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For \[{\text{BC}}{{\text{l}}_3}{\text{, AlC}}{{\text{l}}_3}\] and \[{\text{GaC}}{{\text{l}}_3}\] , the increasing order of ionic character is:
A \[{\text{BC}}{{\text{l}}_3}{\text{ < AlC}}{{\text{l}}_3}{\text{ < GaC}}{{\text{l}}_3}\]
B \[{\text{GaC}}{{\text{l}}_3} < {\text{AlC}}{{\text{l}}_3} < {\text{BC}}{{\text{l}}_3}\]
C \[{\text{BC}}{{\text{l}}_3} < {\text{GaC}}{{\text{l}}_3} < {\text{AlC}}{{\text{l}}_3}\]
D \[{\text{AlC}}{{\text{l}}_3} < {\text{BC}}{{\text{l}}_3} < {\text{GaC}}{{\text{l}}_3}\]

Answer
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Hint: Identify the trend in the electronegativity values. The trend in the ionic character will be the reverse of the trend in the electronegativity values.Electronegativity actually represents the tendency of an element to accept electrons. The atoms having greater effective nuclear charge will tend to receive more readily.

Complete Step by step answer: The chemical formula \[{\text{BC}}{{\text{l}}_3}{\text{, AlC}}{{\text{l}}_3}\] and \[{\text{GaC}}{{\text{l}}_3}\] represents the compounds boron trichloride, aluminum trichloride and gallium trichloride respectively.
The electronegativity of chlorine is 3.16.
 Electronegativity values of boron, aluminum and gallium are 2.0, 1.5 and 1.6 respectively. Write the decreasing order of electronegativities as \[{\text{B > Ga > Al}}\] .
The electronegativity difference between chlorine atom and boron atom in boron trichloride is \[{\text{3}}{\text{.16}} - 2.0 = 1.16\] .
The electronegativity difference between chlorine atom and aluminum atom in aluminum trichloride is \[{\text{3}}{\text{.16}} - 1.5 = 1.66\]
The electronegativity difference between chlorine atom and gallium atom in gallium trichloride is \[{\text{3}}{\text{.16}} - 1.6 = 1.56\]
The increasing order of the electronegativity difference between two atoms in the compounds is \[{\text{BC}}{{\text{l}}_3}\left( {1.16} \right) < {\text{GaC}}{{\text{l}}_3}\left( {1.56} \right) < {\text{AlC}}{{\text{l}}_3}\left( {1.66} \right)\] .
With decrease in the difference in the electronegativity values, the ionic character increases. Write the increasing order of the ionic character as \[{\text{BC}}{{\text{l}}_3} < {\text{GaC}}{{\text{l}}_3} < {\text{AlC}}{{\text{l}}_3}\] .

Hence, the correct option is the option (C).

Note: Atomic size and the nuclear charge determine the electronegativity value of an element. When we move down the boron family, the electronegativity decreases from boron to aluminum due to increase in atomic size. From aluminum to gallium, d-subshells start filling with electrons. The electrons of d subshell poorly shield the nuclear charge. Due to this, the attraction between valence electrons and the nucleus is greater for gallium than for aluminum. Hence, gallium has higher electronegativity than aluminum.