Question

The molar solubility product is K_sp. ‘s’ is given in terms of K_sp by the relation

$straight s space equals space open parentheses straight K subscript sp over 128 close parentheses to the power of 1 divided by 4 end exponent$
$straight s space equals space open parentheses straight K subscript sp over 256 close parentheses to the power of 1 divided by 5 end exponent$

s = (256 K_sp)^1/5

s = (128K_sp) 1^/4

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Solution

straight s space equals space open parentheses straight K subscript sp over 256 close parentheses to the power of 1 divided by 5 end exponent

For space the space solute space straight A subscript straight x straight B subscript straight y space rightwards harpoon over leftwards harpoon with space on top space xA space plus space yB straight K subscript sp space equals space straight x to the power of straight y straight y to the power of straight y space left parenthesis straight s right parenthesis to the power of straight x plus straight y end exponent MX subscript 4 space rightwards harpoon over leftwards harpoon with space on top space straight M to the power of 4 to the power of plus space plus 4 straight X to the power of minus space straight x space equals 1 comma space straight y space equals 4 straight K subscript sp space equals space left parenthesis 4 right parenthesis to the power of 4 left parenthesis 1 right parenthesis to the power of 1 left parenthesis straight s right parenthesis to the power of 5 space equals space 256 space straight s to the power of 5 straight s space equals space open parentheses straight K subscript sp over 256 close parentheses to the power of 1 divided by 5 end exponent

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