# Thermodynamics, Gases, and Temperature

1- A radio station's channel, such as 100.7 FM or 92.3 FM, is actually its frequency in megahertz (MHz ), where 1MHz=10 6 Hz and 1Hz=1s −1 .Calculate the broadcast wavelength of the radio station 94.30 FM.

2- Hospital X-ray generators emit X-rays with wavelength of about 15.0 nanometers (nm ), where 1nm=10 −9 m . What is the energy of the X-rays?

3- What is the azimuthal quantum number (also called the angular-momentum quantum number), ℓ, for the orbital shown here? Express your answer numerically as an integer.

4- What is the change in energy, ΔE , in kilojoules per mole of hydrogen atoms for an electron transition from n=3 to n=2

5- Here are some data collected on a sample of cesium exposed to various energies of light.

Light energy

(eV )

Electron emitted? ElectronKE

(eV )

3.87 no —

3.88 no —

3.89 yes 0

3.90 yes 0.01

3.91 yes 0.02

What is the threshold frequency ν 0 of cesium?Note that 1 eV (electron volt)=1.60×10 −19 J. Answer in Hz

6- The energy difference between two energy shells is calculated using the formula

ΔE=E f −E i where E f is the energy of the final shell, and E i is the energy of the initial shell from which the transition occurs. For example, for the transition n=4 to n=1 , the initial shell is the fourth shell, and the final shell is the first shell. Thus, the change in energy between the fourth and the first shell is denoted as ΔE=E 1 −E 4 . The energy corresponding to a shell is calculated using E n =−2.179×10 −18 /(n) 2 J

where n is the shell number. Calculate the energy difference for a transition in the Paschen series for a transition from the higher energy shell n=4 .Express your answer to four significant figures and include the appropriate units.

7- A gas at 32 ºC occupies a volume of 250 mL. To what temperature must the gas be changed to occupy a volume of 285 mL?

8- An unknown gas effuses through a porous barrier at a rate that is 0.752 times the rate of Ar (g) under the same conditions. Which of the following is the unknown gas?

9- What is the density (g/L) of propane (C3H8) at STP (1 atm, 273 K)?

10- A system gives off 500 kJ of heat and does 100 kJ of work. What is the change in internal energy?

11- The heat of formation (ΔH°f) of MgCO3 (s) is -1095.8 kJ/mol. The chemical equation associated with this reaction is:

12- Consider:

2 B5H9 (g) + 12 O2 (g) → 5 B2O3 (g) + 9 H2O (g) ΔH˚reaction= - 8687 kJ.

What is the enthalpy change when 0.2500 moles of B5H9 are combusted?

13- Which of the following sets of quantum numbers is valid?

n = 1, l = 2, ml = 3, ms = 4

n = 3, l = 2, ml = -2, ms = 1/2

n = 1, l = 0, ml = 1, ms = -1/2

n = 4, l = 4, ml = -1, ms = 1/2

n = 0, l = 1, ml = 0, ms = -1/2

14- Consider the Bohr Model for the hydrogen atom. Which of the following electron transitions releases the MOST energy?

n = 6 to n = 4

n = 5 to n = 3

n = 4 to n = 2

n = 3 to n = 1

n = 2 to n = 1

15- The energy of one mole of photons having a wavelength of 630 nm is:

16- Use the data below to answer the questions.

Substance ΔH ∘ f (kJ/mol)

C(g)

718.4

CF 4 (g)

− 679.9

CH 4 (g)

− 74.8

H(g)

217.94

HF(g)

− 268.61

Keep in mind that the enthalpy of formation of an element in its standard state is zero.

Part A

Calculate the enthalpy change, ΔH ∘ , for the "expansion" of methane:CH 4 (g)→C(g)+4H(g)

Express your answer to one decimal place and include the appropriate units.

Part B

Calculate the enthalpy change, ΔH ∘ , for the reverse of the formation of methane:CH 4 (g)→C(s)+2H 2 (g) Express your answer to one decimal place and include the appropriate units.

17- The following table lists some enthalpy of formation values for selected substances.

