Problem 28 - Chemistry: An Atoms-Focused Approach

Question

Adding sidewalk deicer (calcium chloride) to water causes the temperature of the water to increase. If solid \(\mathrm{CaCl}_{2}\) is the system, what are the signs of \(\Delta S_{\mathrm{sys}}\) and \(\Delta S_{\mathrm{surr}} ?\)

Step-by-Step Solution

Answer

Answer: When calcium chloride is added to water, the entropy change for both the system (solid calcium chloride) and the surroundings (water) is positive. This is due to the increased disorder in the system from dissolving the solid and the increased temperature of the water, causing increased disorder in the surroundings.

Step 1: 1. Determine the entropy change of the system

Since the system is solid calcium chloride, dissolving in water, the system's entropy will increase. This is because the solid calcium chloride particles are scattered through the water, leading to an increase in disorder. Therefore, ΔS_sys is positive. ΔS_sys > 0

Step 2: 2. Determine the entropy change of the surroundings

When the solid calcium chloride dissolves in water, it causes the temperature of the water to increase. An increase in temperature leads to an increase in the entropy of the surroundings. This is because the water molecules will move more rapidly as the temperature increases, causing more disorder in the surroundings. So, ΔS_surr is positive. ΔS_surr > 0

Step 3: 3. Summarize the signs of ΔS_sys and ΔS_surr

In conclusion, the entropy change of both the system (solid calcium chloride) and the surroundings (water) is positive when CaCl₂ is added to water.