Solid A + water [$\longrightarrow$] saturated solution
At $60^{\circ} C$ 24g + 100g [$\rightarrow$] 124g
At $60^{\circ} C$
100g of water saturate 124g solid
80 g of water saturate?
[$=\frac{80g \times 124g}{100g}$]
Answer (1)
Set up a proportion relating the mass of solid A to the mass of water: mass of water mass of solid A = 100 24 .
Let x be the mass of solid A needed to saturate 80g of water: 80 x = 100 24 .
Solve for x : x = 100 24 × 80 .
Calculate the value of x : x = 19.2 . The final answer is 19.2 .
Explanation
Problem Analysis Let's analyze the problem. We are given that at 6 0 ∘ C , 100g of water can saturate with 24g of solid A. This means that 100g of water dissolves 24g of solid A to form a saturated solution. We need to find out how much solid A is required to saturate 80g of water at the same temperature.
Setting up the Proportion We can set up a proportion to solve this problem. Let x be the amount of solid A needed to saturate 80g of water. The proportion is: mass of water mass of solid A = 100 g 24 g We want to find the mass of solid A, x , that saturates 80g of water. So we have: 80 x = 100 24
Solving for x Now, we solve for x by multiplying both sides of the equation by 80: x = 100 24 × 80 x = 100 24 × 80 x = 100 1920 x = 19.2 So, 19.2g of solid A is needed to saturate 80g of water at 6 0 ∘ C .
Final Answer Therefore, 80g of water will saturate with 19.2g of solid A at 6 0 ∘ C .
Examples
Understanding solubility is crucial in many real-world applications. For instance, 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 food science, solubility affects the texture and taste of products, such as how much sugar can dissolve in water to make syrup. In environmental science, understanding the solubility of pollutants helps predict their spread and impact on water sources. Knowing how to calculate saturation points allows us to optimize processes and ensure desired outcomes in various fields.
