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Chapter 3: Problem 74

An 8.129 g sample of \(\mathrm{MgSO}_{4} \cdot x \mathrm{H}_{2} \mathrm{O}\) is heated until all the water of hydration is driven off. The resulting anhydrous compound, \(\mathrm{MgSO}_{4},\) weighs \(3.967 \mathrm{g} .\) What is the formula of the hydrate?

Short Answer

Expert verified
The formula of the hydrate is \(\mathrm{MgSO}_{4} \cdot 7 \mathrm{H}_{2} \mathrm{O}\).

Step by step solution

01

Calculate the mass of water

First, you calculate the mass of the water driven off from the hydrate. This is done by the following subtraction: Mass of hydrate (8.129 g) - Mass of Anhydrous compound (3.967 g).
02

Convert the masses into moles

Convert the mass of water and the mass of anhydrous \(\mathrm{MgSO}_{4}\) into moles by dividing the masses by their respective molecular masses (18 g/mol for water and 120.366 g/mol for \(\mathrm{MgSO}_{4}\)).
03

Determine the ratio of moles

Compare the moles of water to the moles of anhydrous compound to find the ratio that represents \(x\) in the compound formula.

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