a saturated solution of sucrose and 1,000.0 G of boiling water is cold to 20° C is what mass of rock candy will be formed?
To determine the mass of rock candy that will be formed when a saturated solution of sucrose and 1,000.0 g of boiling water is cooled to 20°C, we need to know the solubility of sucrose in water at both boiling point (100°C) and 20°C.
According to the temperature dependence of sucrose solubility, the solubility of sucrose in water is approximately:
- 2000 g/L (or 2 g/mL) at 100°C (boiling point)
- 210 g/L (or 0.21 g/mL) at 20°C
Initially, the boiling water (1000 g) is capable of dissolving a maximum of (2 g/mL * 1,000 mL) = 2,000 g of sucrose.
After cooling to 20°C, the solution can only hold (0.21 g/mL * 1,000 mL) = 210 g of sucrose.
So, when the solution cools down, (2,000 g - 210 g) = 1,790 g of sucrose will crystallize out of the solution as rock candy.
To determine the mass of rock candy that will be formed, we need to calculate the amount of sucrose that can be dissolved in the given amount of boiling water at 100°C, and then determine the mass of sucrose that crystallizes out as the saturated solution cools to 20°C.
1. Calculate the amount of sucrose that can be dissolved in 1,000.0 g of boiling water at 100°C using solubility data. According to solubility tables, the solubility of sucrose in water at 100°C is approximately 2,000 g/L.
So, the maximum amount of sucrose that can be dissolved in 1,000.0 g of boiling water is:
2,000 g/L * (1,000.0 g / 1,000 mL) = 2,000 g
2. Determine the amount of sucrose that crystallizes out as the solution cools to 20°C. We know that the solution is saturated at 100°C, meaning it contains the maximum solute (sucrose) that can be dissolved at that temperature. As the solution cools down to 20°C, some of the sucrose will crystallize out.
To calculate the mass of sucrose that crystallizes out, we need to find the difference between the amount of solute present at 100°C and the solubility of sucrose in water at 20°C. At 20°C, the solubility of sucrose is approximately 200 g/L.
The total amount of sucrose that will crystallize out is:
2,000 g - (200 g/L * (1,000.0 g/1,000 mL)) = 2,000 g - (200 g) = 1,800 g
Therefore, a mass of 1,800 grams of rock candy will be formed as the saturated solution cools from 100°C to 20°C.
To determine the mass of rock candy that will be formed in this situation, we need to understand the concept of solubility and saturation.
The solubility of a substance refers to the maximum amount of solute (in this case, sucrose) that can dissolve in a given amount of solvent (water) at a specific temperature. When a solution is saturated, it means that it contains the maximum amount of solute that can dissolve at that temperature.
To calculate the mass of rock candy formed, we need to know the solubility of sucrose in water at 20°C and the initial amount of sucrose dissolved in the boiling water.
1. Determine the solubility of sucrose in water at 20°C: The solubility of sucrose in water is temperature-dependent. You can consult a solubility chart or database to find the solubility value for sucrose at 20°C. Let's assume it is 200 grams of sucrose per 100 grams of water.
2. Calculate the initial amount of sucrose dissolved: In this case, we have 1000.0 grams of boiling water. Since the solution is saturated, it means 200 grams of sucrose will be dissolved in 100 grams of water.
The mass of sucrose dissolved can be calculated using the proportion:
(200 grams of sucrose / 100 grams of water) = (x grams of sucrose / 1000.0 grams of water)
Solving for x, we get:
x = (200 grams of sucrose / 100 grams of water) * 1000.0 grams of water
x = 2000.0 grams of sucrose
3. Determine the amount of sucrose that will crystallize: Since the solution is saturated, any excess sucrose beyond its solubility will crystallize out to form rock candy. So, the mass of rock candy formed will be the difference between the initial amount of sucrose dissolved and its solubility.
Mass of rock candy = Initial amount of sucrose dissolved - Solubility
Mass of rock candy = 2000.0 grams of sucrose - (200 grams of sucrose / 100 grams of water) * 1000.0 grams of water
Simplifying this expression, we get:
Mass of rock candy = 2000.0 grams of sucrose - 2000.0 grams of sucrose
Mass of rock candy = 0 grams
Therefore, in this case, no rock candy will be formed since the solution is already saturated with sucrose.