CHEM 103 Chapter Notes - Chapter 4: Heat Capacity, Molar Mass, Enthalpy

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27 Oct 2016

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Textbook notes, chapter 4, sections 3, 4 & 5b. Define the system (a region of primary concern) to keep track in which direction the energy is flowing (positive / negative, or in/out) Surroundings = everything that can exchange energy with the system. For a chemical reaction, the system is usually defined to be all of the atoms that make up the reactants. The internal energy of a system is the sum of the individual energies (kinetic and potential) of all nanoscale particles (atoms, molecules, or ions) in that system. Internal energy depends on the temperature and the size of the sample (amount) The change in internal energy is calculated as /\e= e(final) - e (initial) Whenever a change is indicated by /\, a positive value indicates an increase and a negative value indicates a decrease. Direction of a change: negative when e is transferred out of the system, and positive when e is transferred into the system.

Related Questions

Energy cannot be created nor destroyed, but it can be transferred between a reaction and its surroundings. The change in energy, Delta E, is positive if the reaction absorbs energy, and it is negative if the reaction releases energy. You may also see this expressed in terms of change in internal energy, Delta U. For the purposes of this question, Delta U and Delta E are equal. One way a reaction can transfer energy to or from the surroundings is by releasing or absorbing heat. A reaction can also transfer energy, in the form of work, through a change in volume. The total change in energy is the sum of the heat and work: Delta E = q + w At constant pressure, q = Delta H and w = -P Delta V and so Delta E = Delta H - P Delta V Assuming constant pressure, rank these reactions from most energy released by the system to most energy absorbed by the system, based on the following descriptions: Surroundings get colder and the system decreases in volume. Surroundings get hotter and the system expands in volume. Surroundings get hotter and the system decreases in volume. Surroundings get hotter and the system does not change in volume. Also assume that the magnitude of the volume and temperature changes are similar among the reactions. Rank from most energy released to most energy absorbed. To rank items as equivalent, overlap them. Energy cannot be created nor destroyed, but it can be transferred between a reaction and its surroundings. The change in energy, Delta E, is positive if the reaction absorbs energy, and it is negative if the reaction releases energy. You may also see this expressed in terms of change in internal energy, Delta U. For the purposes of this question, Delta U and Delta E are equal. One way a reaction can transfer energy to or from the surroundings is by releasing or absorbing heat. A reaction can also transfer energy, in the form of work, through a change in volume. The total change in energy is the sum of the heat and work: Delta E = q + w At constant pressure, q = Delta H and w = -P Delta V and so Delta E = Delta H - P Delta V A mole of X reacts at a constant pressure of 43.0 atm via the reaction X(g) + 4Y(g) - 2Z(g), Delta H degree = -75.0 kJ Before the reaction, the volume of the gaseous mixture was 5.00 L. After the reaction, the volume was 2.00 L Calculate the value of the total energy change. AE, in kilojoules. Express your answer with the appropriate units.

1.According to the following thermochemical equation, if 31.1 g of NO2 is produced, how much heat is released at constant pressure?how much heat is released at constant pressure?

2NO(g) + O2(g) â 2NO2(g);ÎHÂ° = â114.4 kJ

Select one:

a. 114.4 kJ114.4 kJ

b. 1.183Ã103kJ

c. 2.365Ã103kJ

d. 38.7 kJ

e. 1.088Ã105kJ

2.CalculateâââÎUâââof a gas for a process in which the gas absorbs ââ12 J ââof heat and does ââ20 Jââ of work by expanding.

Select one:

a. 8 J

b. 32 J

c. -32 J

d. 0, because âÎU is a state function

e. -8 J

3.If q = +56 kJ for a certain process, that process

Select one:

a. requires a catalyst.

b. is exothermic.

c. occurs rapidly.

d. is endothermic.

e. cannot occur.

4.If q = 18 kJ and w = 15 kJ for a certain process, that process

Select one:

a. requires a catalyst.

b. has an increase in internal energy.

c. occurs slowly.

d. is exothermic.

e. cannot occur.

5.What is the change in internal energy of the system (ÎU) if 10 kJ of heat energy is released by the system and â70 kJâ of work is done on the system for a certain process?

Select one:

a. â60 kJ

b. 80 kJ

c. 10 kJ

d. 60 kJ

e. â80 kJ

6.What is the quantity of heat evolved at constant pressure when ââ26.3 gââ H2O(l)ââ is formed from the combustion of H2(g) and O2(g)?

