Problem 37 - Chemistry and Chemical Reactivity

Question

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

Step-by-Step Solution

Answer

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

Step 1: Determine moles of Nickel in NiO

To find the moles of Ni, use the mass of NiO produced. \( \text{Molar mass of NiO} = 58.69 + 16.00 = 74.69 \, \text{g/mol} \). Calculate moles of NiO: \[ 0.0426 \text{ g NiO} \times \frac{1 \text{ mol NiO}}{74.69 \text{ g}} = 0.000570 \text{ mol NiO} \]Because there is one mole of Ni in each mole of NiO, \( \text{moles of Ni} = 0.000570 \text{ mol} \).

Step 2: Determine moles of Carbon in CO2

Find the moles of CO2 from its mass. \( \text{Molar mass of CO2} = 12.01 + 2 \times 16.00 = 44.01 \, \text{g/mol} \).Calculate moles of CO2: \[ 0.100 \text{ g CO2} \times \frac{1 \text{ mol CO2}}{44.01 \text{ g}} = 0.00227 \text{ mol CO2} \]Since each molecule of CO2 has one atom of Carbon, the moles of C are \( 0.00227 \text{ mol} \).

Step 3: Calculate moles of Oxygen in CO2 and NiO

We already have the moles of Ni from NiO, but we have to calculate the moles of CO (from the original compound) using the carbon and remaining oxygen in CO2. Since all the carbon in CO is converted to CO2, the moles of oxygen in CO2 from the compound are also \( 0.00227 \text{ mol} \).

Step 4: Calculate the moles of original compound using CO

Each CO molecule has one C and one O. Since moles of carbon are \( 0.00227 \), moles of CO = 0.00227. So in the original compound, moles of CO were \( 0.00227 \).

Step 5: Determine the simplest whole number ratio

Divide the moles of each element by the smallest number of moles, which is 0.000570 (moles of Ni):For Ni: \( \frac{0.000570}{0.000570} = 1 \)For C: \( \frac{0.00227}{0.000570} \approx 4 \)The simplest ratio is Ni:C = 1:4, implying the compound empirical formula is \( \text{Ni}( ext{CO})_4 \).

Key Concepts

Nickel Carbonyl

Nickel carbonyl, or tetracarbonyl nickel, is a chemical compound composed of nickel and carbon monoxide. It is often represented as \(\text{Ni}(\text{CO})_4 \), signifying a nickel atom bonded to four carbon monoxide ligands. Understanding this compound is critical due to its importance in industrial applications, such as nickel purification processes, where it’s often utilized because of its unique properties to decompose into pure nickel and carbon monoxide under controlled conditions. Additionally, nickel carbonyl is noted for its toxicity and volatility, necessitating careful handling and containment measures during its handling. Knowledge of its empirical formula is essential for working safely and effectively with nickel carbonyl in any practical context. This ensures proper safety protocols can be established and maintain environmental health.

Moles Calculation

Mastering moles calculation is a foundational skill in chemistry, essential for understanding how substances interact at a molecular level. Moles act as a bridge between the visible world and the atomic scale, allowing us to quantify substances in a meaningful way. Calculating moles involves determining the number of moles from a given mass using the formula: \[ \text{moles} = \frac{\text{mass}}{\text{molar mass}} \] For instance, in the exercise, to find moles of \( \text{Ni} \) and \( \text{CO}_2 \), you need to apply this formula using the given masses and molar masses. This practice ensures accurate measurement in experiments and facilitates predicting the outcomes of reactions. By mastering these calculations, students develop a critical understanding of quantitative chemical relationships essential in scientific research and applied chemistry fields.

Chemical Formulas

Chemical formulas succinctly convey information about the kinds and quantities of atoms in a compound. They are vital tools in chemistry, representing chemical compounds in a standardized way. For example, in nickel carbonyl \( \text{Ni}(\text{CO})_4 \), the formula indicates one nickel atom bonded to four carbon monoxide molecules. Understanding how to derive a chemical formula involves determining the moles of each constituent element and identifying the simplest ratio, as seen with nickel and carbon monoxide in this exercise.

The importance of chemical formulas includes:

• Predicting the behavior and interaction of substances during chemical reactions.
• Providing a universal language for scientists to communicate compositions easily.
• Enabling the quantitative analysis of compounds, which is crucial in chemical engineering and product development.

Molar Mass

Molar mass is a critical concept that refers to the mass of one mole of a substance, usually given in grams per mole. It is derived by summing the atomic masses of the elements in a compound as found on the periodic table. In practical terms, molar mass allows chemists to convert between the mass of a substance and the amount in moles, which is a common requirement in chemical analysis and reaction predictions. For the compounds in the exercise, calculating the molar mass of \( \text{NiO} \) and \( \text{CO}_2 \) was essential to determine the moles of each element present:

• Calculate molar mass of \( \text{NiO} \) by adding the atomic masses of Nickel (58.69 g/mol) and Oxygen (16.00 g/mol) to arrive at 74.69 g/mol.
• For \( \text{CO}_2 \), add Carbon (12.01 g/mol) and twice the Oxygen to obtain 44.01 g/mol.

Understanding molar mass is key to engaging effectively in quantitative chemical experiments and ensuring precise and meaningful data results.