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## Q. 1.8

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.

## 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