- Identify the physical principle: the solubility of gases in liquids decreases as the temperature of the liquid increases.
- Compare the temperatures provided: \(78^\circ\text{C}\) (Sample 1), \(73^\circ\text{C}\) (Sample 2), \(55^\circ\text{C}\) (Sample 3), and \(63^\circ\text{C}\) (Sample 4).
- Identify the highest temperature, which is \(78^\circ\text{C}\) for Sample 1.
- Conclude that Sample 1 has the lowest solubility due to having the highest temperature. The final answer is \(\boxed{1}\).
Explanation
- Problem Analysis and Physical Principle
We are given four samples of CO2 gas dissolved in water at different temperatures:
- Sample 1: \(78^\circ\text{C}\)
- Sample 2: \(73^\circ\text{C}\)
- Sample 3: \(55^\circ\text{C}\)
- Sample 4: \(63^\circ\text{C}\)
The core principle governing the solubility of gases in liquids is that solubility is inversely proportional to temperature. This means that as the temperature of the solvent (water in this case) increases, the kinetic energy of the gas molecules increases, allowing them to escape the solution more easily, thereby decreasing the solubility of the gas. Therefore, to identify the sample with the lowest solubility, we must identify the sample with the highest water temperature.
- Comparison and Identification
We compare the provided temperatures:
- Sample 1: \(78^\circ\text{C}\)
- Sample 2: \(73^\circ\text{C}\)
- Sample 3: \(55^\circ\text{C}\)
- Sample 4: \(63^\circ\text{C}\)
By comparing these values, we can see that:
\(78 > 73 > 63 > 55\)
The highest temperature is \(78^\circ\text{C}\), which corresponds to Sample 1. Because solubility decreases as temperature increases, Sample 1, being the hottest, will have the lowest solubility of the carbon dioxide gas among the four samples.
- Conclusion
Based on the inverse relationship between temperature and gas solubility, Sample 1 (at \(78^\circ\text{C}\)) has the highest temperature and therefore the lowest solubility. The correct choice is 1. Thus, the sample with the lowest solubility is \(\boxed{1}\).
Examples
In real-world applications, this concept is crucial for environmental science and beverage production. For instance, in carbonated soft drinks, the carbon dioxide is dissolved under pressure at low temperatures to maximize its solubility. If a bottle of soda is left out in the sun, the temperature rises, leading to lower gas solubility and causing the CO2 to escape from the liquid, making the drink go 'flat'. Understanding this relationship helps in proper storage and maintaining the quality of carbonated products.