To solve this problem, we need to understand Dalton's Law of partial pressures.$\\$Dalton's Law states that the total pressure of a gaseous mixture is equal to the sum of the partial pressures of each individual gas in the mixture.$\\$Let's analyze each option:$\\$• Option 1: $p = p_1 + p_2 + p_3 \\$This is a correct representation of Dalton's Law, where $p$ is the total pressure and $p_1, p_2, p_3$ are the partial pressures of the gases.$\\$• Option 2: $\frac{RT}{V} (n_1 + n_2 + n_3) \\$This equation represents the ideal gas law for a mixture of gases, where $R$ is the gas constant, $T$ is the temperature, $V$ is the volume, and $n_1, n_2, n_3$ are the moles of the gases. This is consistent with Dalton's Law.$\\$• Option 3: $p_i = \chi_i p \\$This equation states that the partial pressure $p_i$ of the $i$th gas is the product of its mole fraction $\chi_i$ and the total pressure $p.$ This is a correct application of Dalton's Law.$\\$• Option 4: $p_i = \chi_i p_0 \\$This equation incorrectly states that the partial pressure $p_i$ is the product of the mole fraction $\chi_i$ and the pure gas pressure $p_0.$ This is not a correct representation of Dalton's Law, as $p_0$ is not relevant in this context.$\\$Therefore, the incorrect equation according to Dalton's Law is Option 4.$\\$The correct answer is Option 4.