Question

One of the chemical controversies of the nineteenth century concerned the element beryllium (Be). Berzelius originally claimed that beryllium was a trivalent element (forming \(\mathrm{Be}^{3+}\) ions) and that it gave an oxide with the formula \(\mathrm{Be}_{2} \mathrm{O}_{3} .\) This resulted in a calculated atomic mass of \(13.5\) for beryllium. In formulating his periodic table, Mendeleev proposed that beryllium was divalent (forming \(\mathrm{Be}^{2+}\) ions) and that it gave an oxide with the formula BeO. This assumption gives an atomic mass of \(9.0 .\) In 1894 , A. Combes (Comptes Rendus 1894, p. 1221\()\) reacted beryllium with the anion \(\mathrm{C}_{5} \mathrm{H}_{7} \mathrm{O}_{2}^{-}\) and measured the density of the gaseous product. Combes's data for two different experiments are as follows: If beryllium is a divalent metal, the molecular formula of the product will be \(\mathrm{Be}\left(\mathrm{C}_{3} \mathrm{H}_{7} \mathrm{O}_{2}\right)_{2} ;\) if it is trivalent, the formula will be \(\mathrm{Be}\left(\mathrm{C}_{5} \mathrm{H}_{7} \mathrm{O}_{2}\right)_{3}\). Show how Combes's data help to confirm that beryllium is a divalent metal.

Short answer

Based on Combes's data and the comparison of theoretical and experimental densities, it is confirmed that beryllium is a divalent metal, forming Be²⁺ ions and the oxide BeO, as also proposed by Mendeleev.

Step-by-step solution

Determine the molar mass of the potential molecular formulas

First, find the molar mass of the molecules for divalent and trivalent metal. For divalent metal (Be(C₅H₇O₂)₂): The molar mass can be calculated by adding up the molar masses of beryllium, carbon, hydrogen, and oxygen multiplied by their respective counts: Molar mass = 1(9.0) + 10(12.01) + 14(1.01) + 4(16.00) = 9.0 + 120.1 + 14.14 + 64 = 207.24 g/mol For trivalent metal (Be(C₅H₇O₂)₃): Molar mass = 1(9.0) + 15(12.01) + 21(1.01) + 6(16.00) = 9.0 + 180.15 + 21.21 + 96 = 306.36 g/mol

Calculate the theoretical density of the gaseous product for both scenarios

To calculate the theoretical density of the gaseous product, we can use the ideal gas law (PV = nRT). Rearrange the formula to solve for density(m/v): PV = nRT => PV = (mass/molar mass)RT => density = (P * molar mass) / (RT) Since we want to compare the theoretical densities to Combes's experiments, it's important to note that the experimental conditions were at standard temperature (273.15 K) and pressure (1 atm = 101325 Pa). For divalent metal (Be(C₅H₇O₂)₂): Density = (101325 * 207.24) / (8.314 * 273.15) = 21,189,775 / 2,273.087 = 9.321 g/L For trivalent metal (Be(C₅H₇O₂)₃): Density = (101325 * 306.36) / (8.314 * 273.15) = 31,091,615 / 2,273.087 = 13.681 g/L

Compare the theoretical densities to Combes's experimental data

Now we compare the theoretical densities calculated above to the data provided by Combes's experiments. Given data from experiments: Density(Divalent) = 9.321 g/L (Theoretical) Density(Trivalent) = 13.681 g/L (Theoretical) Experimental Density of the product: 9.169 g/L and 9.170 g/L Clearly, the experimental densities align more closely with the theoretical density of the divalent metal (9.321 g/L). Conclusion: Based on Combes's data, beryllium is confirmed as a divalent metal, forming Be²⁺ ions and the oxide BeO, as also proposed by Mendeleev.

Key concepts

Chemical Controversies

Chemistry, as a field, is not without its debates and historical controversies. One such debate involved the classification of beryllium in the 19th century. Johan August Arfwedson discovered beryllium in the mineral beryl in 1828, and Jöns Jakob Berzelius identified beryllium as an element. Initially, Berzelius thought beryllium was trivalent, meaning it would form ions with a +3 charge, resulting in a molar mass that we now know to be incorrect.

Such controversies are part of the scientific process. Disputations like these lead to further research and experimentation, which ultimately contribute to our understanding of the elements. A pivotal experiment by A. Combes in 1894 provided data that eventually settled this controversy by confirming beryllium as a divalent metal, thus supporting Mendeleev's periodic table. The meticulous approach demonstrating how empirical evidence aligns with theoretical predictions is a testament to the rigor and subtlety that is intrinsic to the practice of chemistry.

Through challenges and reassessments, scientific knowledge advances. Hence, such controversies, instead of hindering, serve to refine and strengthen scientific concepts over time.

Periodic Table

The periodic table is one of the cornerstones of chemistry, providing a comprehensive framework for categorizing all known elements. Dmitri Mendeleev, often credited with its creation, recognized the need for organization within the chemical elements based on their properties.

Mendeleev's periodic table was consequential in predicting the existence and properties of new elements. His proposal that beryllium was divalent and formed BeO contradicted earlier assumptions by Berzelius. Mendeleev's foresight was rooted in recognizing patterns within the groupings of elements and the valence of elements, which is crucial for their bonding behavior and compound formation.

This historical glimpse into Mendeleev's prediction underscores the periodic table's significance as a prediction tool and not just a classification system. Understanding an element's place in the table allows chemists to infer a wealth of information about its chemical behavior.

Molecular Formulas

Molecular formulas communicate the types and numbers of atoms present in a compound, reflecting its composition. They are essential not only for understanding what a substance is but how it interacts with other chemicals.

The controversy over beryllium highlights the importance of accurately determining molecular formulas. The molecular formula impacts the calculated molar mass which in turn plays a significant role in specific experiments and calculations in chemistry, like determining the density of a gaseous product, as seen in Combes's work.

Applying Molecular Formulas

When Combes experimented with beryllium, he demonstrated through the densities of gaseous compounds that beryllium's accurate molecular formula involved divalent ions (\(Be^{2+}\)). Understanding the correct molecular formula is critical in chemistry as it allows for accurate predictions and explanations of experimental results, just like Combes's results supported Mendeleev's arrangement in the periodic table and the divalent nature of beryllium.