- Understand that the solubility of a gas in a liquid generally decreases as the temperature increases (inverse relationship).
- Compare the temperatures: \(78^\circ\text{C} > 73^\circ\text{C} > 63^\circ\text{C} > 55^\circ\text{C}\).
- Identify that the highest temperature (\(78^\circ\text{C}\)) leads to the lowest gas solubility.
- Conclude that Sample 1 represents the lowest solubility.
- Final answer: \(\boxed{1}\)
Explanation
- Analysis of Solubility and Temperature Relationship
The problem asks us to determine which of four samples of carbon dioxide dissolved in water has the lowest solubility, based on the temperature of the water in each sample. The provided data is:
- Sample 1: \(78^\circ\text{C}\)
- Sample 2: \(73^\circ\text{C}\)
- Sample 3: \(55^\circ\text{C}\)
- Sample 4: \(63^\circ\text{C}\)
Solubility is a measure of how much solute can be dissolved in a given amount of solvent at a specific temperature. For most gases dissolved in liquids, such as carbon dioxide in water, the solubility is inversely related to temperature. This means that as the temperature of the liquid increases, the kinetic energy of the gas molecules increases, allowing them to escape the liquid phase more easily, thus decreasing the solubility of the gas. Therefore, the sample with the highest temperature will have the lowest solubility.
- Comparison of Temperatures and Conclusion
To find the sample with the lowest solubility, we must identify the sample with the highest temperature among the four given values. Comparing the temperatures:
- \(55^\circ\text{C} < 63^\circ\text{C} < 73^\circ\text{C} < 78^\circ\text{C}\)
The highest temperature is \(78^\circ\text{C}\). Since temperature and gas solubility are inversely proportional, the highest temperature corresponds to the lowest solubility of the gas in the water. We can see from our data list that \(78^\circ\text{C}\) is the temperature recorded for Sample 1.
Examples
The inverse relationship between temperature and gas solubility is essential in many real-world applications. For example, carbonated beverages lose their carbonation (the dissolved carbon dioxide gas) faster when they are warm than when they are refrigerated. When you open a warm soda, the gas escapes more rapidly because the solubility of the carbon dioxide is much lower at higher temperatures compared to colder temperatures. Understanding this principle helps in industries ranging from food and beverage storage to environmental science, where water temperature significantly affects the levels of dissolved oxygen available to aquatic life.