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Chapter 16: Problem 118

Heat transfer to and from a reaction flask is often a critical factor in controlling reaction rate. The heat transferred \((q)\) depends on a heat transfer coefficient \((h)\) for the flask material, the temperature difference \((\Delta T)\) across the flask wall, and the commonly "wetted" area (A) of the flask and bath: \(q=h A \Delta T\). When an exothermic reaction is run at a given \(T,\) there is a bath temperature at which the reaction can no longer be controlled, and the reaction "runs away" suddenly. A similar problem is often seen when a reaction is "scaled up" from, say, a half-filled small flask to a half-filled large flask. Explain these behaviors.

Short Answer

Expert verified
Runaway reactions occur due to insufficient heat removal as ∆T decreases, and scaling up amplifies this by increasing volume faster than surface area.

Step by step solution

01

Understand the Heat Transfer Formula

The heat transferred ( q ) depends on three factors: h (heat transfer coefficient), A (area), and ∆T (temperature difference), as given by the formula: q = h A ∆T .
02

Identify the Role of Heat Transfer Coefficient

Heat transfer coefficient ( h ) represents the material's ability to transfer heat. A high h indicates efficient heat transfer, whereas a low h suggests poor heat transfer.
03

Analyze Effect of Temperature Difference

The temperature difference ( ∆T ) between the reaction flask and the bath determines the driving force for heat transfer. A higher ∆T increases the heat transferred according to the formula.
04

Consider Wetted Area Impact

The wetted area ( A ) is the surface area in contact with the heat source or sink. Larger A increases the potential heat transfer.
05

Explain Reaction Runaway

In exothermic reactions, if the bath temperature increases, ∆T decreases, reducing the heat that can be removed. This can cause an uncontrollable increase in reaction rate, leading to a runaway reaction.
06

Scaling Up Effects

When scaling up, the flask's volume increases faster than its surface area, reducing the effectiveness of heat transfer relative to the reaction size. This makes temperature control harder and can further contribute to runaway reactions.

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Key Concepts

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

Reaction Rate Control
In chemical reactions, controlling the reaction rate is crucial for both safety and efficiency. The reaction rate is influenced by various factors, including temperature and concentration of reactants.
Ensuring effective heat transfer is essential as it can help maintain the desired temperature and prevent the reaction from going too fast or too slow.
By managing these conditions, one can maintain consistent product quality and avoid dangerous situations like reaction runaway.
Heat Transfer Coefficient
The heat transfer coefficient, denoted as \( h \), is a measure of how well a material can transfer heat. Different materials have different capacities for heat transfer:
  • High \( h \): Efficient heat transfer
  • Low \( h \): Poor heat transfer
This coefficient is crucial in determining how quickly heat can be added or removed from the reaction flask. For a given experiment, selecting materials with suitable heat transfer coefficients can help maintain stability and control over the reaction.
Exothermic Reactions
Exothermic reactions release heat as they proceed. This means that as the reaction continues, the system's temperature tends to increase if the heat is not adequately dissipated.
Key points to understand about exothermic reactions include:
  • They can quickly raise the reaction temperature.
  • Adequate cooling mechanisms must be in place to manage the heat produced.
  • Monitoring these reactions closely can help in avoiding runaway scenarios.
Understanding the nature of exothermic reactions is crucial for implementing proper heat management strategies.
Reaction Runaway
Reaction runaway occurs when a reaction accelerates uncontrollably, often due to insufficient heat dissipation. This typically happens in exothermic reactions where:
  • The temperature difference \( \Delta T \) decreases, reducing heat removal efficiency.
  • Heat generated by the reaction exceeds the dissipated heat, causing a rapid rise in temperature.
Such scenarios can lead to dangerous conditions, making it essential to have control systems that can handle unexpected increases in reaction rates. Regular monitoring and proper cooling are key to preventing reaction runaway.
Scaling Up Reactions
Scaling up a reaction from a small to a large flask poses significant challenges:
  • The volume increases more rapidly than the surface area, which affects the heat transfer efficiency.
  • Larger volumes may require more robust cooling systems to maintain control.
  • Inadequate scaling can lead to uneven temperatures and potential runaway reactions.
To scale up reactions safely, it is vital to carefully consider the changes in heat transfer dynamics and to implement adequate measures for maintaining consistent temperature control across different flask sizes.

