A hydrate of copper(II) chloride has the following formula: CuCl₂ • x H₂O. The water in a 3.41-g sample of the hydrate is driven off by heating. The remaining sample has a mass of 2.69 g. Find the number of waters of hydration (x) in the hydrate.

Verified step by step guidance

1. Calculate the mass of water lost by subtracting the mass of the anhydrous sample from the mass of the hydrate: \( \text{mass of water} = 3.41\, \text{g} - 2.69\, \text{g} \).
2. Determine the moles of water lost using the molar mass of water (\( \text{H}_2\text{O} \)), which is approximately 18.02 g/mol: \( \text{moles of water} = \frac{\text{mass of water}}{18.02\, \text{g/mol}} \).
3. Calculate the moles of anhydrous copper(II) chloride (CuCl2) using its molar mass, which is approximately 134.45 g/mol: \( \text{moles of CuCl}_2 = \frac{2.69\, \text{g}}{134.45\, \text{g/mol}} \).
4. Determine the ratio of moles of water to moles of CuCl2 to find the value of \( x \): \( x = \frac{\text{moles of water}}{\text{moles of CuCl}_2} \).
5. Round the value of \( x \) to the nearest whole number to find the number of waters of hydration in the hydrate.

Key Concepts

Hydrates

Hydrates are compounds that contain water molecules within their crystalline structure. The water molecules are typically incorporated in a fixed ratio, represented as 'x' in the formula CuCl2 # x H2O. Understanding hydrates is essential for determining the amount of water lost upon heating and calculating the number of water molecules associated with the compound.

Mass Loss Calculation

To find the number of waters of hydration, one must calculate the mass of water lost during heating. This is done by subtracting the mass of the anhydrous compound (after heating) from the initial mass of the hydrate. This mass loss directly correlates to the number of water molecules, allowing for the determination of 'x' in the hydrate's formula.

Molar Mass and Stoichiometry

Molar mass is the mass of one mole of a substance, which is crucial for converting between grams and moles. In this context, stoichiometry helps relate the mass of the anhydrous copper(II) chloride and the mass of water lost to the number of moles of each component. This relationship is key to solving for 'x' in the hydrate formula by establishing a ratio based on their respective molar masses.