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Chapter 5: Problem 33

Enthalpy Changes Nitrogen monoxide, a gas recently found to be involved in a wide range of biological processes, reacts with oxygen to give brown \(\mathrm{NO}_{2}\) gas. $$ \begin{aligned} 2 \mathrm{NO}(\mathrm{g})+\mathrm{O}_{2}(\mathrm{g}) \rightarrow & 2 \mathrm{NO}_{2}(\mathrm{g}) \\ \Delta_{r} H^{\circ} &=-114.1 \mathrm{kJ} / \mathrm{mol}-\mathrm{pxn} \end{aligned} $$ Is this reaction endothermic or exothermic? What is the enthalpy change if \(1.25 \mathrm{g}\) of \(\mathrm{NO}\) is converted completely to \(\mathrm{NO}_{2} ?\)

Short Answer

Expert verified
The reaction is exothermic. The enthalpy change for 1.25 g of NO is approximately -2.378 kJ.

Step by step solution

01

Determine Reaction Type

First, examine the given standard enthalpy change of the reaction, \(\Delta_r H^{\circ} = -114.1\, \text{kJ/mol-pxn}\). A negative sign indicates that the reaction releases energy, meaning it is an exothermic reaction.
02

Find Molar Mass of NO

Calculate the molar mass of nitrogen monoxide (NO). Nitrogen (N) has an atomic mass of approximately 14.01 amu, and oxygen (O) has an atomic mass of about 16.00 amu. Therefore, the molar mass of NO is \(14.01 + 16.00 = 30.01\, \text{g/mol}\).
03

Calculate Moles of NO in 1.25 g

To find the number of moles of NO in 1.25 g, use the formula: \(\text{moles} = \text{mass} / \text{molar mass}\). Thus, \[ \text{moles of NO} = \frac{1.25\, \text{g}}{30.01\, \text{g/mol}} \approx 0.04165\, \text{mol}. \]
04

Compute Enthalpy Change for 1.25 g of NO

The reaction given is for 2 moles of NO leading to \(\Delta_r H^{\circ} = -114.1\, \text{kJ/mol-pxn}\). For 0.04165 moles of NO, since the reaction releases \(-114.1\, \text{kJ}\) for every 2 moles, calculate the enthalpy change as: \[ \Delta H = 0.04165\, \text{mol} \times \frac{-114.1\, \text{kJ/mol}}{2\, \text{mol}} \approx -2.378\, \text{kJ}. \]

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Key Concepts

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

Exothermic Reactions
An exothermic reaction is a chemical process that releases energy, typically in the form of heat, to its surroundings. When you are dealing with such reactions, you often notice a temperature increase in the surrounding environment. This is because energy is leaving the reaction.
Some key characteristics of exothermic reactions include:
  • They have a negative enthalpy change (\( \Delta H < 0 \)), meaning that the energy of the products is less than that of the reactants.
  • They often occur spontaneously because releasing energy is a favorable process.
  • Combustion, for instance, is a common example of an exothermic reaction.
In the case of the reaction between nitrogen monoxide and oxygen forming nitrogen dioxide, the reaction is exothermic. This deduction is supported by the negative enthalpy change (\(\Delta_{r} H^{\circ} = -114.1 \text{kJ/mol-pxn}\)), indicating the release of energy.
Molar Mass Calculation
Calculating molar mass is a foundational skill in chemistry, essential for converting between grams and moles. This involves summing the atomic masses of all the atoms in a molecular formula.
For nitrogen monoxide (NO), the calculation proceeds as follows:
  • Nitrogen (N) has an atomic mass of about 14.01 amu.
  • Oxygen (O) has an atomic mass of about 16.00 amu.
  • Thus, the molar mass of NO is the sum of these two values: \(14.01 + 16.00 = 30.01 \text{g/mol}\).
Understanding molar mass is crucial when performing unit conversion in chemical reactions, such as determining how many moles a given mass corresponds to. This step is critical when calculating reaction yields or enthalpy changes for specific amounts of reactants.
Reaction Enthalpy Calculation
The enthalpy change of a reaction provides insight into whether the process absorbs or releases energy. Calculating the enthalpy change for specific amounts of reactants is a common task in thermochemistry.
In this scenario, calculating the enthalpy change involves:
  • Knowing the reaction's enthalpy change per mole, given as \(\Delta_{r} H^{\circ} = -114.1 \text{kJ/mol-pxn}\).
  • Determining the molar quantity of a reactant, here 1.25 g of NO is used.
  • Calculating the number of moles using the formula: \(\text{moles} = \frac{\text{mass}}{\text{molar mass}}\).
  • The moles of NO calculated are approximately 0.04165 mol.
    Since the enthalpy change applies to 2 moles, we divide the total enthalpy release by this factor to find: \(\Delta H = 0.04165 \times \frac{-114.1}{2} \approx -2.378 \text{kJ}\).
This calculation shows the specific energy change when 1.25 g of NO reacts under standard conditions.
Nitrogen Monoxide Reactions
Nitrogen monoxide (NO) is a colorless gas and plays essential roles in various chemical and biological processes. It is notably reactive with oxygen, leading to the formation of nitrogen dioxide (NO\(_2\)). The reaction can be described as follows:\[ 2 \text{NO}(g) + \text{O}_2(g) \rightarrow 2 \text{NO}_2(g)\]
Nitrogen monoxide's environmental and health impacts include:
  • Contributing to air pollution and forming smog when reacted with other atmospheric components.
  • Playing a role in biological systems, acting as a signaling molecule in the body, for example, in vasodilation.
  • Its reaction with oxygen is exothermic, releasing substantial energy as described by the reaction's enthalpy change.
Understanding the behavior and reactions of nitrogen monoxide is crucial in both chemistry and environmental sciences due to its widespread implications.

