Question

A historian discovers a nineteenth-century notebook in which some observations, dated 1822 , on a substance thought to be a new element, were recorded. Here are some of the data recorded in the notebook: Ductile, silverwhite, metallic looking. Softer than lead Unaffected by water. Stable in air. Melting point: \(153^{\circ} \mathrm{C}\) Density: \(7.3 \mathrm{~g} / \mathrm{cm}^{3} .\) Electrical conductivity: \(20 \%\) that of copper. Hardness. About \(1 \%\) as hard as iron. When \(4.20 \mathrm{~g}\) of the unknown is heated in an excess of oxygen, \(5.08 \mathrm{~g}\) of a white solid is formed. The solid could be sublimed by heating to over \(800^{\circ} \mathrm{C}\). (a) Using information in the text and a handbook of chemistry, and making allowances for possible variations in numbers from current values, identify the element reported. (b) Write a balanced chemical equation for the reaction with oxygen. (c) Judging from Figure 7.2, might this nineteenth- century investigator have been the first to discover a new element?

Short answer

The unknown element's properties closely match that of Indium (In) based on a chemistry handbook. The balanced chemical equation for the reaction with oxygen is \(4 \mathrm{~In} + 3 \mathrm{~O}_2 \rightarrow 2 \mathrm{~In}_2\mathrm{O}_3\). The 19th-century investigator might have discovered Indium before it was officially recognized in 1863, but further historical data and analysis would be required to confirm this.

Step-by-step solution

Match the properties of the element with a chemistry handbook

To identify the element, we need to find an element that matches the properties described in the text. The properties are as follows: - Ductile, silver-white, metallic looking. - Softer than lead. - Unaffected by water. - Stable in air. - Melting point: \(153^\circ \mathrm{C}\). - Density: \(7.3 \mathrm{~g} / \mathrm{cm}^3\). - Electrical conductivity: \(20\%\) that of copper. - About \(1\%\) as hard as iron. Looking up these properties in a chemistry handbook, we find that the element closely matches the properties of Indium (In). #Part B: Writing a balanced chemical equation for the reaction with oxygen#

Determine the empirical formula of the white solid

We are given that 4.20 grams of the unknown element (Indium) reacts with an excess of oxygen to form 5.08 grams of a white solid. To find the empirical formula of the product, we need to find the moles of oxygen that reacted with Indium. First, we find the moles of Indium: Moles of Indium = \(\frac{4.20 \mathrm{~g}}{114.82 \mathrm{~g/mol}} = 0.0366 \mathrm{~mol}\) Next, we find the mass of oxygen in the product: Mass of Oxygen = Total mass of the product - Mass of Indium = \(5.08 \mathrm{~g} - 4.20 \mathrm{~g} = 0.88 \mathrm{~g}\) Now, we find the moles of oxygen in the product: Moles of Oxygen = \(\frac{0.88 \mathrm{~g}}{16.00 \mathrm{~g/mol}} = 0.0550 \mathrm{~mol}\) Finally, we find the mole ratio of Indium to Oxygen: Mole Ratio = \(\frac{0.0366 \mathrm{~mol}}{0.0550 \mathrm{~mol}} = 0.665\) Since the ratio closest to the fraction is \(2:3\), the empirical formula of the white solid is \(In_2O_3\).

Write the balanced chemical equation

Now that we have established the empirical formula of the product, we can write the balanced chemical equation: \(4 \mathrm{~In} + 3 \mathrm{~O}_2 \rightarrow 2 \mathrm{~In}_2\mathrm{O}_3\) #Part C: Evaluating the possibility of the first discovery of a new element#

Examine historical data on the discovery of elements

To determine whether the 19th-century investigator could have been the first to discover a new element, we need to look at historical data from Figure 7.2 (or similar sources), which represent each element's discovery date. We then look at the discovery date of Indium. Indium was discovered in 1863. Since the notebook with the recorded observations is dated to 1822, the investigator might have discovered Indium before it was officially recognized. However, it is important to verify this statement with more information and data from other sources.

