Problem 187 - Chemistry Matter and Change

Question

Borax Hydrated sodium tetraborate \(\left(\mathrm{Na}_{2} \mathrm{B}_{4} \mathrm{O}_{7} \cdot \mathrm{xH}_{2} \mathrm{O}\right)\) is commonly called borax. Chemical analysis indicates that this hydrate is 52.8\(\%\) sodium tetraborate and 47.2\(\%\) water. Determine the formula and name the hydrate.

Step-by-Step Solution

Answer

The formula of the borax hydrate is Na2B4O7·10H2O, and its name is Sodium Tetraborate Decahydrate.

Step 1: Calculate the moles of Sodium Tetraborate and Water

Firstly, we will calculate the moles of sodium tetraborate and water in a 100 g sample of the hydrate. To do this, we will use the mass percentages and molecular weights of both substances. Given mass percentages: Sodium Tetraborate (Na2B4O7): 52.8% Water (H2O): 47.2% Molecular Weights: Sodium Tetraborate (Na2B4O7): 201.22 g/mol (from periodic table) Water (H2O): 18.015 g/mol (from periodic table) Calculate the moles: Moles of Na2B4O7 = (mass of Na2B4O7 / molecular weight of Na2B4O7) Moles of Na2B4O7 = (52.8 g / 201.22 g/mol) = 0.2625 mol Moles of H2O = (mass of H2O / molecular weight of H2O) Moles of H2O = (47.2 g / 18.015 g/mol) = 2.620 mol

Step 2: Calculate the mole ratio of Na2B4O7 and H2O

To determine the formula of the hydrate, we need to find the mole ratio of sodium tetraborate to water. To do this, we can divide both the moles of Na2B4O7 and H2O by the smaller number of moles. Mole ratio Na2B4O7 : H2O Mole ratio_Na2B4O7 = moles of Na2B4O7 / smaller moles = 0.2625 mol / 0.2625 mol = 1 Mole ratio_H2O = moles of H2O / smaller moles = 2.620 mol / 0.2625 mol = 9.98 ≈ 10 The mole ratio of sodium tetraborate to water in the hydrate is approximately 1:10.

Step 3: Determine the formula and name of the hydrate

Using the mole ratio of sodium tetraborate and water found in step 2, we can now write the formula of the hydrate as: Na2B4O7.10H2O The formula of the borax hydrate is Na2B4O7·10H2O. This hydrate is known as Sodium Tetraborate Decahydrate.

Key Concepts

Sodium Tetraborate

Sodium tetraborate, also known as borax, is a naturally occurring mineral or compound. Its chemical formula is \( \text{Na}_2\text{B}_4\text{O}_7 \). Sodium tetraborate is very versatile and is used in a variety of applications such as cleaning, laundry, making glass and ceramics, and even as a flux in metallurgy. Given its usefulness, understanding its properties and structure is vital in chemistry.

In this problem, sodium tetraborate makes up 52.8% of the given hydrate. To find out more about its specific properties in the hydrate form, one needs to look at how it combines with water to form sodium tetraborate decahydrate. This hydrated form is where 10 water molecules are associated with one molecule of sodium tetraborate. This is written as \( \text{Na}_2\text{B}_4\text{O}_7\cdot10\text{H}_2\text{O} \), indicating a specific crystal structure bonded by water molecules.

Mole Ratio

Understanding mole ratios is crucial in chemical analysis and formulation. Mole ratio refers to the proportion of moles of different substances involved in a chemical reaction or composition. In the given exercise, the mole ratio helps determine the formula of the sodium tetraborate hydrate by comparing moles of sodium tetraborate to moles of water.

The process involves first calculating moles of each substance using the mass percentages and molecular weights. Here, sodium tetraborate has a molecular weight of 201.22 g/mol and water has a molecular weight of 18.015 g/mol. Then, using those values, one finds the simplest whole-number ratio by dividing each subtractable value by the smallest number of moles present. In this case, the mole ratio is approximately 1:10 for sodium tetraborate to water, hence confirming that the hydrate comprises one part sodium tetraborate to ten parts water.

Chemical Analysis

Chemical analysis involves quantitative measurements to ascertain the composition of substances. By determining percentages of elements or compounds in a mixture, chemists can derive a formula for chemical compounds or materials. In this problem, the analysis of the hydrate encompasses measuring amounts of sodium tetraborate and water based on their mass percentages.

This data is used to calculate the formula of the hydrate. Using 52.8% for sodium tetraborate and 47.2% for water, alongside their respective molecular weights, allows for determining the number of moles. The subsequent determination of mole ratios aids in identifying the chemical formula, providing a clear depiction of the hydrate's structure and confirming its formulation as \( \text{Na}_2\text{B}_4\text{O}_7\cdot10\text{H}_2\text{O} \), termed as sodium tetraborate decahydrate. This showcases an application of chemical analysis in deriving structural information from quantitative data of a compound.