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The following equation shows how nitrogen dioxide reacts with water to produce nitric acid: $$ 3 \mathrm{NO}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(l) \longrightarrow 2 \mathrm{HNO}_{3}(l)+\mathrm{NO}(g) $$ Predict the sign of \(\Delta S^{\circ}\) for this reaction.

Short Answer

Expert verified
\(\Delta S^{\circ}\) is expected to be negative due to decreased gas and increased liquid states.

Step by step solution

01

Identify the Reactants and Products

The reaction equation shows that the reactants are 3 moles of nitrogen dioxide \(\mathrm{NO}_2(g)\) and 1 mole of water \(\mathrm{H}_2\mathrm{O}(l)\), resulting in the production of 2 moles of nitric acid \(\mathrm{HNO}_3(l)\) and 1 mole of nitrogen monoxide \(\mathrm{NO}(g)\).
02

Determine the Phase State Change

Note the phase states of reactants and products: Reactants include 3 moles of gas and 1 mole of liquid, while the products comprise 2 moles of liquid and 1 mole of gas.
03

Assess the Change in Molecular Complexity and Phase

Since the reaction goes from having 3 moles of gaseous \(\mathrm{NO}_2\) to only 1 mole of gaseous \(\mathrm{NO}\), gas molecules are reduced, implying decreased disorder, or entropy. The increase in liquid moles, from 1 to 2, also tends to decrease entropy in gaseous to liquid transitions.
04

Predict the Sign of \\(\Delta S^{\circ}\\)

Since the overall system transitions from having more gaseous molecules to having more liquid molecules and fewer overall particles, the entropy change \(\Delta S^{\circ}\) is expected to be negative.

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Key Concepts

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

Phase changes
Phase changes, or transitions between different states of matter, play a crucial role in understanding chemical reactions. In the context of the chemical reaction provided, we observe molecules in gaseous and liquid phases. A gas to liquid transition, as seen with the reactants and products, usually results in a decrease in entropy—or disorder—of the system.
When nitrogen dioxide (NO2) is in its gaseous form and reacts to form liquid nitric acid (HNO3), the molecules move from a highly disordered gaseous state to a more ordered liquid state.
This transition typically decreases the randomness of the molecules.
  • Gases have higher entropy due to their free movement.
  • Liquids have a lower entropy because of intermolecular attractions that restrict movement.
Therefore, evaluating phase changes in a chemical reaction helps in predicting the behavior of the system's entropy.
Entropy
Entropy refers to the degree of disorder or randomness in a system. Within a chemical reaction, changes in entropy ( extDelta S o) are significant for understanding how the system's energy is dispersed.
In this specific reaction of nitrogen dioxide reacting with water to form nitric acid, we see a decrease in entropy.
This is because more gaseous molecules are converted into liquid molecules.
  • Reactions that result in fewer gas molecules typically have a decrease in entropy.
  • Similarly, transitioning from gas to liquid also often indicates a decrease in entropy.
The overall trend in such reactions indicates that the disorder of the system is reduced, leading to a negative extDelta S o. This means the products are less disordered compared to the reactants.
Nitrogen dioxide
Nitrogen dioxide (NO2) is a reddish-brown gas with a characteristic sharp and biting odor. It is a significant component in atmospheric chemistry and plays an essential role in forming pollutants such as smog.
In our reaction scenario, NO2 is a reactant combining with water to produce nitric acid.
Understanding NO2's properties as a gas helps predict the changes in entropy described in the reaction.
  • NO2 molecules in the gas phase contribute to higher disorder compared to liquids.
Moving from a state containing three moles of gaseous NO2 leads to decreased entropy when forming products with fewer gas moles. Recognizing the behavior of NO2 in reactions is fundamental for predicting reaction outcomes, especially in industrial applications and environmental systems.
Nitric acid production
Nitric acid (HNO3) production from nitrogen dioxide involves reacting NO2 with water, yielding a more stable liquid product along with gaseous nitrogen monoxide.
The reaction represents an essential process within industrial chemistry—and it's crucial for producing fertilizers, explosives, and other chemicals. In the given reaction:
3NO2(g) + H2O(l) → 2HNO3(l) + NO(g)
  • Nitric acid appears as a liquid product, which increases the complexity compared to its gaseous reactants.
  • Gaseous products are minimized in consideration of overall entropy changes.
Producing nitric acid with fewer gas moles means a reduction in disorder, aligning with the predicted negative entropy change. This practical chemical transformation highlights the concepts of phase and entropy changes in a real-world scenario.