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Most popular questions from this chapter

The effect of substrate concentration on the first-order growth rate of a microbial population follows the Monod equation: \(\mu=\frac{\mu_{\max } S}{K_{\mathrm{s}}+S}\) where \(\mu\) is the first-order growth rate \(\left(\mathrm{s}^{-1}\right), \mu_{\max }\) is the maximum growth rate \(\left(\mathrm{s}^{-1}\right), S\) is the substrate concentration \(\left(\mathrm{kg} / \mathrm{m}^{3}\right),\) and \(K_{\mathrm{s}}\) is the value of \(S\) that gives one-half of the maximum growth rate (in \(\mathrm{kg} / \mathrm{m}^{3}\) ). For \(\mu_{\max }=1.5 \times 10^{-4} \mathrm{~s}^{-1}\) and \(K_{\mathrm{s}}=0.03 \mathrm{~kg} / \mathrm{m}^{3}\). (a) Plot \(\mu\) vs. \(S\) for \(S\) between 0.0 and \(1.0 \mathrm{~kg} / \mathrm{m}^{3}\). (b) The initial population density is \(5.0 \times 10^{3}\) cells \(/ \mathrm{m}^{3}\). What is the density after \(1.0 \mathrm{~h}\), if the initial \(S\) is \(0.30 \mathrm{~kg} / \mathrm{m}^{3} ?\) (c) What is it if the initial \(S\) is \(0.70 \mathrm{~kg} / \mathrm{m}^{3}\) ?

(a) For a reaction with a given \(E_{a},\) how does an increase in \(T\) affect the rate? (b) For a reaction at a given \(T,\) how does a decrease in \(E_{\mathrm{a}}\) affect the rate?

Many drugs decompose in blood by a first-order process. (a) Two tablets of aspirin supply \(0.60 \mathrm{~g}\) of the active compound. After 30 min, this compound reaches a maximum concentration of \(2 \mathrm{mg} / 100 \mathrm{~mL}\) of blood. If the half-life for its breakdown is \(90 \mathrm{~min},\) what is its concentration (in \(\mathrm{mg} / 100 \mathrm{~mL}\) ) \(2.5 \mathrm{~h}\) after it reaches its maximum concentration? (b) For the decomposition of an antibiotic in a person with a normal temperature \(\left(98.6^{\circ} \mathrm{F}\right)\), \(k=3.1 \times 10^{-5} \mathrm{~s}^{-1} ;\) for a person with a fever (temperature of \(\left.101.9^{\circ} \mathrm{F}\right), k=3.9 \times 10^{-5} \mathrm{~s}^{-1}\). If the person with the fever must take another pill when \(\frac{2}{3}\) of the first pill has decomposed, how many hours should she wait to take a second pill? A third pill? (Assume that the pill is effective immediately.) (c) Calculate \(E_{\mathrm{a}}\) for decomposition of the antibiotic in part (b).

Aqua regia, a mixture of \(\mathrm{HCl}\) and \(\mathrm{HNO}_{3},\) has been used since alchemical times to dissolve many metals, including gold. Its orange color is due to the presence of nitrosyl chloride. Consider this one-step reaction for the formation of this compound: \(\mathrm{NO}(g)+\mathrm{Cl}_{2}(g) \longrightarrow \operatorname{NOCl}(g)+\mathrm{Cl}(g) \quad \Delta H^{\circ}=83 \mathrm{~kJ}\) (a) Draw a reaction energy diagram, given \(E_{\text {affwd }}=86 \mathrm{~kJ} / \mathrm{mol}\). (b) Calculate \(E_{\text {arrev }}\). (c) Sketch a possible transition state for the reaction. (Note: The atom sequence of nitrosyl chloride is \(\mathrm{Cl}-\mathrm{N}-\mathrm{O} .)\)

Give the individual reaction orders for all substances and the overall reaction order from this rate law: $$ \text { Rate }=k\left[\mathrm{NO}_{2}\right]^{2}\left[\mathrm{Cl}_{2}\right] $$
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