A student was comparing the solubility of equal amounts of table salt and table sugar at different temperatures. The table below shows the four samples that the student used and the temperature of the water that they were dissolved in.
| Sample | Name | Chemical formula | Temperature of water (${}^{\circ} C$) |
| ------ | ----------- | ---------------- | ---------------------------------------- |
| 1 | Table sugar | $C_{12}H_{22}O_{11}$ | 80 |
| 2 | Table sugar | $C_{12}H_{22}O_{11}$ | 45 |
| 3 | Table salt | NaCl | 55 |
| 4 | Table salt | NaCl | 63 |
Which of the samples most likely had the highest solubility?
1. 1
2. 2
3. 3
4. 4
Answer (2)
Solubility generally increases with temperature.
Sample 1 (table sugar) was at 80 ∘ C .
Sample 2 (table sugar) was at 45 ∘ C .
Sample 3 (table salt) was at 55 ∘ C .
Sample 4 (table salt) was at 63 ∘ C .
Sample 1 had the highest temperature, so it most likely had the highest solubility. The answer is 1 .
Explanation
Understanding the Problem We are asked to determine which of the four samples most likely had the highest solubility. Solubility generally increases with temperature. We need to compare the temperatures of the samples to determine which one had the highest temperature.
Analyzing Sample 1 Sample 1 (table sugar) was dissolved in water at 80 ∘ C .
Analyzing Sample 2 Sample 2 (table sugar) was dissolved in water at 45 ∘ C .
Analyzing Sample 3 Sample 3 (table salt) was dissolved in water at 55 ∘ C .
Analyzing Sample 4 Sample 4 (table salt) was dissolved in water at 63 ∘ C .
Determining the Answer Comparing the temperatures, we see that Sample 1 (table sugar at 80 ∘ C ) had the highest temperature. Therefore, it most likely had the highest solubility.
Examples
Understanding solubility is crucial in many real-world applications. For example, when making tea or coffee, the higher the water temperature, the more flavor is extracted from the tea leaves or coffee grounds. Similarly, in cooking, dissolving sugar in warm water allows for a smoother and more consistent distribution of sweetness throughout the dish. In industrial processes, controlling temperature to optimize solubility is essential for the efficient production of various chemical compounds and materials. This concept is also vital in environmental science, where the solubility of pollutants affects their distribution and impact on ecosystems.
Sample 1, which is table sugar dissolved at 80 °C, has the highest temperature and thus most likely the highest solubility. Other samples, while at elevated temperatures, are not as high as Sample 1. Therefore, the answer is 1.
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