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 \(C_{5} \mathrm{H}_{7} \mathrm{O}_{2}^{-}\) and measured the density of the gaseous product. Combes's data for two different experiments are as follows: $$\begin{array}{lll}{\text { Mass }} & {0.2022 \mathrm{g}} & {0.2224 \mathrm{g}} \\ {\text { Volume }} & {22.6 \mathrm{cm}^{3}} & {26.0 \mathrm{cm}^{3}} \\ {\text { Temperature }} & {13^{\circ} \mathrm{C}} & {17^{\circ} \mathrm{C}} \\ {\text { Pressure }} & {765.2 \mathrm{mm} \mathrm{Hg}} & {764.6 \mathrm{mm}}\end{array}$$ If beryllium is a divalent metal, the molecular formula of the product will be \(\mathrm{Be}\left(\mathrm{C}_{5} \mathrm{H}_{7} \mathrm{O}_{2}\right)_{2} ;\) 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

Using the Ideal Gas Law and the experimental data provided, we calculated the molar mass of the gaseous product for both experiments. Comparing these molar masses with the expected molar masses for divalent (\(\mathrm{Be}\left(\mathrm{C}_{5} \mathrm{H}_{7} \mathrm{O}_2\right)_2\)) and trivalent (\(\mathrm{Be}\left(\mathrm{C}_{5} \mathrm{H}_{7} \mathrm{O}_2\right)_3\)) formulas, we found that the calculated molar mass is closer to the divalent formula. This confirms that beryllium is a divalent metal.

Step-by-step solution

Convert the data to appropriate units

We need to convert the given data to the appropriate units to use in the Ideal Gas Law equation. 1. Volume: Convert cm³ to L 2. Temperature: Convert Celsius to Kelvin 3. Pressure: Convert mmHg to atm

Calculate the number of moles using the Ideal Gas Law equation

Using the converted data, plug the values into the Ideal Gas Law equation and solve for the number of moles (n) for both experiments.

Calculate the molar mass of the gaseous product from both experiments

Divide the mass (in g) by the number of moles (in mol) to get the molar mass of the gaseous product for both experiments.

Deduce the valency of beryllium

Using the molar mass of the gaseous product, deduce if beryllium is divalent or trivalent. For divalent formula, \(\mathrm{Be}\left(\mathrm{C}_{5} \mathrm{H}_{7} \mathrm{O}_2\right)_2\), molar mass: \(1 \times M_{\mathrm{Be}} + 2 \times M_{\mathrm{C_5H_7O_2}}\) For trivalent formula, \(\mathrm{Be}\left(\mathrm{C}_{5} \mathrm{H}_{7} \mathrm{O}_2\right)_3\), molar mass: \(1 \times M_{\mathrm{Be}} + 3 \times M_{\mathrm{C_5H_7O_2}}\) Where: - \(M_{\mathrm{Be}}\) is the molar mass of beryllium - \(M_{\mathrm{C_5H_7O_2}}\) is the molar mass of the anion \(\mathrm{C_5H_7O_2^-}\) Compare the calculated molar mass of the gaseous product with the divalent and trivalent formulas and determine which one is closer to the actual data. This will help confirm if beryllium is divalent or trivalent.

Key concepts

Valency of Beryllium

The valency of an element refers to its ability to combine with other elements, i.e., the number of bonds it can form. For beryllium, there was a debate in the 19th century on whether it is trivalent or divalent.

• Berzelius, an early chemist, thought beryllium was trivalent, represented by the ion \(\mathrm{Be}^{3+}\), due to early experimental data.
• Mendeleev, famous for his periodic table, believed it was divalent with a \(\mathrm{Be}^{2+}\) ion based on revised observations.

The experiment reported by A. Combes in 1894 involved measuring the density of a gaseous compound of beryllium to resolve this discrepancy. By comparing calculated molar masses for both divalent and trivalent compounds of beryllium with actual experimental data, chemists deduced that beryllium is indeed divalent. This means beryllium typically forms two bonds, aligning with modern chemistry's understanding of its position in the periodic table.

Molar Mass Calculation

Calculating the molar mass involves determining the mass of one mole of a substance, a fundamental concept in chemistry. It is pivotal in verifying the valency of beryllium from Combes's experiment.

• Mass: Take the mass of the gaseous product measured in grams.
• Moles: Use the Ideal Gas Law to find the moles present in the measured gas volume.

Using the formula, \(\text{Molar Mass} = \frac{\text{Mass (g)}}{\text{Moles (mol)}}\), the molar mass for the product from each experiment was ascertained.These values were crucial in comparing the theoretical molar mass values calculated for divalent \((\text{\(\mathrm{Be(C_5H_7O_2)_2}\))})\) and trivalent \((\text{\(\mathrm{Be(C_5H_7O_2)_3}\))})\) formulations, finally affirming beryllium's divalent nature.

Ideal Gas Law

The Ideal Gas Law is an equation of state for a hypothetical ideal gas. It's expressed as \(PV = nRT\), where:

• \(P\): pressure (in atm)
• \(V\): volume (in liters)
• \(n\): number of moles
• \(R\): ideal gas constant (0.0821 L·atm/mol·K)
• \(T\): temperature (in Kelvin)

Before applying this formula, data from Combes's experiments was converted to the correct units:- Volume from cm³ to liters (1 L = 1000 cm³)- Temperature from Celsius to Kelvin (\(K = ^\circ C + 273.15\))- Pressure from mmHg to atm (1 atm = 760 mmHg)Substituting these values into the Ideal Gas Law allowed chemists to solve for \(n\), the number of moles. With the moles calculated, the molar mass of the product was computable, aiding in the determination of beryllium's valency.

Periodic Table History

The periodic table is a tabular arrangement of chemical elements, ordered by their atomic number, electron configuration, and recurring chemical properties. The history behind it reveals evolutionary strides in chemistry, particularly in understanding element valency.

• Dmitri Mendeleev is credited for creating the first widely recognized periodic table in 1869.
• He organized elements by increasing atomic mass and grouped elements with similar properties together.

Mendeleev's table predicted the properties of new elements and corrected known data, such as the atomic mass and valency of beryllium, showcasing its divalent nature. This periodic table laid the groundwork for modern chemistry, allowing scientists to foresee undiscovered elements and resolve ongoing controversies, including the beryllium controversy. This systematic arrangement continues to be a fundamental tool in both educational and professional chemistry settings.