Key concepts

Chemical Properties

Chemical properties describe the behavior and characteristics of a substance in chemical reactions. They determine how an element interacts with other substances. Let's delve into Indium's specific chemical properties based on the clues provided in the exercise:

• **Ductility** refers to an element's ability to be stretched into a wire. Indium is known to be ductile and can be easily shaped.
• **Metallic appearance** indicates that Indium has a shiny surface, common among metals.
• **Reactivity** with water and stability in air show that Indium does not oxidize or react vigorously with water or oxygen at room temperature, which is reflective of its stable nature.
• **Melting point (153°C)** reveals how temperature affects Indium's state change from solid to liquid. It melts at a relatively low temperature compared to other metals.
• **Density (7.3 g/cm³)** signifies how closely packed Indium’s atoms are in its solid state, adding to its weight despite being softer than lead.
• **Electrical conductivity (20% of copper)** provides a measure of its ability to conduct electricity, which is moderate compared to highly conductive metals like copper.
• **Hardness (1% of iron's hardness)** helps us understand that Indium is soft and malleable.

These properties collectively guide the identification of Indium as the likely element in question.

Empirical Formula

The empirical formula of a compound provides the simplest integer ratio of the atoms present. To find this formula for the white solid formed from Indium, we use the provided mass data.

First, we calculated the number of moles of Indium by dividing its mass by its molar mass. Then, we did the same for the mass of oxygen that combined with it. By comparing the number of moles of each element, we derived the simplest ratio.

The exercise revealed that the reaction ended up with a white solid composed of Indium and Oxygen, simplifying to the formula \(In_2O_3\).

The calculation pathway was:

• Find moles of Indium: \( \frac{4.20 \,g}{114.82 \,g/mol} = 0.0366 \,mol \)
• Calculate moles of Oxygen: From the leftover mass of \(0.88 \,g\) oxygen: \( \frac{0.88 \,g}{16.00 \,g/mol} \approx 0.0550 \,mol \)
• Determine mole ratio: \( \frac{0.0366}{0.0550} \approx 0.665 \rightarrow 2:3 \)

The empirical formula helps in understanding the composition of the compound that Indium forms with oxygen by reflecting the simplest whole number ratio of their elements.

Reaction with Oxygen

Chemical reactions often involve elements bonding with oxygen, a process called oxidation. For Indium, this involves forming compounds that are represented in a balanced chemical equation.

From the exercise, we determined the reaction of Indium with oxygen using the empirical formula \(In_2O_3\). We confirmed the reaction balanced as follows:

\[4 \mathrm{In} + 3 \mathrm{O}_2 \rightarrow 2 \mathrm{In}_2\mathrm{O}_3\]

Here, each side of the equation has equal numbers of each type of atom, reflecting the law of conservation of mass.

This equation shows that four moles of Indium atoms react with three moles of oxygen molecules to create two moles of the Indium oxide compound. This illustrates the characteristic reaction of metals with oxygen, often forming metal oxides. It highlights the pathway of Indium transitioning from pure metal to a compound by gaining oxygen.

Historical Discovery

The discovery of elements involves piecing together various historical records and scientific observations. In analyzing the historical context provided in the exercise, we focus on whether the unknown substance was discovered before its official recognition.

The mentioned notebook is dated 1822, while Indium is documented to have been discovered in 1863. This suggests that the investigator might have indeed stumbled upon Indium early, preceding its formal discovery by 41 years.

In light of this, historical discoveries often rely on leveraging both written accounts and physical evidence from experiments. Such documents reflect preliminary work that might not have been widely acknowledged at the time.

Determining an element’s historical discovery involves:

• Reviewing dated references and experimental notes.
• Cross-referencing known discovery timelines from archives or scientific literature.
• Ensuring chemical properties match the element in question.

While the investigator appears to have discovered the properties and reactions of what we now know as Indium, official recognition was only achieved later, illustrating that sometimes scientific discoveries remain unrecognized until further validated.