Ron and Hermione begin with 1.50 g of the hydrate copper(II)sulfate·x-hydrate (CuSO4·xH2O), where x is an integer. Part of their practical exam is to determine this integer x. They are working in pairs, though Hermione is doing most of the work. This should be discouraged! After dehydration they find that they are left with 0.96 g of the an-hydrate CuSO4. What is the unknown integer x. Round the answer to the nearest integer.

5

Explanation:

We can obtain the value of x by doing the following:

Mass of hydrated salt (CuSO4.xH2O) = 1.50g

Mass of anhydrous salt (CuSO4) = 0.96g

Mass of water molecule(xH2O) = 1.50 — 0.96 = 0.54g

Molar Mass of CuSO4.xH2O = 63.5 + 32 + (16x4) + x(2 +16) = 63.5 + 32 + 64 + 18x = 159.5 + 18x

Mass of water(xH2O) molecules in the hydrate salt is given by:

xH2O/CuSO4.xH2O = 0.54/1.5

18x/(159.5 + 18x) = 0.36

Cross multiply to express in linear form

18x = 0.36 (159.5 + 18x)

18x = 57.42 + 6.48x

Collect like terms

18x — 6.48x = 57.42

11.52x = 57.42

Divide both side by 11.52

x = 57.42/11.52

x = 5

Therefore, the unknown integer x is 5 and the formula for the hydrated salt is CuSO4.5H2O

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