- Solubility of both sugar and salt increases with temperature, but sugar is much more soluble than salt overall.
- Sugar's solubility increases dramatically with higher temperatures, while salt's solubility changes only slightly.
- Sample 1 uses table sugar at the highest temperature (\(80^\circ\text{C}\)).
- Therefore, Sample 1 has the highest solubility among the four options, resulting in \(\boxed{1}\).
Explanation
- Analyzing Solubility Characteristics
To determine which sample has the highest solubility, we need to compare the solubility characteristics of the substances involved and the effect of temperature on these substances. The two substances are table sugar (sucrose, \(C_{12}H_{22}O_{11}\)) and table salt (sodium chloride, \(NaCl\)). In general, the solubility of solids in water increases as the temperature of the water increases. However, the degree to which solubility increases varies greatly between different substances. Specifically, the solubility of table sugar increases dramatically with temperature, while the solubility of table salt remains relatively stable, showing only a very slight increase as temperature rises. Furthermore, at elevated temperatures, table sugar is intrinsically far more soluble in water than table salt is.
- Comparing the Samples
Now, let's examine the specific conditions for each of the four samples:
- Sample 1: Table sugar at \(80^\circ\text{C}\)
- Sample 2: Table sugar at \(45^\circ\text{C}\)
- Sample 3: Table salt at \(55^\circ\text{C}\)
- Sample 4: Table salt at \(63^\circ\text{C}\)
Comparing these, we can see that Samples 1 and 2 involve sugar, which already has a higher baseline solubility than salt. Between Sample 1 and Sample 2, Sample 1 is at a higher temperature (\(80^\circ\text{C}\) vs \(45^\circ\text{C}\)), which further enhances the solubility of the sugar. Comparing these to the salt samples (Samples 3 and 4), even at the higher temperatures, salt remains significantly less soluble than sugar at the given temperatures. Thus, the sample with the combination of the most soluble substance (sugar) and the highest temperature (\(80^\circ\text{C}\)) will have the highest solubility.
- Conclusion
Based on our analysis, Sample 1 contains the substance with inherently higher solubility (table sugar) at the highest temperature (\(80^\circ\text{C}\)). Since sugar's solubility increases dramatically with temperature, Sample 1 exhibits the highest solubility among the four choices. Therefore, the correct sample is 1.
Examples
This principle of solubility is essential in culinary arts and industrial food production. For instance, creating a simple syrup for cocktails or candies requires dissolving high concentrations of sugar in water. By heating the water, chefs can significantly increase the amount of sugar that dissolves, allowing for thicker, sweeter syrups than would be possible at room temperature. Understanding how temperature affects solubility ensures that these culinary processes are efficient and yield the desired textures and flavors.