 mL, @ 100° is 487 g/ 100 mL.

Step 1 – Determine number of moles of sucrose in 4 g

Solute is 4 g of $C_{12} H_{22} O_{11}$

$C_{12} H_{22} O_{11}$ = (12)(12) + (1)(22) + (16)(11)
$C_{12} H_{22} O_{11}$ = 144 + 22+ 176
$C_{12} H_{22} O_{11}$ = 342 g/mol
divide this amount into the size of the sample
$4 g /(342 g/mol) = 0.0117 mol$

Step 2 – Determine mass of solvent in kg.

density = mass/volume
mass = density x volume
mass = 0.975 g/ml x 350 ml
mass = 341.25 g
mass = 0.341 kg

Step 3 – Determine molality of the sugar solution.

$molality = mol_{solute}/ m_{solvent}$

$molality_{80c} = 0.0117 mol/ 0.341 kg = 0.034 kg$

$molality_{80c} = 0.0117 mol/ 0.500 kg = 0.033 kg$

Sugar has a solubility in water of 2000g / L @ 25°.

 Temperature,degrees C. Grams of sucrose in 100 grams of solution, or per cent Grams of sucrose dissolved by 100 grams of water Specific gravity of solution 0 64.18 179.2 1.31490 5 64.87 184.7 1.31920 10 65.58 190.5 1.32353 15 66.30 197.0 1.32804 20 67.09 203.9 1.33272 25 67.89 211.4 1.33768 30 68.70 219.5 1.34273 35 69.55 228.4 1.34805 40 70.42 238.1 1.35353 45 71.32 248.7 1.35923 50 72.25 260.4 1.36515 55 73.20 273.1 1.37124 60 74.18 287.3 1.37755 65 75.18 302.9 1.38404 70 76.22 320.5 1.39083 75 77.27 339.9 1.39772 80 78.36 362.1 1.40493 85 79.46 386.8 1.41225 90 80.61 415.7 1.41996 95 81.77 448.6 1.42778 100 82.87 487.2 1.43594

Based on the chart above, twice as much sucrose would be dissolved in water at 85C (the brewing temperature of most teas) as compared to the temperature of ice water, just above 0C.