Problem 92 - Chemistry and Chemical Reactivity

Question

Chlorine trifluoride, \(\mathrm{ClF}_{3,}\) is a valuable reagent because it can be used to convert metal oxides to metal fluorides: \(6 \mathrm{NiO}(\mathrm{s})+4 \mathrm{ClF}_{3}(\mathrm{g}) \rightarrow\) \(6 \mathrm{NiF}_{2}(\mathrm{s})+2 \mathrm{Cl}_{2}(\mathrm{g})+3 \mathrm{O}_{2}(\mathrm{g})\) (a) What mass of NiO will react with \(\mathrm{ClF}_{3}\) gas if the gas has a pressure of \(250 \mathrm{mm}\) Hg at \(20^{\circ} \mathrm{C}\) in a 2.5 -L flask? (b) If the \(\mathrm{ClF}_{3}\) described in part (a) is completely consumed, what are the partial pressures of \(\mathrm{Cl}_{2}\) and of \(\mathrm{O}_{2}\) in the 2.5 -L flask at \(20^{\circ} \mathrm{C}\) (in mm Hg)? What is the total pressure in the flask?

Step-by-Step Solution

Answer

(a) 3.85 g of NiO; (b) Partial pressures: Cl2 = 125.7 mm Hg, O2 = 188.7 mm Hg; Total pressure = 314.4 mm Hg.

Step 1: Calculate Moles of ClF3

First, use the ideal gas law to calculate the number of moles of \( \mathrm{ClF}_3 \). The ideal gas law is given by \( PV = nRT \), where \( P \) is the pressure, \( V \) is the volume, \( n \) is the moles, \( R \) is the ideal gas constant, and \( T \) is the temperature in Kelvin. Convert \( 20^{\circ} \text{C} \) to Kelvin: \( 273 + 20 = 293 \text{ K} \).Convert mm Hg to atm: \( \frac{250}{760} = 0.3289 \text{ atm} \).Using \( R = 0.0821 \text{ L atm mol}^{-1} \text{ K}^{-1} \):\[ n = \frac{PV}{RT} = \frac{0.3289 \times 2.5}{0.0821 \times 293} \approx 0.0344 \text{ mol} \].

Step 2: Determine Mass of NiO

Based on the stoichiometry of the reaction, \( 4 \text{ moles of } \mathrm{ClF}_3 \) react with \( 6 \text{ moles of } \mathrm{NiO} \). Calculate the moles of \( \mathrm{NiO} \) that will react with the available \( \mathrm{ClF}_3 \):\[\text{Moles of } \mathrm{NiO} = \left(\frac{6}{4}\right) \times 0.0344 = 0.0516 \text{ mol}\].Now, find the mass of \( \mathrm{NiO} \):- Molar mass of \( \mathrm{NiO} \) is approximately \( 58.69 + 16.00 = 74.69 \text{ g/mol} \).Mass of \( \mathrm{NiO} = 0.0516 \times 74.69 \approx 3.85 \text{ g} \).

Step 3: Calculate Partial Pressure of Cl2

According to the stoichiometry, \( 4 \text{ mol of } \mathrm{ClF}_3 \) produce \( 2 \text{ mol of } \mathrm{Cl}_2 \). Calculate the moles of \( \mathrm{Cl}_2 \) formed:\[\text{Moles of } \mathrm{Cl}_2 = \left(\frac{2}{4}\right) \times 0.0344 = 0.0172 \text{ mol}\].Use the ideal gas law to find the pressure of \( \mathrm{Cl}_2 \):\[P = \frac{nRT}{V} = \frac{0.0172 \times 0.0821 \times 293}{2.5} \approx 0.165 \text{ atm}\].Convert to mm Hg: \( 0.165 \times 760 = 125.7 \text{ mm Hg} \).

