solid $A+$ water $\longrightarrow$ saturated solution
At $60^{\circ} C 24g+100 g \rightarrow 124 g$
At $60^{\circ} C$
100g of water is mixing 124 g solid
$=30 g$ of water saturate?
$\begin{array}{l}
=\frac{30g \times 124g}{100g} \\
=37.2g
\end{array}$
Answer (2)
Set up a proportion to relate the amount of solid A to the amount of water: 100 g water 124 g solid A = 30 g water x g solid A .
Solve for x by multiplying both sides by 30: x = 100 124 × 30 .
Calculate the value of x : x = 37.2 .
State the final answer: 37.2
Explanation
Understanding the Problem We are given that at 6 0 ∘ C , 100g of water can dissolve 124g of solid A to form a saturated solution. We need to find out how much solid A is required to saturate 30g 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 30g of water. The proportion is: 100 g water 124 g solid A = 30 g water x g solid A .
Solving for x To solve for x , we multiply both sides of the equation by 30 g water: x = 100 g water 124 g solid A × 30 g water .
Calculating the Value of x Now, we perform the calculation: x = 100 124 × 30 = 100 3720 = 37.2 .Therefore, 37.2g of solid A is needed to saturate 30g of water at 6 0 ∘ C .
Final Answer Therefore, 37.2 grams of solid A are needed to saturate 30 grams of water at 6 0 ∘ C .
Examples
Understanding solubility is crucial in many real-world applications. For example, in the pharmaceutical industry, it's important to know how much of a drug can dissolve in a particular solvent to create a stable and effective medication. Similarly, in the food industry, solubility affects the texture and stability of products. Knowing how to calculate the amount of solute needed to saturate a solution helps in formulating products with desired properties and ensuring their stability over time. This principle is also used in environmental science to determine the concentration of pollutants in water samples.
To saturate 30 grams of water at 60°C, you need 37.2 grams of solid A. This was calculated using a proportion based on the given saturating conditions of 100 grams of water dissolving 124 grams of solid A. The final calculated value confirms how much solid A is necessary for the smaller quantity of water.
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