The solubility of solid $A$ at $60^{\circ} C$ is $24 g / 100 g$ water.
(a) What is the amount of solid required to saturate 30 g of water at $60^{\circ} C$?
(b) What will be the amount of saturated solution obtained at $60^{\circ} C$ when 12 the solid $A$ is used to prepare a saturated solution?
Answer (2)
To saturate 30 g of water at 6 0 ∘ C , we set up a proportion: 30 x = 100 24 , and solve for x .
The amount of solid A required is x = 7.2 g.
To find the amount of saturated solution with 12 g of solid A , we determine the amount of water it saturates: y 12 = 100 24 , and solve for y .
12 g of solid A saturates 50 g of water, so the total mass of the saturated solution is 12 + 50 = 62 g, thus the final answer is 62 .
Explanation
Understanding the Problem We are given that the solubility of solid A at 6 0 ∘ C is 24 g /100 g water. This means that 24 grams of solid A can dissolve in 100 grams of water to form a saturated solution at 6 0 ∘ C . We need to find the amount of solid A required to saturate 30 g of water at 6 0 ∘ C , and the amount of saturated solution obtained when 12 g of solid A is used.
Calculating Solid Required (a) To find the amount of solid A needed to saturate 30 g of water, we can set up a proportion using the given solubility. Let x be the amount of solid A needed. Then we have: 30 x = 100 24 Multiplying both sides by 30, we get: x = 100 24 × 30 = 100 24 × 30 = 100 720 = 7.2 So, 7.2 grams of solid A are required to saturate 30 g of water at 6 0 ∘ C .
Calculating Saturated Solution (b) Now, we need to find the amount of saturated solution obtained when 12 g of solid A is used. First, we need to determine how much water can be saturated by 12 g of solid A . Let y be the amount of water that can be saturated by 12 g of solid A . We can set up another proportion: y 12 = 100 24 Multiplying both sides by y , we get: 12 = 100 24 × y Multiplying both sides by 24 100 , we get: y = 12 × 24 100 = 24 1200 = 50 So, 12 g of solid A can saturate 50 g of water. The total mass of the saturated solution is the sum of the mass of solid A and the mass of water: T o t a l ma ss = ma ss o f so l i d A + ma ss o f w a t er = 12 + 50 = 62 Therefore, the amount of saturated solution obtained is 62 g.
Final Answer (a) The amount of solid required to saturate 30 g of water at 6 0 ∘ C is 7.2 g. (b) The amount of saturated solution obtained at 6 0 ∘ C when 12 g of solid A is used is 62 g.
Examples
Understanding solubility is crucial in many real-world applications. For example, in the pharmaceutical industry, it's essential to know how much of a drug can dissolve in a solvent to create a stable and effective medication. Similarly, in the food industry, solubility affects the texture and stability of products like sugar in beverages or salt in soups. In environmental science, understanding the solubility of pollutants helps predict their movement and impact in water systems. By mastering these concepts, you can make informed decisions in various fields, ensuring product quality, safety, and environmental protection.
To saturate 30 g of water at 60°C, 7.2 g of solid A is required. When using 12 g of solid A, a total of 62 g of saturated solution is obtained. This includes both the solid and the water it saturates.
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