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Most popular questions from this chapter

What is a spontaneous process? Give three examples of spontaneous processes. Give three examples of nonspontaneous processes.

\( K_{s p}\) for silver chloride at \(25.0^{\circ} \mathrm{C}\) is \(1.782 \times 10^{-10}\) At \(35.0^{\circ} \mathrm{C}, K_{s p}\) is \(4.159 \times 10^{-10} .\) What are \(\Delta H^{\circ}\) and \(\Delta S^{\circ}\) for the reaction?

a. Calculate \(K_{1}\) at \(25^{\circ} \mathrm{C}\) for phosphoric acid: \(\mathrm{H}_{3} \mathrm{PO}_{4}(a q) \rightleftharpoons \mathrm{H}^{+}(a q)+\mathrm{H}_{2} \mathrm{PO}_{4}^{-}(a q)\) $$ \begin{array}{cccc} & \boldsymbol{H}_{3} \boldsymbol{P O}_{4}(\mathrm{aq}) & \boldsymbol{H}^{+}(\mathrm{aq}) & \boldsymbol{H}_{2} \boldsymbol{P O}_{4}^{-}(\mathrm{aq}) \\ \Delta H_{f}^{\circ}(\mathrm{kJ} / \mathrm{mol}) & -1288.3 & 0 & -1285 \\ S^{\circ}(\mathrm{J} / \mathrm{mol} \cdot \mathrm{K}) & 158.2 & 0 & 89 \end{array} $$ b. Which thermodynamic factor is the most significant in accounting for the fact that phosphoric acid is a weak acid? Why?

Predict the sign of the entropy change for each of the following processes. a.A drop of food coloring diffuses throughout a glass of water. b.A tree leafs out in the spring. c.Flowers wilt and stems decompose in the fall. d.A lake freezes over in the winter. e.Rainwater on the pavement evaporates.

Adenosine triphosphate, ATP, is used as a freeenergy source by biological cells. (See the essay on page \(624 .)\) ATP hydrolyzes in the presence of enzymes to give ADP: $$ \begin{aligned} \mathrm{ATP}(a q)+\mathrm{H}_{2} \mathrm{O}(l) \longrightarrow & \mathrm{ADP}(a q)+\mathrm{H}_{2} \mathrm{PO}_{4}^{-}(a q) \\ & \Delta G^{\circ}=-30.5 \mathrm{~kJ} / \mathrm{mol} \text { at } 25^{\circ} \mathrm{C} \end{aligned} $$ Consider a hypothetical biochemical reaction of molecule A to give molecule \(\mathrm{B}\) : $$ \mathrm{A}(a q) \longrightarrow \mathrm{B}(a q) ; \Delta G^{\circ}=+15.0 \mathrm{~kJ} / \mathrm{mol} \text { at } 25^{\circ} \mathrm{C} $$ a.Calculate the ratio \([\mathrm{B}] /[\mathrm{A}]\) at \(25^{\circ} \mathrm{C}\) at equilibrium. b.Now consider this reaction "coupled" to the reaction for the hydrolysis of ATP: $$ \begin{array}{r} \mathrm{A}(a q)+\mathrm{ATP}(a q)+\mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \mathrm{B}(a q)+\operatorname{ADP}(a q)+ \\ \mathrm{H}_{2} \mathrm{PO}_{4}(a q) \end{array} $$ If a cell maintains a high ratio of ATP to ADP and \(\mathrm{H}_{2} \mathrm{PO}_{4}^{-}\) by continuously making ATP, the conversion of \(\mathrm{A}\) to \(\mathrm{B}\) can be made highly spontaneous. A characteristic value of this ratio is $$ \frac{[\mathrm{ATP}]}{[\mathrm{ADP}]\left[\mathrm{H}_{2} \mathrm{PO}_{4}^{-}\right]}=500 $$ Calculate the ratio [B][A] in this case and compare it with the uncoupled reaction. Compared with the uncoupled reaction, how much larger is this ratio when coupled to the hydrolysis of ATP?

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