Problem 120 - Chemistry The Central Science In Si Units

Question

The gas-phase reaction of NO with \(\mathrm{F}_{2}\) to form NOF and \(\mathrm{F}\) has an activation energy of \(E_{a}=6.3 \mathrm{~kJ} / \mathrm{mol}\). and a frequency factor of \(A=6.0 \times 10^{8} M^{-1} \mathrm{~s}^{-1}\). The reaction is believed to be bimolecular: $$ \mathrm{NO}(g)+\mathrm{F}_{2}(g) \longrightarrow \mathrm{NOF}(g)+\mathrm{F}(g) $$ (a) Calculate the rate constant at \(100^{\circ} \mathrm{C}\). (b) Draw the Lewis structures for the NO and the NOF molecules, given that the chemical formula for NOF is misleading because the nitrogen atom is actually the central atom in the molecule. (c) Predict the shape for the NOF molecule. (d) Draw a possible transition state for the formation of NOF, using dashed lines to indicate the weak bonds that are beginning to form. (e) Suggest a reason for the low activation energy for the reaction.

Step-by-Step Solution

Answer

At 100°C, the rate constant is approximately \(7.9 \times 10^7 \, M^{-1} \mathrm{~s}^{-1}\). NOF is bent, and transition state has weak intermediate bonds. Low activation energy is due to reactive intermediates.

Step 1: Calculate Temperature in Kelvin

To find the rate constant at a particular temperature, we need to convert the temperature from Celsius to Kelvin. Since 1 Celsius degree is equivalent to Kelvin:\[ T(K) = 100 + 273.15 = 373.15 \, K \]

Step 2: Use Arrhenius Equation for Rate Constant

The Arrhenius equation is used to calculate the rate constant, \( k \), given by:\[ k = A e^{-E_a / (R T)} \]where:- \( A = 6.0 \times 10^8 \, M^{-1} \mathrm{~s}^{-1} \)- \( E_a = 6.3 \times 10^3 \, J/mol \) (since \(1 \, \text{kJ} = 1000 \, \text{J} \))- \( R = 8.314 \, J/(mol \, K) \)- \( T = 373.15 \, K \)Plug the values into the formula:\[ k = (6.0 \times 10^8) e^{-6300 / (8.314 \times 373.15)} \]

Step 3: Compute Exponential Factor

Calculate the exponential factor of the Arrhenius equation:\[ -\frac{E_a}{RT} = -\frac{6300}{8.314 \times 373.15} \approx -2.027 \]Then, compute the exponential:\[ e^{-2.027} \approx 0.1316 \]

Step 4: Calculate the Rate Constant k

Substitute the exponential factor calculated into the Arrhenius equation:\[ k = (6.0 \times 10^8) \times 0.1316 \approx 7.896 \times 10^7 \, M^{-1} \mathrm{~s}^{-1} \]

Step 5: Draw Lewis Structures for NO and NOF

For NO, nitrogen and oxygen are bonded with a single bond and nitrogen has one lone pair while oxygen has two lone pairs, considering NO as a radical species. For NOF, nitrogen is the central atom with a double-bond to oxygen and a single bond to fluorine, with one lone pair on nitrogen.

Step 6: Predict Molecular Shape of NOF

NOF has a bent shape due to the lone pair on nitrogen causing repulsion, following VSEPR theory predictions for a steric number of 3 (two bonds, one lone pair).

Step 7: Transition State Structure

To indicate the transition state, draw NOF forming where N is bond to both O and F, depicted with dashed bonds from N to F and N to O to represent bonds in the process of forming and breaking.

Step 8: Reason for Low Activation Energy

The low activation energy might be due to the small difference in bond strength between the reactants and products, and the presence of radical species like NO that can stabilize intermediates, facilitating reaction turnover.

Key Concepts

Arrhenius Equation

Chemical reactions occur more quickly as temperature increases, and this relationship is quantitatively described by the Arrhenius Equation. It provides a way to calculate the rate constant, \( k \), using the formula: \[ k = A e^{-E_a / (R T)} \]. Here, \( A \) is the frequency factor, representing the number of times reactants approach the activation barrier per second. The exponential term \( e^{-E_a / (R T)} \) describes how temperature \( T \) and activation energy \( E_a \) impact reaction rates.

• As temperature (\( T \)) increases, \( k \) also increases, making reactions faster.
• A higher activation energy (\( E_a \)) generally means a slower reaction, as it's harder to overcome the energy barrier.
• The gas constant \( R \) has a value of 8.314 J/(mol K), ensuring consistent units across calculations.

Using this equation, you can determine reaction rates at different temperatures, helping predict how conditions affect the speed of chemical processes.

Activation Energy

Activation energy, denoted as \( E_a \), is the minimum energy required to initiate a chemical reaction. It plays a crucial role in determining the rate at which a reaction proceeds.

• Reactions with low activation energy proceed rapidly since less energy is required to form activated complexes and transition states.
• In the reaction of NO and \( \text{F}_2 \), the low \( E_a \) of 6.3 kJ/mol suggests that the reaction can occur with relatively little effort, implying an accessible energy barrier.
• This is often influenced by the nature of the reactant molecules and the energy released during bond formation in product molecules.

Understanding \( E_a \) is essential for controlling reactions in labs and industrial processes, allowing chemists to manipulate conditions for desired reaction speeds.

Lewis Structures

Lewis structures are diagrams that represent the bonding between atoms within a molecule and the lone pairs of electrons that may exist. They provide insight into molecular structure and help predict geometry and reactivity.

• For nitric oxide (NO), the structure includes a nitrogen and an oxygen atom bonded with a double bond and an unpaired electron, illustrating its radical nature. There's one lone pair on nitrogen and two on oxygen.
• In nitrosyl fluoride (NOF), nitrogen is the central atom. It forms a double bond with oxygen and a single bond with fluorine, with a lone pair remaining on the nitrogen atom. This arrangement supports the formation of a molecule with distinct angular geometry.

Drawing these structures helps in understanding the distribution of electrons and predicting molecular behavior, as the bonding and lone pairs significantly influence the shape and reactivity of molecules.

Molecular Geometry

Molecular geometry is the three-dimensional arrangement of the atoms in a molecule, which is crucial for understanding reactions and properties.

• The shape of a molecule influences its reactivity, polarity, phase of matter, and biological activity.
• NOF, with its single pair of lone electrons on nitrogen, adopts a bent geometry as predicted by the Valence Shell Electron Pair Repulsion (VSEPR) theory. This theory indicates that electron pairs will arrange themselves to minimize repulsion, giving rise to its specific shape.
• This bent shape is typical for molecules with a central atom surrounded by two bonded atoms and one lone pair of electrons (AX2E type).

Molecular geometry is a fundamental concept for chemists as it affects how substances interact at the molecular level, crucial for designing reactions and industrial applications.