Washing soda, a compound used to prepare hard water for washing laundry, is a hydrate, which means that a certain number of water molecules are included in the solid structure. Its formula can be written as \(\mathrm{Na}_{2} \mathrm{CO}_{3} \cdot x \mathrm{H}_{2} \mathrm{O},\) where \(x\) is the number of moles of \(\mathrm{H}_{2} \mathrm{O}\) per mole of \(\mathrm{Na}_{2} \mathrm{CO}_{3}\). When a \(2.558-\mathrm{g}\) sample of washing soda is heated at \(25^{\circ} \mathrm{C},\) all the water of hydration is lost, leaving \(0.948 \mathrm{~g}\) of \(\mathrm{Na}_{2} \mathrm{CO}_{3} .\) What is the value of \(x ?\)

Hydrate compounds are a unique group of substances that incorporate water molecules into their molecular structure. The water is not merely attached to the compound; it is an integral part of its crystal lattice. The general formula used to represent hydrates is written as follows: \( \text{Compound} \cdot x\text{H}_2\text{O} \), where \( x \) signifies the number of water molecules (or moles of water) associated with each formula unit of the compound.

Hydrates can be found in various applications, from construction materials such as cement to household items like the washing soda mentioned in the exercise. Determining the correct value of \( x \), the number of hydrates, is crucial because it can significantly impact the substance's properties, such as its reactivity or stability.

During a dehydration process, hydrates lose water to become anhydrous, which is a critical step in calculating the water content. This process also played a central role in the given exercise, where heating washing soda led to the release of the water of hydration, allowing for the calculation of \( x \).

The molar mass is a fundamental concept in chemistry, representing the mass of one mole of a substance. It's expressed in grams per mole (g/mol) and is equivalent to the molecular weight of a compound. For hydrates, the calculation of molar mass must include the mass of the bound water molecules as well as the anhydrous compound.

To calculate the molar mass, one would sum up the atomic masses of all atoms present in the formula unit, including the water molecules. For instance, in the exercise's case with washing soda \( \mathrm{Na}_2\mathrm{CO}_3 \cdot x\mathrm{H}_2\mathrm{O} \), the molar mass calculation first involved finding the mass of the anhydrous sodium carbonate and then accounting for the mass of water molecules corresponding to \( x \) hydrates.

Understanding molar mass is essential for converting between the mass of a substance and the number of moles, which is a fundamental step for stoichiometry and chemical calculations as shown in the provided step-by-step problem-solving method.

Stoichiometry is the section of chemistry that deals with the quantitative relationships between reactants and products in a chemical reaction. It relies heavily on the law of conservation of mass and the concept of moles. Stoichiometry comes into play when balancing chemical equations, calculating reacting masses, or in this exercise, finding the number of water molecules in a hydrate.

In the provided exercise, stoichiometry was used to solve for \( x \), the number of water molecules bound in the hydrate. This was done by employing the stoichiometric relationship between the mass of lost water upon heating and the mass of the remaining anhydrous compound. The ratio of the moles of water to the moles of anhydrous sodium carbonate directly gave the value of \( x \).

Through stoichiometry, one can understand how materials react and combine, how much product to expect from a reaction, and the composition of hydrates, which reinforces the principles of molar mass and hydrate formulas.