Step 4: Calculate Partial Pressure of O2

According to the stoichiometry, \( 4 \text{ mol of } \mathrm{ClF}_3 \) produce \( 3 \text{ mol of } \mathrm{O}_2 \). Calculate the moles of \( \mathrm{O}_2 \) formed:\[\text{Moles of } \mathrm{O}_2 = \left(\frac{3}{4}\right) \times 0.0344 = 0.0258 \text{ mol}\].Use the ideal gas law to find the pressure of \( \mathrm{O}_2 \):\[P = \frac{nRT}{V} = \frac{0.0258 \times 0.0821 \times 293}{2.5} \approx 0.248 \text{ atm}\].Convert to mm Hg: \( 0.248 \times 760 = 188.7 \text{ mm Hg} \).

Step 5: Determine Total Pressure in Flask

The total pressure in the flask is the sum of the partial pressures of \( \mathrm{Cl}_2 \) and \( \mathrm{O}_2 \).Total pressure = \( 125.7 + 188.7 = 314.4 \text{ mm Hg} \).

Key Concepts

Stoichiometry

Stoichiometry is a branch of chemistry that deals with the relative quantities of reactants and products in chemical reactions. In the given reaction,

• 6 moles of nickel oxide (\( \text{NiO} \))
• react with 4 moles of chlorine trifluoride (\( \text{ClF}_3 \)) to produce 6 moles of nickel fluoride (\( \text{NiF}_2 \)),
• 2 moles of chlorine gas (\( \text{Cl}_2 \)),
• and 3 moles of oxygen gas (\( \text{O}_2 \)).

Understanding this stoichiometric relationship helps determine how much of each reactant is needed and how much product will be formed.
To solve for the mass of \( \text{NiO} \), use the given moles of \( \text{ClF}_3 \) and the stoichiometric ratio from the balanced equation.
The central idea is that chemical equations can be used like a recipe, showing the proportions in which elements and compounds interact.

Ideal Gas Law

The Ideal Gas Law is a fundamental equation used to relate the pressure, volume, temperature, and number of moles of a gas. The equation \( PV = nRT \), where:

• \( P \) is pressure,
• \( V \) is volume,
• \( n \) is moles,
• \( R \) is the ideal gas constant,
• \( T \) is temperature.

By converting temperatures into Kelvin and pressure into atmospheres, you can calculate the moles of gas in a given sample.
In the problem, this law is used to find out how many moles of \( \text{ClF}_3 \) are available in a 2.5 L flask under specified conditions.
Understanding the Ideal Gas Law is crucial when dealing with gases in chemical reactions, as it allows conversion between the physical properties of gases and the amount present.

Gas Pressure Calculations

When gases are involved in a reaction, it is important to know their partial pressures, as well as the total pressure in a container. Partial pressure is the pressure exerted by a single gas in a mixture of gases, while total pressure is the sum of the partial pressures of all gases present.
Using the Ideal Gas Law, the partial pressures of the resultant gases, \( \text{Cl}_2 \) and \( \text{O}_2 \), are calculated based on their moles produced from the reaction.
For example, after determining the moles of each gas, you can calculate their respective pressures by substituting back into the ideal gas equation.

• For \( \text{Cl}_2 \), you compute the pressure in atm, then convert it to mm Hg for convenience.
• The same process is repeated for \( \text{O}_2 \).

Finally, add these partial pressures to get the total pressure in the flask, providing insight into the gaseous state post-reaction.

Reagents and Reactants

Reagents and Reactants are fundamental to understanding chemical reactions. The terms are related but distinct:

• **Reactants**: substances consumed in the reaction.
• **Reagents**: substances used to cause a chemical reaction, often present in excess or used to target specific transformations.

In our example, \( \text{ClF}_3 \) is the reagent transforming metal oxides like \( \text{NiO} \) into metal fluorides.
This conversion process is a classic example where the roles of reagents and reactants are highlighted.
A comprehensive understanding of these terms helps in predicting the outcomes of reactions and understanding the role each chemical plays in the process.