Substance ΔH f ∘ (kJ/mol)

HCl(g)

−92

Al(OH) 3 (s)

−1277

H 2 O(l)

−285.8

AlCl 3 (s)

−705.6

H 2 O(g)

−241.8

Part A

Determine the enthalpy for this reaction:Al(OH) 3 (s)+3HCl(g)→AlCl 3 (s)+3H 2 O(l)

Express your answer in kilojoules per mole to four significant figures.

18- The standard enthalpy of formation (ΔH ∘ f )is the enthalpy change that occurs when exactly 1 mol of a compound is formed from its constituent elements under standard conditions. The standard conditions are 1 atm pressure, a temperature of 25 ∘ C and all the species present at a concentration of 1 M .A "standard enthalpies of formation table" containing ΔH ∘ f values might look something like this:

Substance ΔH ∘ f

H(g)

218 kJ/mol

H 2 (g)

0 kJ/mol

Ba(s)

0 kJ/mol

Ba 2+ (aq)

− 538.4 kJ/mol

C(g)

71 kJ/mol

C(s)

0 kJ/mol

N(g)

473 kJ/mol

O 2 (g)

0 kJ/mol

O(g)

249 kJ/mol

S 2 (g)

129 kJ/mol

Part A

What is the balanced chemical equation for the reaction used to calculate ΔH ∘ f of BaCO 3 (s)?If fractional coefficients are required, enter them as a fraction (i.e. 1/3). Indicate the physical states using the abbreviation (s), (l ), or (g ) for solid, liquid, or gas, respectively. Use (aq ) for aqueous solution.

Express your answer as a chemical equation.

19- For the reaction 2A+B⇌2C+2D, how much heat is absorbed when 3.10mol of A reacts?

Express your answer to three significant figures and include the appropriate units.

20- Ozone, O 3 , is destroyed when ClOlevels are high. ClO is likely formed from the decomposition of chlorofluorocarbons (CFCs) in sunlight.

Standard enthalpies of formation for selected substances are given in the table below.

Substance ΔH ∘ f

(kJ/mol )

ClO(g)

101.0

ClO 2 (g)

102.0

O(g)

247.5

O 2 (g)

0

O 3 (g)

142.3

Part A

Calculate the standard enthalpy change of the reaction ClO(g)+O 3 (g)→ClO 2 (g)+O 2 (g) Express your answer in kilojoules using four significant figures.

21- What is the enthalpy for reaction 1 reversed? reaction 1 reversed: N 2 O 4 →N 2 + 2O 2

Express your answer numerically in kilojoules per mole.

22- When 0.501g of biphenyl (C 12 H 10 ) undergoes combustion in a bomb calorimeter, the temperature rises from 25.2 ∘ C to 29.4 ∘ C .Find ΔE rxn for the combustion of biphenyl in kJ/mol biphenyl. The heat capacity of the bomb calorimeter, determined in a separate experiment, is 5.86 kJ/ ∘ C

23- Instant cold packs, often used to ice athletic injuries on the field, contain ammonium nitrate and water separated by a thin plastic divider. When the divider is broken, the ammonium nitrate dissolves according to the following endothermic reaction: NH 4 NO 3 (s)→NH 4 + (aq)+NO 3 − (aq) In order to measure the enthalpy change for this reaction, 1.25 g of NH 4 NO 3 is dissolved in enough water to make 25.0 mL of solution. The initial temperature is 25.8 ∘ C and the final temperature (after the solid dissolves) is 21.9 ∘ C .Calculate the change in enthalpy for the reaction. (Use 1.0g/mL as the density of the solution and 4.18J/g⋅ ∘ C as the specific heat capacity.)

24- The change in internal energy for the combustion of 1.0 mol of octane at a pressure of 1.0 atm is 5084.2kJ .If the change in enthalpy is 5074.4kJ , how much work is done during the combustion?answer in kJ

25- It takes 47.0J to raise the temperature of an 11.3g piece of unknown metal from 13.0 ∘ C to 24.1 ∘ C . What is the specific heat for the metal?

26- The molar heat capacity of silver is 25.35 J/mol⋅ ∘ C How much energy would it take to raise the temperature of 11.3g of silver by 19.0 ∘ C? Express your answer with the appropriate units.

