Question

\(\mathrm{Ni}(\mathrm{CO})_{4}\) can be made by reacting finely divided nickel with gaseous CO. If you have \(\mathrm{CO}\) in a 1.50-L flask at a pressure of \(418 \mathrm{mm}\) Hg at \(25.0^{\circ} \mathrm{C},\) along with \(0.450 \mathrm{g}\) of \(\mathrm{Ni}\) powder, what is the theoretical yield of \(\mathrm{Ni}(\mathrm{CO})_{4} ?\)

Short answer

The theoretical yield of \(\mathrm{Ni(CO)}_4\) is 1.31 grams.

Step-by-step solution

Write the Balanced Chemical Equation

The reaction between nickel (Ni) and carbon monoxide (CO) to form nickel carbonyl is given by the balanced chemical equation: \[ \mathrm{Ni} + 4\mathrm{CO} \rightarrow \mathrm{Ni(CO)}_4. \] This equation shows that one mole of nickel reacts with four moles of carbon monoxide to form one mole of nickel carbonyl.

Calculate Moles of CO

Use the ideal gas law to find the moles of CO. The ideal gas equation is \( PV = nRT \). First, convert the pressure from mm Hg to atm: \[ 418 \text{ mm Hg} \times \frac{1 \text{ atm}}{760 \text{ mm Hg}} = 0.550 \text{ atm}. \] Now, use the ideal gas law: \[ n = \frac{PV}{RT} = \frac{(0.550 \text{ atm})(1.50 \text{ L})}{(0.0821 \text{ L atm/mol K})(298 K)} \approx 0.0337 \text{ moles of CO}. \]

Calculate Moles of Ni

Calculate the moles of nickel using its molar mass. Nickel has a molar mass of 58.69 g/mol: \[ n = \frac{0.450 \text{ g}}{58.69 \text{ g/mol}} \approx 0.00767 \text{ moles of Ni}. \]

Determine Limiting Reactant

The balanced equation shows that 1 mole of Ni reacts with 4 moles of CO. We have 0.0337 moles of CO, which could react with \( \frac{1}{4} \times 0.0337 \approx 0.00843 \text{ moles of Ni} \). Since we have only 0.00767 moles of Ni, Ni is the limiting reactant.

Calculate Theoretical Yield of Ni(CO)₄

Since Ni is the limiting reactant, use its mole amount to find the yield of Ni(CO)₄. From the balanced equation, 1 mole of Ni gives 1 mole of Ni(CO)₄: \[ \text{Moles of } \mathrm{Ni(CO)}_4 = 0.00767 \text{ moles}. \] Convert this to grams using the molar mass of Ni(CO)₄, which is \(58.69 + 4(12.01 + 16.00)\) g/mol = 170.73 g/mol: \[ 0.00767 \text{ moles} \times 170.73 \text{ g/mol} = 1.31 \text{ g}. \]

Key concepts

Ideal Gas Law

The Ideal Gas Law is a fundamental equation that relates the pressure, volume, temperature, and amount of a gas. This equation is expressed as \( PV = nRT \), where:

• \( P \) stands for pressure, typically measured in atmospheres (atm).
• \( V \) is the volume, usually measured in liters (L).
• \( n \) represents the number of moles of gas.
• \( R \) is the ideal gas constant, and its value is \(0.0821 \text{ L atm/mol K}\).
• \( T \) is the absolute temperature in Kelvin (K).

To solve problems involving gases, it's crucial to first convert all units to align with the equation. For instance, pressure should be converted from mm Hg to atm by using the conversion \(1 \text{ atm} = 760 \text{ mm Hg}\). Calculating the moles of gas involves rearranging the equation to \( n = \frac{PV}{RT} \). This equation provides a comprehensive understanding of how gases will behave under different conditions.

Limiting Reactant

In a chemical reaction, the Limiting Reactant is the substance that is completely used up first, and thus limits the amount of product that can be formed. Understanding this concept is crucial for predicting the theoretical yield of a reaction. To identify the limiting reactant:

• Calculate the moles of each reactant present in the reaction using their respective molar masses.
• Use the balanced chemical equation to determine the stoichiometric ratio between reactants and products.
• Compare the actual mole ratios from your calculations to the ratio dictated by the balanced equation.

The limiting reactant is the one that satisfies the stoichiometric needs first, leading to the cessation of the reaction. By focusing on the limiting reactant, we can determine the maximum amount of product that can be generated during the reaction. It serves as a practical application of stoichiometry in real-world chemical calculations.

Stoichiometry

Stoichiometry is the branch of chemistry that deals with the quantitative relationships between reactants and products in a chemical reaction. It originates from the balanced chemical equation, which shows the proportion of moles involved in the chemical transformation. Here’s a simple breakdown of stoichiometry:

• Write the balanced chemical equation for the reaction.
• Use the coefficients in the equation to understand how many moles of one substance react or produce how many moles of another substance.
• Apply these ratios to convert between moles of different substances in the reaction.

Stoichiometry is essential in predicting how much product will be formed or what reactants will be needed in excess. This systematic approach helps chemists scale reactions for laboratory or industrial purposes. By mastering stoichiometry, one can efficiently plan and utilize resources in chemical reactions.

Nickel Carbonyl

Nickel Carbonyl, with the formula \( \text{Ni(CO)}_4 \), is a volatile and liquid compound at room temperature. It is a good example of a coordination compound formed between nickel and carbon monoxide.This compound is noteworthy due to its historical and industrial significance in nickel refining via the Mond process. It is formed when nickel reacts with carbon monoxide in a well-defined stoichiometric ratio depicted by the equation:\[ \text{Ni} + 4\text{CO} \rightarrow \text{Ni(CO)}_4 \].Characteristics of Nickel Carbonyl include:

• It is highly toxic and must be handled with extreme care.
• It is used in chemical vapor deposition processes to produce high-purity nickel coatings or films.
• Its volatility is an important factor in its role in industrial processes.

Understanding Nickel Carbonyl is essential for those looking into nickel's industrial applications and comprehensive chemical synthesis. It highlights the intersection of practical applications and theoretical chemistry.