Consider the sugar–water phase diagram of Figure.
(a) How much sugar will dissolve in 1500 g water at 90(C (194(F)?
(b) If the saturated liquid solution in part (a) is cooled to 20(C (68(F), some of the sugar will precipitate out as a solid. What will be the composition of the saturated liquid solution (in wt% sugar) at 20(C?
(c) How much of the solid sugar will come out of solution upon cooling to20(C?
The Correct Answer and Explanation is :
To address the questions regarding the sugar-water phase diagram:
(a) How much sugar will dissolve in 1500 g of water at 90°C (194°F)?
At 90°C, the solubility limit of sugar in water is approximately 77 wt%. citeturn0search0
Using the formula for weight percent:
[ \text{Weight percent} = \frac{\text{Mass of solute}}{\text{Mass of solution}} \times 100 ]
Let the mass of sugar be ( m_{\text{sugar}} ). The mass of the solution is the sum of the mass of sugar and water:
[ \text{Mass of solution} = m_{\text{sugar}} + 1500\,\text{g} ]
Setting up the equation:
[ 77 = \frac{m_{\text{sugar}}}{m_{\text{sugar}} + 1500} \times 100 ]
Solving for ( m_{\text{sugar}} ):
[ m_{\text{sugar}} = 5022\,\text{g} ]
Therefore, 5022 grams of sugar will dissolve in 1500 grams of water at 90°C.
(b) What will be the composition of the saturated liquid solution (in wt% sugar) at 20°C?
At 20°C, the solubility limit of sugar in water is approximately 64 wt%. citeturn0search0
Using the same formula:
[ 64 = \frac{m’{\text{sugar}}}{m’{\text{sugar}} + 1500} \times 100 ]
Solving for ( m’_{\text{sugar}} ):
[ m’_{\text{sugar}} = 2667\,\text{g} ]
Therefore, the composition of the saturated liquid solution at 20°C is 64 wt% sugar.
(c) How much of the solid sugar will come out of solution upon cooling to 20°C?
The initial amount of sugar dissolved at 90°C is 5022 grams.
At 20°C, the maximum amount that can remain dissolved is 2667 grams.
The difference represents the amount of sugar that precipitates out:
[ 5022\,\text{g} – 2667\,\text{g} = 2355\,\text{g} ]
Therefore, 2355 grams of sugar will precipitate out upon cooling to 20°C.
Explanation:
The sugar-water phase diagram illustrates the solubility of sugar in water at various temperatures. As temperature increases, the solubility of sugar in water also increases, allowing more sugar to dissolve. Conversely, cooling the solution reduces the solubility, leading to the precipitation of excess sugar. By referencing the phase diagram, we can determine the maximum amount of sugar that can remain dissolved at a given temperature and calculate the amount that will precipitate upon cooling.
For a visual explanation, you might find the following video helpful:
videoHow to Determine the Solubility Limit Using Phase Diagramsturn0search8