From the calculations, the value of x is found to be 7.
The anhydrous salt is the salt that does not contain the water of crystallization.
We know that;
Number of moles of anhydrous salt = number of moles of hydrated salt
Number of moles of anhydrous salt = 77.5g/155 g/mol = 0.5 moles
Number of moles of hydrated NiSO4= 140.05g/155 + 18x
Thus;
0.5 = 140.05g/155 + 18x
0.5 (155 + 18x) = 140.05
77.5 + 9x = 140.05
x = 140.05 - 77.5 /9
= 7
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