Question

Transition metals can combine with carbon monoxide (CO) to form compounds such as \(\mathrm{Fe}_{x}(\mathrm{CO})_{y}\) (Study Question 123). Assume that you combine 0.125 g of nickel with CO and isolate \(0.364 \mathrm{g}\) of \(\mathrm{Ni}(\mathrm{CO})_{x} .\) What is the value of \(x ?\)

Short answer

The value of \(x\) is 4.

Step-by-step solution

Determine Molar Mass of Nickel

Nickel (Ni) has an atomic mass of approximately 58.69 g/mol. This will be used to convert the given mass of nickel into moles.

Calculate Moles of Nickel

Convert the mass of nickel into moles using the formula: \[ \text{moles of Ni} = \frac{\text{mass of Ni}}{\text{molar mass of Ni}} = \frac{0.125 \text{ g}}{58.69 \text{ g/mol}} \approx 0.00213 \text{ mol} \]

Determine the Mass of CO in the Compound

Find the mass of CO in the compound by subtracting the mass of nickel from the mass of the complex:\[ \text{mass of CO} = 0.364 \text{ g} - 0.125 \text{ g} = 0.239 \text{ g} \]

Determine Molar Mass of CO

Carbon monoxide (CO) has a molar mass of approximately 28.01 g/mol.

Calculate Moles of CO

Convert the mass of CO into moles using its molar mass:\[ \text{moles of CO} = \frac{\text{mass of CO}}{\text{molar mass of CO}} = \frac{0.239 \text{ g}}{28.01 \text{ g/mol}} \approx 0.00853 \text{ mol} \]

Determine Molar Ratio of CO to Ni

The ratio of moles of CO to moles of Ni gives the value of \(x\):\[ x = \frac{0.00853 \text{ mol CO}}{0.00213 \text{ mol Ni}} \approx 4 \]

Key concepts

Nickel Carbonyl

Nickel carbonyl is a highly unique transition metal compound, which forms when nickel combines with carbon monoxide (CO). This compound is notable for its formation at room temperature, where nickel, a solid metal, reacts with gaseous carbon monoxide to create a volatile and potentially toxic metallic compound.
These kinds of metal carbonyls typically appear as colorless gases or yellow to brown colored liquids, depending on their state at room temperature.
Nickel carbonyl in particular is used in some industrial processes, especially in the purification and refinement of nickel, due to its volatility allowing easy separation and decomposition.

• Nickel reacts with CO to form nickel carbonyl, often represented as \(\text{Ni(CO)}_x\), where \(x\) refers to the number of CO molecules attached.
• This compound is illustrative of the broader family of metal carbonyls, which share the characteristic of transition metal bonds with carbon monoxide.

Understanding the composition and properties of nickel carbonyl is crucial, especially because it showcases the versatility of transition metals in complex chemical bonding and reactions.

Mole Calculations

Mole calculations are essential in chemistry to determine the amount of substances involved in reactions. They help bridge the gap between the mass of a substance and the number of particles or molecules it contains. In the context of determining nickel carbonyl composition, mole calculations allow us insight into the exact ratio of nickel to carbon monoxide in the compound.

Begin by finding the moles of each individual component. For instance, to calculate the moles of nickel, use the formula:\[\text{moles of Ni} = \frac{\text{mass of Ni}}{\text{molar mass of Ni}}\]This calculation transforms the given mass of nickel into its molar equivalent.

• The moles of nickel serve as a base to determine how many moles of CO have combined with it.
• Similarly, to find the moles of CO, the mass of CO derived from its separation from the final compound is used to perform calculations.

For example, if 0.125 g of nickel were used, converting it to moles, and comparing with the moles of CO, which is calculated from subtracting nickel’s weight from the compound's total weight, gives insight into the proportion of nickel and CO present. This proportion directly helps us understand "\(x\)", the number of CO molecules bonded to nickel.

Chemical Formulas

Chemical formulas convey a wealth of information about the composition and structuring of compounds. In the case of metal carbonyls, particularly nickel carbonyl, the formula \(\text{Ni(CO)}_x\) indicates the ratio of nickel to carbon monoxide within the molecule.

To derive this formula accurately, understanding both the qualitative and quantitative aspects is key:

• A chemical formula like \(\text{Ni(CO)}_x\) implies structural information about the compound, where \(x\) represents the number of CO ligands coordinator to the central nickel atom.
• This formula helps visualize how a transition metal like nickel can seamlessly integrate CO into its coordination sphere.

Calculating the formula involves determining the molar amounts of each component separately, as demonstrated in mole calculations, and then deriving the simplest integer ratio to represent the compound explicitly. Once we know the exact number of CO molecules per atom of nickel, we can write or understand the chemical formula \(\text{Ni(CO)}_4\), reflecting that four CO molecules attach to each nickel atom.