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?
A. 1
B. 2
C. 3
D. 4
Answer (2)
Solubility increases with temperature.
Sample 1 (sugar at 80°C) has the highest temperature among all samples.
Therefore, Sample 1 most likely has 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 has the highest solubility.
Listing the Samples and Temperatures Sample 1 is table sugar at 80°C. Sample 2 is table sugar at 45°C. Sample 3 is table salt at 55°C. Sample 4 is table salt at 63°C.
Comparing Sugar and Salt Samples Comparing the two sugar samples, Sample 1 (80°C) has a higher temperature than Sample 2 (45°C), so Sample 1 has a higher solubility than Sample 2. Comparing the two salt samples, Sample 4 (63°C) has a higher temperature than Sample 3 (55°C), so Sample 4 has a higher solubility than Sample 3.
Comparing Sugar and Salt Now we compare the highest solubility between sugar and salt samples. Sample 1 (sugar at 80°C) and Sample 4 (salt at 63°C). Since 80°C is greater than 63°C, Sample 1 most likely has the highest solubility.
Final Answer Therefore, Sample 1 most likely had the highest solubility.
Examples
Understanding solubility is crucial in many real-world applications. For instance, when making tea, the hotter the water, the more tea and sugar will dissolve, leading to a sweeter and more flavorful beverage. Similarly, in pharmaceutical manufacturing, controlling the temperature and solubility of different compounds is essential for creating effective medications. In geology, the solubility of minerals in water affects the formation of caves and other geological features. By understanding these principles, we can better control and predict outcomes in various fields.
Sample 1 (table sugar at 80°C) most likely has the highest solubility because solubility generally increases with temperature. It has the highest temperature compared to the other samples. Thus, the answer is option A: 1.
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