Question

In the laboratory you combine 0.125 g of nickel with CO and isolate 0.364 g of \(\mathrm{Ni}(\mathrm{CO})_{x}\) What is the value of \(x ?\)

Short answer

The value of \(x\) is 4.

Step-by-step solution

Write down the chemical equation

The chemical reaction for the formation of nickel carbonyl can be represented as \( ext{Ni} + x ext{CO} ightarrow ext{Ni(CO)}_x \). Here, we need to determine the value of \(x\), which is the number of carbon monoxide molecules coordinated with one nickel atom.

Calculate the moles of nickel

Convert the mass of nickel to moles using its molar mass. Nickel has a molar mass of approximately 58.69 g/mol. Thus, the number of moles of nickel is: \( \text{moles of Ni} = \frac{0.125 ext{ g}}{58.69 ext{ g/mol}} \approx 0.00213 ext{ moles} \).

Determine the moles of Ni(CO)_x formed

Convert the mass of \( ext{Ni(CO)}_x \) to moles using its molar mass, which is \( 58.69 ext{ g/mol} + x imes 28.01 ext{ g/mol} \) where 28.01 g/mol is the molar mass of CO. So, \( 0.00213 ext{ moles of } ext{Ni} ightarrow 0.00213 ext{ moles of } ext{Ni(CO)}_x \), since reaction produces a 1:1 mole ratio.

Set up an equation to find x

Use the molar mass of \( ext{Ni(CO)}_x \) to find \(x\): \( 58.69 + x imes 28.01 = \frac{0.364 ext{ g}}{0.00213 ext{ moles}} \approx 170.89 \text{ g/mol} \).

Solve for x

Now solve the equation for \(x\): \( 58.69 + 28.01x = 170.89 \). Rearranging gives \( 28.01x = 170.89 - 58.69 = 112.20 \). Divide both sides by 28.01 to find \(x\): \( x = \frac{112.20}{28.01} \approx 4 \).

Key concepts

Chemical Equations

Chemical equations are symbolic representations used to describe chemical reactions. The reactive molecules, called reactants, are converted into products. In a chemical equation, these conversions are represented using chemical symbols. Reactants are displayed on the left side, while products appear on the right.
In our specific problem, the chemical equation involves nickel (Ni) and carbon monoxide (CO) reacting to form nickel carbonyl, denoted as \(\text{Ni(CO)}_x\).

The general form of the equation is:

• \( \text{Ni} + x\, \text{CO} \longrightarrow \text{Ni(CO)}_x \)

Here, \(x\) represents the number of carbon monoxide molecules attached to one nickel atom. Chemical equations must be balanced, meaning the number of atoms for each element must be equal on both sides of the equation. This is a key concept in stoichiometry, which helps us understand how reactants transform into products.

Molar Mass

Molar mass is a critical concept in stoichiometry, essentially acting as the bridge between the mass of a compound and the amount in moles. It is the mass of one mole of a substance, usually expressed in grams per mole (g/mol).
Atoms and molecules each have distinct molar masses, aiding in the conversion of grams to moles in chemical calculations.

In our exercise, the molar mass of nickel (Ni) is approximately 58.69 g/mol. Additionally, carbon monoxide (CO) has a molar mass of 28.01 g/mol. Thus, for nickel carbonyl \( \text{Ni(CO)}_x \), its molar mass is calculated as:

• 58.69 g/mol (for Ni) + \(x \times\) 28.01 g/mol (for CO)

Understanding and using molar mass is essential for solving the exercise accurately, helping predict how much product is formed based on the reactants used.

Mole Calculations

Mole calculations are fundamental when dealing with chemical reactions. The mole is a basic unit in chemistry that represents a quantity of 6.022 x 10²³ particles, which could be atoms, molecules, or ions.
Calculating moles involves using the relationship between a substance's mass and its molar mass.

In this exercise, we first find the number of moles of nickel by dividing its mass by its molar mass:

• \( \text{moles of Ni} = \frac{0.125 \text{ g}}{58.69 \text{ g/mol}} \approx 0.00213 \text{ moles} \)

Since the reaction between Ni and CO produces nickel carbonyl in a 1:1 mole ratio, we can use the same number of moles to estimate the moles of the resulting \( \text{Ni(CO)}_x \). Mole calculations enable us to determine the stoichiometry of a reaction, indicating the proportions of reactants and predicting the amount of product.

Nickel Carbonyl

Nickel carbonyl, chemically represented as \( \text{Ni(CO)}_x \), is a coordination compound formed by nickel and carbon monoxide. This compound is an example of a metal carbonyl, where carbon monoxide molecules are bound to a transition metal.
Nickel carbonyl has significant industrial importance and intriguing properties. It is widely used in the nickel refining process through a method called "carbonyl process," where it facilitates the extraction and purification of nickel.

In the exercise, we needed to identify \(x\), the number of carbon monoxide molecules bound to a nickel atom. This was achieved using stoichiometry and mole calculations, allowing us to deduce that \(x = 4\). Hence, the chemical formula for the compound formed is nickel tetracarbonyl—\( \text{Ni(CO)}_4 \), a stable and volatile organometallic compound. Understanding nickel carbonyl's formation is vital for insights into coordination chemistry and industrial applications.