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Most popular questions from this chapter

The specific heat capacity of copper metal is \(0.385 \mathrm{J} / \mathrm{g} \cdot \mathrm{K} .\) How much energy is required to heat 168 g of copper from \(-12.2^{\circ} \mathrm{C}\) to \(+25.6^{\circ} \mathrm{C} ?\)

You want to heat the air in your house with natural gas \(\left(\mathrm{CH}_{4}\right) .\) Assume your house has \(275 \mathrm{m}^{2}\) (about \(2800 \mathrm{ft}^{2}\) ) of floor area and that the ceilings are \(2.50 \mathrm{m}\) from the floors. The air in the house has a molar heat capacity of \(29.1 \mathrm{J} / \mathrm{mol} \cdot \mathrm{K}\). (The number of moles of air in the house can be found by assuming that the average molar mass of air is \(28.9 \mathrm{g} / \mathrm{mol}\) and that the density of air at these temperatures is \(1.22 \mathrm{g} / \mathrm{L} .\) ) What mass of methane do you have to burn to heat the air from \(15.0^{\circ} \mathrm{C}\) to \(22.0^{\circ} \mathrm{C} ?\)

In the lab, you plan to carry out a calorimetry experiment to determine \(\Delta_{r} H\) for the exothermic reaction of \(\mathrm{Ca}(\mathrm{OH})_{2}(\mathrm{s})\) and \(\mathrm{HCl}(\mathrm{aq}) .\) Predict how each of the following will affect the calculated value of \(\Delta_{t} H .\) (The value calculated for \(\Delta_{i} H\) for this reaction is a negative value so choose your answer from the following: \(\Delta, H\) will be too low [that is, a larger negative valuel, \(\Delta_{r} H\) will be unaffected, \(\Delta_{r} H\) will be too high [that is, a smaller negative value].) (a) You spill a little bit of the \(\mathrm{Ca}(\mathrm{OH})_{2}\) on the benchtop before adding it to the calorimeter. (b) Because of a miscalculation, you add an excess of HCl to the measured amount of \(\mathrm{Ca}(\mathrm{OH})_{2}\) in the calorimeter. (c) \(\mathrm{Ca}(\mathrm{OH})_{2}\) readily absorbs water from the air. The \(\mathrm{Ca}(\mathrm{OH})_{2}\) sample you weighed had been exposed to the air prior to weighing and had absorbed some water. (d) After weighing out \(\mathrm{Ca}(\mathrm{OH})_{2},\) the sample sat in an open beaker and absorbed water. (e) You delay too long in recording the final temperature. (f) The insulation in your coffee-cup calorimeter was poor, so some energy as heat was lost to the surroundings during the experiment. (g) You have ignored the fact that energy as heat also raised the temperature of the stirrer and the thermometer in your system.

Chloromethane, \(\mathrm{CH}_{3} \mathrm{Cl},\) arises from microbial fermentation and is found throughout the environment. It is also produced industrially, is used in the manufacture of various chemicals, and has been used as a topical anesthetic. How much energy is required to convert \(92.5 \mathrm{g}\) of liquid to a vapor at its boiling point, \(-24.09^{\circ} \mathrm{C} ?\) (The heat of vaporization of \(\mathrm{CH}_{3} \mathrm{Cl}\) is \(21.40 \mathrm{kJ} / \mathrm{mol} .\) )

A Three \(45-g\) ice cubes at \(0^{\circ} \mathrm{C}\) are dropped into \(5.00 \times 10^{2} \mathrm{mL}\) of tea to make iced tea. The tea was initially at \(20.0^{\circ} \mathrm{C} ;\) when thermal equilibrium was reached, the final temperature was \(0^{\circ} \mathrm{C}\) How much of the ice melted, and how much remained floating in the beverage? Assume the specific heat capacity of tea is the same as that of pure water.
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