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Equilibrium

Question
CBSEENCH11006607

Calculate the solubility of A2X3 in pure water, assuming that neither kind of ion reacts with water. The solubility product of A2X3, Ksp = 1·1 × 10–23

Solution
straight A subscript 2 straight X subscript 3 space is space dissociated space as
              straight A subscript 2 straight X subscript 3 space rightwards arrow space space space space 2 straight A to the power of 3 plus end exponent space plus space 3 straight X to the power of 2 minus end exponent
Let space the space solubility space of space straight A subscript 2 straight X subscript 3 space be space straight S space mol space straight L to the power of negative 1 end exponent
therefore space space open square brackets straight A to the power of 3 plus end exponent close square brackets space equals space 2 straight S semicolon space space space space open square brackets straight X to the power of 2 minus end exponent close square brackets space equals space 3 straight S
Applying space the space law space of space solubility space product
space space space space space space space space space space straight K subscript sp space equals space open square brackets straight A to the power of 3 plus end exponent close square brackets squared space open square brackets straight X to the power of 2 minus end exponent close square brackets cubed space space space space space space... left parenthesis 1 right parenthesis
Putting space the space values space in space expression space left parenthesis 1 right parenthesis comma space we space have
space 1.1 space cross times space 10 to the power of negative 23 end exponent space equals space left parenthesis 2 straight S right parenthesis squared space left parenthesis 3 straight S right parenthesis cubed space equals space 108 straight S to the power of 5
or space space space space space space space space space space space straight S to the power of 5 space equals space 1 space cross times space 10 to the power of negative 25 end exponent
or space space space space space space space space space space space straight S space equals space left parenthesis 1.0 space cross times space 10 to the power of negative 25 end exponent right parenthesis to the power of 1 divided by 5 end exponent
space space space space space space space space space space space space space space space space space space equals space 1.0 space cross times space 10 to the power of negative 5 end exponent space mol space straight L to the power of negative 1 end exponent space space space space space space space space space