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I know that this constant tells us the strength of the interaction between the metal and the ligand, so should it also mean that the higher the constant, the stable the complex ? I need to make sure of it because in photometric titration, all that matters is the stability of complex, and if the constant is given, one should know which complex is formed earlier.

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As $K$ is a thermodynamic constant, and if you define your reaction as

$A + B \rightarrow{} C + D$

leading to

$K = \frac{c_C \cdot{} c_D}{c_A \cdot{}c_B}$

then -- thermodynamically -- yes. Especially for chelate complexes (like with EDTA), entropically favoured. This answer excludes (macroscopic) kinetics

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