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Chapter 7: Problem 140

Is it possible for a chemical reaction to have \(\Delta U<0\) and \(\Delta H>0 ?\) Explain.

Short Answer

Expert verified
Yes, a chemical reaction can have \( \Delta U<0 \) and \( \Delta H>0 \) if the system is exothermic and simultaneously doing more work on the surroundings, which results in heat absorption from the surroundings.

Step by step solution

01

Understanding Symbols

First, understand what these symbols represent in a chemical reaction. \( \Delta U \) represents the change (increase or decrease) in the internal energy which could be due to heat transfer or work done. \( \Delta H \) represents the enthalpy change which is the heat absorbed or released in a chemical reaction at constant pressure.
02

Assessing the Feasibility of \( \Delta U0 \)

Consider a system where heat is released, signifying an exothermic process making \( \Delta U<0 \). However, let's say the work done by the system on the surroundings is significantly high. Therefore, even though the system is losing energy, it's still absorbing heat energy from the surroundings to do the work. Hence, \( \Delta H \), which is the heat absorbed at constant pressure, would be greater than zero.
03

Conclusion

To conclude, it is possible for a chemical reaction to have \( \Delta U<0 \) and \( \Delta H>0 \). Such a scenario would require the system to perform work on the surroundings while absorbing heat from the surroundings, which is plausible

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Most popular questions from this chapter

For the reaction \(\mathrm{C}_{2} \mathrm{H}_{4}(\mathrm{g})+\mathrm{Cl}_{2}(\mathrm{g}) \longrightarrow \mathrm{C}_{2} \mathrm{H}_{4} \mathrm{Cl}_{2}(1)\) determine \(\Delta H^{\circ},\) given that $$\begin{array}{r} 4 \mathrm{HCl}(\mathrm{g})+\mathrm{O}_{2}(\mathrm{g}) \longrightarrow 2 \mathrm{Cl}_{2}(\mathrm{g})+2 \mathrm{H}_{2} \mathrm{O}(1) \\ \Delta H^{\circ}=-202.4 \mathrm{kJ} \end{array}$$ $$\begin{aligned} 2 \mathrm{HCl}(\mathrm{g})+\mathrm{C}_{2} \mathrm{H}_{4}(\mathrm{g})+\frac{1}{2} \mathrm{O}_{2}(\mathrm{g}) \longrightarrow \\ \mathrm{C}_{2} \mathrm{H}_{4} \mathrm{Cl}_{2}(1)+\mathrm{H}_{2} \mathrm{O}(1) & \Delta H^{\circ}=-318.7 \mathrm{kJ} \end{aligned}$$

The heat of solution of \(\mathrm{NaOH}(\mathrm{s})\) in water is \(-41.6 \mathrm{kJ} / \mathrm{mol} \mathrm{NaOH} .\) When \(\mathrm{NaOH}(\mathrm{s})\) is dissolved in water the solution temperature (a) increases; (b) decreases; (c) remains constant; (d) either increases or decreases, depending on how much NaOH is dissolved.

What is the change in internal energy of a system if the surroundings (a) transfer 235 J of heat and 128 J of work to the system; (b) absorb 145 J of heat from the system while doing \(98 \mathrm{J}\) of work on the system; (c) exchange no heat, but receive 1.07 kJ of work from the system?

The metabolism of glucose, \(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6},\) yields \(\mathrm{CO}_{2}(\mathrm{g})\) and \(\mathrm{H}_{2} \mathrm{O}(\mathrm{l})\) as products. Heat released in the process is converted to useful work with about \(70 \%\) efficiency. Calculate the mass of glucose metabolized by a \(58.0 \mathrm{kg}\) person in climbing a mountain with an elevation gain of \(1450 \mathrm{m}\). Assume that the work performed in the climb is about four times that required to simply lift \(58.0 \mathrm{kg}\) by \(1450 \mathrm{m} \cdot\left(\Delta H_{\mathrm{f}}^{2} \text { of } \mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}(\mathrm{s}) \text { is }-1273.3 \mathrm{kJ} / \mathrm{mol} .\right)\)

Look up the specific heat of several elements, and plot the products of the specific heats and atomic masses as a function of the atomic masses. Based on the plot, develop a hypothesis to explain the data. How could you test your hypothesis?
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