To solve this problem, we need to understand the properties of an ideal solution.$\\$An ideal solution is defined by the following characteristics:$\\$• The enthalpy change of mixing $(\Delta H_{mix})$ is zero.$\\$• The volume change of mixing $(\Delta V_{mix})$ is zero.$\\$• The vapor pressure of the solution follows Raoult's Law exactly,$\\$ which means $\Delta p = p_{observed} - p_{Raoult}$ is zero.$\\$However, the entropy change of mixing $(\Delta S_{mix})$ is not zero.$\\$This is because when two substances mix, there is an increase in disorder,$\\$leading to a positive entropy change.$\\$Let's analyze each option:$\\$Option 1: $\Delta S_{mix}$ is not zero for an ideal solution.$\\$Option 2: $\Delta V_{mix}$ is zero for an ideal solution.$\\$Option 3: $\Delta p = p_{observed} - p_{Raoult}$ is zero for an ideal solution.$\\$Option 4: $\Delta H_{mix}$ is zero for an ideal solution.$\\$Therefore, the correct answer is Option 1: $\Delta S_{mix}$ is not equal to zero for an ideal solution.