Question

Hydrogen cyanide is produced industrially by the following exothermic reaction: $$2{\mathrm{NH}}_3(g)+3{\mathrm{O}}_2(g)+2{\mathrm{CH}}_4(g)⟶2\mathrm{HCN}(g)+6{\mathrm{H}}_2\mathrm{O}(g)$$ Is the high temperature needed for thermodynamic or kinetic reasons?

Short answer

The high temperature needed for hydrogen cyanide production in the given exothermic reaction is primarily for kinetic reasons. Since the reaction is not thermodynamically favored at high temperatures, the high temperature is required to increase the reaction rate, enabling faster production of hydrogen cyanide at an industrial scale.

Step-by-step solution

Understand the effect of temperature on reaction rates

For most chemical reactions, increasing the temperature increases the reaction rate. This is because higher temperatures lead to a higher average kinetic energy of the reacting molecules, which results in more successful collisions between them. The increased reaction rate is generally described by the Arrhenius equation: $k=A{e}^{\frac{-E_a}{RT}}$, where k is the rate constant, A is the pre-exponential factor, Ea is the activation energy, R is the gas constant, and T is the temperature in Kelvin. Clearly, as the temperature increases, the rate constant k increases, leading to faster reactions.

Understand the effect of temperature on equilibrium constants

Temperature also affects equilibrium constants (K) of reactions. For exothermic reactions ($\Delta H<0$), increasing the temperature reduces the equilibrium constant, meaning the reaction shifts toward the reactants. On the other hand, for endothermic reactions ($\Delta H>0$), increasing the temperature increases the equilibrium constant, favoring the products. This is described by the Van't Hoff equation: $\frac{d\ln K}{dT}=\frac{\Delta H°}{R\cdot T^2}$.

Analyze the given reaction

The industrial production of hydrogen cyanide is given by the exothermic reaction: $2{\mathrm{NH}}_3(g)+3{\mathrm{O}}_2(g)+2{\mathrm{CH}}_4(g)⟶2\mathrm{HCN}(g)+6{\mathrm{H}}_2\mathrm{O}(g)$. Since this reaction is exothermic, increasing the temperature should result in a lower equilibrium constant and shift the reaction toward the reactants according to thermodynamics. This implies that the high temperature needed for this process is not for thermodynamic reasons.

Determine the dominant reason

Since the reaction is not favored by high temperatures for thermodynamic reasons, we can conclude that the high temperature needed for hydrogen cyanide production is primarily for kinetic reasons. High temperature increases the reaction rate, enabling faster production of hydrogen cyanide at an industrial scale.

Key concepts

Activation Energy

Activation energy is the minimum energy required for a chemical reaction to occur. Think of it as the energy barrier that the reactants need to overcome to transform into products. In a reaction, molecules must collide with sufficient energy to allow the rearrangement of their chemical bonds. The energy required for these successful collisions is what we call activation energy.

It plays a crucial role in determining the speed or rate of a chemical reaction. The higher the activation energy, the slower the reaction since fewer molecules have enough energy to overcome this barrier. Understanding activation energy helps us manipulate reactions to occur at desired rates by altering conditions, such as temperature.

Arrhenius Equation

The Arrhenius Equation highlights how temperature and activation energy affect the rate of a reaction. It is expressed as: $$k=A{e}^{\frac{-E_a}{RT}}$$ Where:

• $k$ is the rate constant of the reaction.
• $A$ is the pre-exponential factor or frequency factor, related to the frequency of collisions.
• $E_a$ is the activation energy.
• $R$ is the universal gas constant.
• $T$ is the temperature in Kelvin.

The Arrhenius Equation indicates that a higher temperature will increase the rate constant $k$ because it reduces the magnitude of $e^{\frac{-E_a}{RT}}$.

Consequently, the reaction proceeds more quickly as the number of molecules with energy greater than the activation energy increases.

Exothermic Reaction

Exothermic reactions release energy, usually in the form of heat, as they proceed. In other words, they release more energy by forming products than what is required to break the reactants. This is why these reactions can often seem self-sustaining once started. A common everyday example is the combustion of fuels, which releases heat energy.

In the case of the hydrogen cyanide production reaction, it is exothermic because it releases energy, indicated by a negative change in enthalpy ($\Delta H<0$). This type of reaction will typically have a lower equilibrium position at increased temperatures due to the effect on equilibrium constants, shifting towards the reactants.

Equilibrium Constant

The equilibrium constant ($K$) measures the ratio of products to reactants at equilibrium for a given reaction. It tells us which side of the reaction is favored. For an exothermic reaction, the equilibrium constant decreases with an increase in temperature. This is described by the Van't Hoff equation: $$\frac{d\ln K}{dT}=\frac{\Delta H°}{R\cdot T^2}$$ Exothermic reactions have $\Delta H<0$, leading to $K$ decreasing with rising temperatures.

As a result, the equilibrium position shifts towards the reactants. This means that at higher temperatures, less product is favored, which can influence the reaction conditions needed industrially.

Temperature Effect on Reactions

Temperature dramatically influences chemical reactions. As temperature increases, molecular motion and kinetic energy also increase. This results in more frequent and energetic collisions, thereby increasing the reaction rate.

High temperature can be crucial for overcoming large activation energy barriers, enhancing the likelihood of success for each collision. This kinetic perspective is essential for processes like the industrial production of hydrogen cyanide, where the reaction rate is key to practical applications.

However, while it accelerates reaction rates, increasing temperature might not always be thermodynamically favorable, especially for exothermic reactions, where the equilibrium constant will decrease, shifting the balance towards the reactants.