Problem 121 - Chemistry: An Atoms-Focused Approach

Question

In a high-temperature gas-phase reaction, methanol \(\left(\mathrm{CH}_{3} \mathrm{OH}\right)\) reacts with \(\mathrm{N}_{2}\) to produce \(\mathrm{HCN}\) and \(\mathrm{NH}_{3}\). The reaction is endothermic, requiring \(164 \mathrm{kJ}\) of thermal energy per mole of methanol under standard conditions. a. Write a balanced chemical equation for this reaction. b. Is energy a reactant or a product? c. What is the change in enthalpy under standard conditions if \(60.0 \mathrm{g}\) of \(\mathrm{CH}_{3} \mathrm{OH}(g)\) reacts with excess \(\mathrm{N}_{2}(g),\) forming \(\mathrm{HCN}(g),\) and \(\mathrm{NH}_{3}(g) ?\)

Step-by-Step Solution

Answer

Question: Calculate the change in enthalpy under standard conditions for a high-temperature gas-phase reaction involving 60.0 g of methanol and nitrogen, if the reaction requires 164 kJ of energy per mole of methanol and is endothermic. Answer: The change in enthalpy under standard conditions for 60.0 g of methanol reacting with nitrogen is 306.98 kJ.

Step 1: Write a balanced chemical equation

In this step, identify the reactants and products and balance the chemical equation. The reactants are methanol (CH3OH) and nitrogen (N2), and the products are hydrogen cyanide (HCN) and ammonia (NH3). Balancing the equation gives: $$CH_{3}OH + N_{2} \rightarrow HCN + NH_{3}$$

Step 2: Determine if energy is a reactant or a product

The problem states that the reaction is endothermic, which means it requires 164 kJ of thermal energy per mole of methanol. Since the reaction is endothermic, it requires energy to proceed, so energy is a reactant in this reaction.

Step 3: Calculate the change in enthalpy for 60.0 g of CH3OH(g)

To find the change in enthalpy, use the provided information that the reaction requires 164 kJ of energy per mole of methanol. First, find the moles of methanol reacting. The molar mass of methanol is \(12.01 + 4(1.01) + 16.00 = 32.05\, g/mol\). To find the moles of methanol, divide the given mass by its molar mass: $$moles\,of\, methanol =\frac{60.0\,g}{32.05\,g/mol} = 1.872\, mol$$ Now, since there is 164 kJ of energy required per mole of methanol, multiply the moles of methanol by 164 kJ to find the change in enthalpy: $$\Delta H = (1.872\, mol \, methanol) \times (164\, kJ/mol\, methanol) = 306.98\, kJ$$ So, the change in enthalpy under standard conditions for 60.0 g of methanol reacting with excess nitrogen is 306.98 kJ.

Key Concepts

Balanced Chemical Equation

In chemical reactions, a balanced equation is crucial because it shows the relationship between reactants and products. It ensures that the number of atoms for each element is the same on both sides of the equation. This is rooted in the law of conservation of mass, where matter cannot be created or destroyed. Let's consider our example: the reaction of methanol \(\text{CH}_3\text{OH}\) with nitrogen gas \(\text{N}_2\) to form hydrogen cyanide \(\text{HCN}\) and ammonia \(\text{NH}_3\). When we balance this equation:\[\text{CH}_3\text{OH} + \text{N}_2 \rightarrow \text{HCN} + \text{NH}_3}\]We see that each type of atom (carbon, hydrogen, nitrogen, and oxygen) has the same count on both sides of the reaction, satisfying the conservation of mass. Steps to Balance:

• Identify the number of atoms in reactants and products.
• Adjust coefficients to get equal numbers of each type on both sides.
• Review to ensure all atoms are balanced and make sense with the law of conservation of mass.

Now we've successfully balanced the chemical equation for our endothermic reaction!

Enthalpy Change

Enthalpy change \((\Delta H)\) is a measure of the heat absorbed or released during a chemical reaction under constant pressure. For our reaction involving methanol, the process is endothermic, meaning it absorbs heat from the surroundings. The enthalpy change here is indicated as \(164 \, \text{kJ/mol}\) for methanol. In exothermic reactions, heat is released and \(\Delta H\) is negative. But since this reaction absorbs energy, \(\Delta H\) is positive.This energy absorption is crucial because it indicates the reaction needs an external energy source to proceed, classifying it into endothermic processes where energy is essential as a reactant. You can think of this energy as fuel that sustains the reaction. In summary, endothermic reactions show a positive enthalpy change, meaning they require more energy than they release—an interesting contrast to the typically more spontaneous exothermic reactions.

Moles Calculation

The concept of moles is an important one in chemistry, allowing scientists to count entities like atoms or molecules using a standard unit. A mole represents \(6.022 \times 10^{23}\) of something, usually atoms, molecules, or ions. In our scenario, we calculate moles of methanol \((\text{CH}_3\text{OH})\) involved in the reaction to determine how much energy the reaction will require. Given \(60.0 \, g\) of methanol and its molar mass as \(32.05 \, g/mol\), we determine the moles by dividing the mass by the molar mass:\[\text{moles} = \frac{60.0 \, \text{g}}{32.05 \, \text{g/mol}} = 1.872 \, \text{mol}\]Once you find the number of moles, you can calculate the total enthalpy change by multiplying the number of moles by the energy per mole (\(164 \, \text{kJ/mol}\) here). This provides the overall energy change in the reaction:\[\Delta H = (1.872 \, \text{mol}) \times (164 \, \text{kJ/mol}) = 306.98 \, \text{kJ}\]This kind of calculation is fundamental when analyzing reactions' energy needs or outputs, especially in the context of industrial processes or energy resource management.