Problem 43 - Chemistry and Chemical Reactivity

Question

Nickel forms a compound with carbon monoxide, \(\mathrm{Ni}_{x}(\mathrm{CO})_{r}\). To determine its formula, you carefully heat a 0.0973 -g sample in air to convert the nickel to \(0.0426 \mathrm{g}\) of NiO and the CO to \(0.100 \mathrm{g}\) of \(\mathrm{CO}_{2} .\) What is the empirical formula of \(\mathrm{Ni}_{x}(\mathrm{CO})_{y} ?\)

Step-by-Step Solution

Answer

The empirical formula is \( \text{Ni(CO)}_4 \).

Step 1: Determine Moles of Ni

First, calculate the moles of Ni in the NiO produced. The molar mass of NiO is approximately 74.69 g/mol (Ni: 58.69 g/mol, O: 16 g/mol). Use the formula \( n = \frac{m}{M} \) where \( m \) is mass and \( M \) is molar mass.\[ \text{Moles of NiO} = \frac{0.0426 \text{ g}}{74.69 \text{ g/mol}} \approx 5.70 \times 10^{-4} \text{ mol} \]Since each mol of NiO contains exactly one mol of Ni, the moles of Ni are also approximately \( 5.70 \times 10^{-4} \text{ mol} \).

Step 2: Determine Moles of CO2

Next, we calculate moles of \( \text{CO}_2 \) produced. The molar mass of \( \text{CO}_2 \) is approximately 44.01 g/mol.\[ \text{Moles of } \text{CO}_2 = \frac{0.100 \text{ g}}{44.01 \text{ g/mol}} \approx 2.27 \times 10^{-3} \text{ mol} \]

Step 3: Determine Moles of CO

Since \( \text{CO}_2 \) production comes from \( \text{CO} \), and \( \text{CO} \) converts to \( \text{CO}_2 \) in a 1:1 molar ratio (1 mol of \( \text{CO} \) gives 1 mol of \( \text{CO}_2 \)), there are also \( 2.27 \times 10^{-3} \text{ mol} \) of \( \text{CO} \).

Step 4: Determine Empirical Formula

Use the mole ratio to find the empirical formula of \( \text{Ni}_x(\text{CO})_y \). The ratio of moles is\[ \frac{5.70 \times 10^{-4}}{5.70 \times 10^{-4}} : \frac{2.27 \times 10^{-3}}{5.70 \times 10^{-4}} \approx 1 : 4 \]Thus, the empirical formula is \( \text{Ni(CO)}_4 \).

Key Concepts

Nickel Carbonyl

Nickel carbonyl, known scientifically as tetracarbonylnickel, is a fascinating compound with the formula \( \text{Ni(CO)}_4 \). This compound features nickel, a silvery metal, tightly bonded with carbon monoxide molecules. This arrangement results in a volatile compound often used in nickel refining and purification.
Nickel carbonyl is notable for its ability to form quickly at room temperature, yet decomposes readily when heated. Due to its volatility and toxic nature, handling it requires precise safety measures.

• It exemplifies the concept of organometallic chemistry, where metals form stable bonds with organic ligands like CO.
• The Ni-CO bond is characterized by a overlap between nickel's orbitals and the orbitals of CO, facilitating its unique stability.
• Naturally formed at low temperatures, this compound is used industrially in nickel production.

The study of nickel carbonyl helps underscore the importance of understanding molecular interactions and the impact these interactions have on compound properties and applications.

Chemical Reactions

Chemical reactions describe the transformation of substances into new products with different properties. In the context of nickel carbonyl, a significant chemical reaction occurs when it is heated in air:
The nickel reverts to its oxide form (\( \text{NiO} \)), and the carbon monoxide is converted to carbon dioxide (\( \text{CO}_2 \)). This transformation is an example of an oxidation reaction, a type of chemical reaction where substances combine with oxygen.
The reaction can be succinctly described by the equation:

• Conversion of \( \text{Ni(CO)}_4 \) to \( \text{NiO} \) releases carbon monoxide, followed by its oxidation to \( \text{CO}_2 \).
• This two-step process highlights not only the reactivity of nickel carbonyl but the sequential nature of reactions.

Understanding these reactions is crucial as it illustrates basic principles such as conservation of mass, stoichiometry, and chemical equilibrium. It also holds practical importance, especially in industrial processes and pollution control.

Mole Calculation

Mole calculations play a fundamental role in chemistry, allowing us to relate the measured mass of substances to the number of atoms or molecules present in a sample. The mole is a standard unit used to quantify amounts in chemistry, aligning perfectly with Avogadro's number, \( 6.022 \times 10^{23} \) units/mole.
In our problem, mole calculation was key to determining the empirical formula of nickel carbonyl. By knowing the mass of the products, \( \text{NiO} \) and \( \text{CO}_2 \), solutions were calculated by converting these masses into moles:

• The moles of \( \text{Ni} \) from \( \text{NiO} \) were determined by dividing by NiO's molar mass.
• Similarly, the moles of \( \text{CO} \) were obtained using the mass of \( \text{CO}_2 \) due to their stoichiometric relationship.

From these calculations, we can deduce the precise ratio of elements, leading directly to the empirical formula. Mastering mole calculations allows chemists to perform more complex quantitative analysis with ease, making them indispensable in scientific research and industrial applications.

Stoichiometry

Stoichiometry is the area of chemistry that quantifies the relationships within chemical reactions. It is founded on the conservation of mass principle, demanding a balanced representation of the reaction, where the number of atoms for every element must be equal on both sides.
In determining the empirical formula of \( \text{Ni(CO)}_4 \), stoichiometry was used to set up the mole ratios of nickel to carbon monoxide. By dividing the moles of each element by the smallest number of moles calculated, a simple ratio was established:

• For each reaction mass, the same precision allowed us to determine the smallest integer ratio.
• This ratio pinpointed the empirical formula reflecting the smallest whole number of atoms in the compound.

This exercise exemplifies fundamental stoichiometric calculations by finding a balanced equation that mirrors the simplest molecular formula possible. Understanding these concepts is crucial not only for academic learning but also for practical chemical problem-solving encountered in various fields of research and industry.