Identify the following elements based on their electron configurations and rank them in order of increasing electronegativity: \([\mathrm{Ar}] 4 s^{1} 3 d^{5} ;[\mathrm{Ne}] 3 s^{2} 3 p^{3} ;[\mathrm{Ar}] 4 s^{2} 3 d^{10} 4 p^{3} ;[\mathrm{Ne}] 3 s^{2} 3 p^{5}\).

Transformer notation can be used to find the electron configurations of the given elements: 1. \([\mathrm{Ar}] 4s^1 3d^5\) 2. \([\mathrm{Ne}] 3s^2 3p^3\) 3. \([\mathrm{Ar}] 4s^2 3d^{10} 4p^3\) 4. \([\mathrm{Ne}] 3s^2 3p^5\) Now let's identify the elements. 1. The element that has configuration \([\mathrm{Ar}]4s^1 3d^5\) is the 6th element in the 4th period (as Argon is the last element in the 3rd period). The 6th element in the 4th period is Chromium (Cr). 2. The element with configuration \([\mathrm{Ne}] 3s^2 3p^3\) is the 5th element in the 3rd period (as Neon is the last element in the 2nd period). The 5th element in the 3rd period is Phosphorus (P). 3. The element with configuration \([\mathrm{Ar}] 4s^2 3d^{10} 4p^3\) is the 5th element in the 4th period after Argon. The 5th element in the 4th period after Argon is Arsenic (As). 4. The element with configuration \([\mathrm{Ne}] 3s^2 3p^5\) is the 2nd last element in the 3rd period (as Neon is the last element in the 2nd period). The 2nd last element in the 3rd period is Chlorine (Cl). So, the elements are Chromium (Cr), Phosphorus (P), Arsenic (As), and Chlorine (Cl).

Now that we have identified the elements, we need to rank them in order of increasing electronegativity. Using the periodic table, we can determine the electronegativity values of these elements: - Chromium (Cr): 1.66 - Phosphorus (P): 2.19 - Arsenic (As): 2.18 - Chlorine (Cl): 3.16 The electronegativity values tell us that these elements can be ranked in the following order (from the least electronegative to the most electronegative): Chromium (Cr) < Arsenic (As) < Phosphorus (P) < Chlorine (Cl) In conclusion, the given elements, identified by their electron configurations, can be ranked in order of increasing electronegativity as follows: Chromium (Cr), Arsenic (As), Phosphorus (P), and Chlorine (Cl).