Predicting qualitatively how entropy changes with mixing and separation
Madison
For each system listed in the first column of the table below, decide (if possible) whether the change described in the second column will increase the entropy $S$ of the system, decrease $S$, or leave $S$ unchanged. If you don't have enough information to decide, check the "not enough information" button in the last column.

Note for advanced students: you may assume ideal gas and ideal solution behaviour.
$$\text{Unknown environment 'tabular'}$$ & $$\text{Unknown environment 'tabular'}$$ & $$\text{Unknown environment 'tabular'}$$
\end{tabular} \
\hline $$\text{Unknown environment 'tabular'}$$ & $$\text{Unknown environment 'tabular'}$$ & $$\text{Unknown environment 'tabular'}$$
\end{tabular} \
\hline $$\text{Unknown environment 'tabular'}$$ & $$\text{Unknown environment 'tabular'}$$ & $$\text{Unknown environment 'tabular'}$$
\end{tabular} \
\hline & $x$ & 5 \
\hline
\end{tabular}

Step 1 ：The question is asking about the change in entropy for different systems under different conditions. Entropy is a measure of the disorder or randomness of a system. Generally, processes that increase the disorder of a system will increase the entropy.

Step 2 ：For the first system, dissolving potassium chloride in water will increase the disorder of the system as the ions become dispersed in the water.

Step 3 ：For the second system, mixing two gases will also increase the disorder of the system as the gas molecules become more randomly distributed.

Step 4 ：For the third system, adding water to a solution will also increase the disorder of the system as the water molecules become dispersed in the solution.

Step 5 ：Therefore, for all three systems, the change in entropy ($\mathrm{\Delta }S$) should be greater than 0.

Step 6 ：This is a qualitative analysis based on the principles of thermodynamics and does not require a Python code for calculation.

Step 7 ：Final Answer: For all three systems, the change in entropy ($\mathrm{\Delta }S$) is greater than 0, i.e., $\boxed{{\displaystyle \mathrm{\Delta }S>0}}$.