2H2(g) + O2(g) â 2H2O(l);ÎHÂ° = â571.6 kJ

Select one:

a. 15033 kJ

b. 15.03 kJ

c. 1.72Ã104âkJ

d. 417.6 kJ

e. 9.57Ã102âkJ

7.What quantity, in moles, of hydrogen is consumed when 76.8 kJ of energy is evolved from the combustion of a mixture of H2(g) and O2(g)?

H2(g) + O2(g) â2H2O(l);ÎHÂ° = â571.6 kJ

Select one:

a. 2.368 mol

b. 1.184 mol

c. 0.4223 mol

d. 0.2687 mol

e. 1.368 mol

8. Which of the following is an exothermic process?

Select one:

a. work is done by the system on the surroundings

b. heat energy flows from the system to the surroundings

c. work is done on the system by the surroundings

d. heat energy is absorbed by the system

e. none of the above

9. Which of the following statements is correct?

Select one:

a. Internal energy is not a state function.

b. The value of q is negative when heat flows into a system from the surroundings.

c. The value of q is negative in an endothermic process.

d. Heat flows from a system into the surroundings in an exothermic process.

e. Enthalpy is not a state function.

10.X2and F2react according to the following equation, forming XF. (X is an unknown diatomic element)

X2(g)+ F2(g)â2XF(g);ÎHÂ°=+271 kJ

If X2(g) and F2(g) were mixed in a thermally insulated vessel, the reaction that occurred would be

Select one:

a. endothermic, and the temperature of the reaction system would fall.

b. We could not tell unless the original and final temperatures were given.

c. exothermic, and the temperature of the reaction system would fall.

d. exothermic, and the temperature of the reaction system would rise.

e. endothermic, and the temperature of the reaction system would rise.

10. In this question, mean field theory will be used to derive the van der Waals equation. Consider a gas of interacting, indistinguishable particles. In principle, the potential energy from these interactions depends upon the positions of the particles so detailed structural information is needed to describe it. This is a difficult problem. However, we can take a much simpler, albeit approximate, approach by treating the interactions with a one-body energy term. The physical argument goes as follows. The interaction (potential) energies in principle will vary among microstates. However, we expect fluctuations to be small. Let's replace the exact potential U in the partition function with its average value (that is, the "mean field") eMF divided among the particles, and assume each particle has the same contribution regardless of its position. In other words, rather than considering the particles as interacting with each other (via a potential that depends upon particle positions) we treat them as interacting with the mean field (which is independent of particle positions and other particles). In this way, EMF becomes a one-body energy term that can be included in the usual non-interacting partition function as an additional energy contribution. That is, the interacting system is approximated by the non-interacting partition function with a one-body energy term approximating the particle interactions. With this mean-field approximation, the energy of our particles becomes E=E;deal + EMF , in which Eideal is the energy of a particle in an ideal gas. Since these energy contributions are independent, the particle partition function is q = qidealqMF . Normally, qideal would be the product of partition functions for translation, vibration, rota- tion, etc. but because the volume dependence will be important, let's write qidealc(T)V where c(T) includes all the constants and temperature dependencies arising from vibrations and rotations, and where the volume factor in the translational partition function has been explicitly accounted for. The remaining part of the translational partition function in included in c(T). In the present case though, we imagine the particles each occupy some volume b, so the "effective volume" of our system is V- Nb. In other words, take qideal cT)(V - Nb) We don't know the value of eMF but physical arguments suggest it must vary with the av- erage distance between particles, which in turn varies with density, N/V. So, let's suppose a linear dependence and write EMF =-aN/V with a some unknown constant. A minus sign is included here because it is anticipated EME will be negative (attractive interaction) so this will make a a positive number. This one energy is the same for each particle so 4 a) Derive the expression for the average pressure and show the system obeys the van der Waals equation of state. Note: as defined b is the volume per particle not per mole of particles as usually tabulated. Similarly, as defined a is per particle not per mole squared as usually tabulated. So, write Nb as nb, and aN2 as an2 if you want to use a and b as the usually tabulated molar values b) Show that the internal energy and heat capacity are given by an - - U ==ideal and Cv=CV,ideal, where Eideal and Cvideal are the internal energy and heat capacity for the ideal gas, respectively. Show that the first relation is consistent with (UaVTan2/V2, a relation derived from thermodynamics. Give a physical argument to explain why the van der Waals gas (an interacting system) could have the same Cv as the ideal gas (a non-interacting system)

CHEM 103 Chapter Notes - Chapter 4: Heat Capacity, Molar Mass, Enthalpy

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