Chapter 8: Problem 52

When ammonia reacts with dinitrogen oxide gas ( \(\Delta H_{\mathrm{f}}^{\circ}=82.05 \mathrm{~kJ} / \mathrm{mol}\) ), liquid water and nitrogen gas are formed. How much heat is liberated or absorbed by the reaction that produces \(345 \mathrm{~mL}\) of nitrogen gas at \(25^{\circ} \mathrm{C}\) and \(717 \mathrm{~mm} \mathrm{Hg}\) ?

### Short Answer

## Step by step solution

## Calculate the moles of nitrogen gas produced

## Stoichiometry and moles of dinitrogen oxide gas reacted

## Calculate the heat liberated or absorbed

## Key Concepts

These are the key concepts you need to understand to accurately answer the question.

###### Understanding the Ideal Gas Law

Here's a breakdown of each variable:

- \( P \) is the pressure of the gas. We convert the pressure from mmHg to atm for consistency with the gas constant R, which is given in L atm / mol K.
- \( V \) stands for volume, usually expressed in liters in this equation. In our case, we convert the volume of nitrogen gas from milliliters to liters.
- \( n \) symbolizes the number of moles, which we are solving for in this particular exercise.
- \( R \) is the ideal gas constant, which has a value of 0.0821 L atm / mol K for the purposes of this equation.
- \( T \) represents temperature in Kelvin, so we must convert Celsius to Kelvin by adding 273.15.

###### The Role of Stoichiometry in Chemical Reactions

The stoichiometric coefficients in the balanced equation tell us the proportions in which the reactants combine and the products form, making it possible to convert between moles of one substance to moles of another. For this problem, we use stoichiometry to find the moles of dinitrogen oxide that reacted, based on the moles of nitrogen gas produced.

Here's the critical point:

- For every mole of nitrogen gas produced, one mole of dinitrogen oxide is consumed, as shown in the balanced equation.

###### Calculating the Enthalpy of Reaction

For our exercise, the enthalpy of formation specifically refers to the dinitrogen oxide gas and tells us how much energy is involved in its formation from its constituent elements under standard conditions (1 atm pressure and 25°C). The value can be either positive or negative, indicating endothermic and exothermic reactions, respectively.

By multiplying the moles of dinitrogen oxide reacted by its enthalpy of formation, we calculate the total heat (enthalpy change) for the reaction under our given conditions. This step is crucial to understanding the energy exchange in the reaction and is a direct application of Hess's Law, which allows us to add the enthalpy changes of individual steps in a reaction sequence to find the overall enthalpy change.