Question

In 1871 Mendeleev predicted the undiscovered element ekaaluminum. In 1875 the element was discovered in Gaul (France) and was given the name gallium. If \(0.500 \mathrm{~g}\) of gallium reacts with oxygen gas to give \(0.672 \mathrm{~g}\) of gallium oxide, what is its empirical formula?

Short answer

The empirical formula for gallium oxide is \(\mathrm{Ga}_2\mathrm{O}_3\).

Step-by-step solution

Determine Mass of Oxygen

Calculate the mass of oxygen in the compound by subtracting the mass of gallium from the mass of gallium oxide. \[\text{Mass of oxygen} = 0.672\,\mathrm{g} - 0.500\,\mathrm{g} = 0.172\,\mathrm{g}\]

Calculate Moles of Gallium

Use the molar mass of gallium (approximately 69.72 g/mol) to convert grams of gallium to moles:\[\text{Moles of gallium} = \frac{0.500\,\mathrm{g}}{69.72\,\mathrm{g/mol}} \approx 0.00717\,\mathrm{mol}\]

Calculate Moles of Oxygen

Use the molar mass of oxygen (approximately 16.00 g/mol) to convert grams of oxygen to moles:\[\text{Moles of oxygen} = \frac{0.172\,\mathrm{g}}{16.00\,\mathrm{g/mol}} \approx 0.01075\,\mathrm{mol}\]

Determine the Simplest Mole Ratio

Divide the number of moles of each element by the smallest number of moles to find the simplest ratio:\[\text{Ratio of gallium} = \frac{0.00717}{0.00717} = 1\]\[\text{Ratio of oxygen} = \frac{0.01075}{0.00717} \approx 1.5\]

Convert to Whole Numbers

Since the ratio is 1 : 1.5, multiply both numbers by 2 to get whole numbers:\[\text{Gallium} : \text{Oxygen} = 2 : 3\]

Key concepts

Mendeleev's Predictions

In the late 19th century, Dmitri Mendeleev made groundbreaking predictions that reshaped the scientific community. He is mostly remembered for organizing the periodic table in a way that not only reflected the known elements but also left spaces for those yet to be discovered. Mendeleev's prediction of eka-aluminum is a shining example of this foresight. This hypothetical element, based solely on periodic trends, was later discovered as gallium. This showcases Mendeleev's profound understanding of the periodic system's predictive power. His confidence in the periodic table allowed him to foresee the properties and relative atomic masses of undiscovered elements, also providing a powerful tool to identify the empirical formula of new compounds.

Element Discovery

The discovery of new elements relies heavily on both empirical and predictive science, a key principle realized in the tale of gallium. When gallium was discovered in 1875, it was immediately linked to Mendeleev's predictions because its properties matched those of the proposed eka-aluminum. The excitement of discovering a new element is not merely about adding it to the table but confirming theoretical predictions. This element discovery process often follows these steps:

• Identifying unknown properties through experimentation.
• Comparing these properties with predicted values from models like Mendeleev's periodic table.
• Finally, validating the new element's identity through chemical reactions and empirical analysis.

Discovery doesn't stop at identification; understanding how the new element reacts and forms compounds is equally vital.

Stoichiometry

Stoichiometry is the calculation of reactants and products in chemical reactions, and it's crucial for determining empirical formulas. In our example with gallium oxide, stoichiometry guided the calculation. First, we determined the mass difference between gallium and gallium oxide to find the exact mass of oxygen involved. With stoichiometry, you convert these masses into moles using their respective molar masses:

• Moles of Gallium: Using the mass and molar mass of gallium.
• Moles of Oxygen: Similarly determined using oxygen's mass and molar mass.

The subsequent step is finding the simplest whole number ratio, crucial to deriving the empirical formula. This systematic approach illustrates the straightforward yet powerful nature of stoichiometric calculations in chemistry.

Chemical Reactions

Chemical reactions are transformations where substances convert into entirely new products. These processes are the foundation for understanding everything from simple compounds to modern nanotechnology. In the context of gallium reacting with oxygen to form gallium oxide, we see a direct application of a chemical reaction's principles.

• A chemical reaction involves reactants (gallium and oxygen) reacting under certain conditions to yield products (gallium oxide).
• These reactions can be tracked quantitatively to derive insights like empirical formulas by applying the law of conservation of mass, ensuring mass is the same before and after reaction.

Studying reactions such as the formation of gallium oxide helps in understanding empirical relationships and structural compositions which are vital aspects of chemical research.