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Chapter 1

Q. 1.8

GRADED

Sucrose is the chemical name for the sugar we consume. Its solubility at 20°C is 204 g/100 g water, and at 100°C is 487 g/100 g water. A solution is prepared by mixing 139 g of sugar in 33.0 g of water at 100°C.
ⓐ What is the minimum amount of water required to dissolve the sugar at 100°C?
ⓑ What is the maximum amount of sugar that can be dissolved in the water at 100°C?
ⓒ The solution is cooled to 20°C. How much sugar (if any) will crystallize out?
ⓓ How much more water is required to dissolve all the sugar at 20°C?

ANALYSIS
sucrose solubility at 100°C (487 g/100 g water)
composition of solution: sucrose (139 g), water (33.0 g)
Information given:
minimum amount of H_{2}O to dissolve 139 g sucrose at 100°C Asked for:

STRATEGY

Relate the mass H_{2}O required to the mass sucrose to be dissolved at 100°C by using the solubility at 100°C as a conversion factor.

ANALYSIS
sucrose solubility at 100°C (487 g/100 g water)
composition of solution: sucrose (139 g), water (33.0 g)
Information given:
maximum amount of sucrose that can be dissolved in 33.0 g H2O at 100°C Asked for:

STRATEGY

Relate the mass of H_{2}O required to the mass of sucrose to be dissolved at 100°C by using the solubility at 100°C as a conversion factor.

ANALYSIS
sucrose solubility at 20°C (204 g/100 g water)
composition of solution: sucrose (139 g), water (33.0 g)
Information given:
mass of sucrose in the solution that will not dissolve at 20°C Asked for:

STRATEGY

1. The question really is: How much sucrose will dissolve in 33.0 g water at 20°C? Relate the mass of sucrose that can be dissolved by 33.0 g H_{2}O at 20°C by using the solubility at 20°C as a conversion factor.
2. Take the difference between the calculated amount that can be dissolved and the amount of sucrose that was in solution at 100°C.

ANALYSIS
sucrose solubility at 20°C (204 g/100 g water)
composition of solution: sucrose (139 g), water (33.0 g)
Information given:
amount of additional water required to dissolve all the sucrose Asked for:

STRATEGY

1. Relate the mass H_{2}O required to the mass sucrose (139 g) to be dissolved at 20°C by using the solubility at 20°C as a conversion factor.
2. Take the difference between the amount of water required and the amount of water already in solution. That is how much more water has to be added.

Step-by-Step

Verified Solution

139 g sucrose × \frac{100  g  H_{2}O}{487  g  sucrose} = 28.5 g H_{2}O mass H_{2}O required

33.0 g H_{2}O × \frac{487  g  sucrose}{100  g  H_{2}O} = 161 g sucrose mass  sucrose

33.0 g H_{2}O × \frac{204  g  sucrose}{100  g  H_{2}O} = 67.3 g sucrose will dissolve at 20°C. 1. mass sucrose
139 g in solution − 67.3 g can be dissolved = 72 g undissolved 2. undissolved sucrose

139 g sucrose × \frac{100  g  H_{2}O}{204  g  sucrose} = 68.1 g H_{2}O 1. mass water required
(68.1 g H_{2}O needed) – (33.0 g already in solution) = 35.1 g 2. water to be added