27- What is the specific heat of silver?

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#### Solution Preview

1) A radio station's channel, such as 100.7 FM or 92.3 FM, is actually its frequency in megahertz (MHz ), where 1MHz=10 6 Hz and 1Hz=1s −1 .Calculate the broadcast wavelength of the radio station 94.30 FM.

Speed of light ( c ) = 3.00 X 10^8 m*s-1

Wavelength (w) * frequency (v) = speed of light (c )

Frequency = 94.30 FM or 94.30 MHz or 94.30 X10^6 s-1

Since wv = c, w = c/ v = 3.00 X 10^8 m*s-1 / 94.30 X 10^6 s-1

= 0.0318 X 10^2 m = 3.18 m

2) Hospital X-ray generators emit X-rays with wavelength of about 15.0 nanometers (nm ), where 1nm=10 −9 m. What is the energy of the X-rays?

Wavelength = 15 nm

Using formula E = hv; where E is the energy of the radiation, v is the frequency of radiation, and h is a proportional constant called Planck's constant

You also need the formula wv = c;

h = 6.626 X 10^ -34 J*s

Find the frequency of the X-ray: v = c/ w = 3.00 X 10^8 m*s-1 / 15 X 10^-9 m

= 2 s-1

Substituting for E = hv;

= 6.626 X10^-34 J*s X 2 s^-1

= 13.25 X 10^-34 J

3) What is the azimuthal quantum number (also called the angular-momentum quantum number), ℓ, for the orbital shown here? Express your answer numerically as an integer.

n= 4, l= 0, 1,2,3

4) What is the change in energy, ΔE , in kilo-joules per mole of hydrogen atoms for an electron transition from n=3 to n=2

En = -2.18 X 10-18 J / n^2

E3 = -2.18 X 10-18 J / 3^2 = -2.18 X 10^-18 / 9 = -0.24 X 10^-18

E2 = -2.18 X10^-18 J/ 2^2 = -2.18 X 10 ^-18/ 4 = -0.55 X 10^-18

ΔE = E 3- E2

= -0.55 X10^-18 - - 0.24 X 10^-18 = -0.31 X 10^-18

ΔE=E f −E I = E2 - E3

5) Here are some data collected on a sample of cesium exposed to various energies of light.

Light energy

(eV )

Electron emitted? ElectronKE

(eV )

3.87 no —

3.88 no —

3.89 yes 0

3.90 yes 0.01

3.91 yes 0.02

What is the threshold frequency ν 0 of cesium?Note that 1 eV (electron volt)=1.60×10 −19 J. Answer in Hz

Using the equation, Ф = hv0, where Ф stands for work function or energy required to emit electron, h is constant, and v0 is the frequency threshold

1eV = 1.60 X 10-19 J, so 0.01 eV = 0.016 X10^-19 J

V0 = Ф / h = 0.016 X 10^-19 J/ 6.626 X 10^-34 J*s

= 0.0024 X 10^15 s

6) The energy difference between two energy shells is calculated using the formula

ΔE=E f −E i where E f is the energy of the final shell, and E i is the energy of the initial shell from which the transition occurs. For example, for the transition n=4 to n=1 , the initial shell is the fourth shell, and the final shell is the first shell. Thus, the change in energy between the fourth and the first shell is denoted as ΔE=E 1 −E 4 . The energy corresponding to a shell is calculated using E n =−2.179×10 −18 /(n) 2 J

where n is the shell number. Calculate the energy difference for a transition in the Paschen series for a transition from the higher energy shell n=4 .Express your answer to four significant figures and include the appropriate units.

ΔE=E f −E i;

ΔE=E 1 −E 4;

E1 = -2.18 X 10^-18 J/ 1^1 = -2.18 X 10^-18 J

E4 = -2.18 X 10 ^-18 J/ 4^2 = -0.136 X 10^-18J

So E1- E4 = -2.18 X10^-18J - -0.136 X 10^-18J

= -2.04 X10^-18 J

7) A gas at 32 ºC occupies a volume of 250 mL. To what temperature ...

#### Solution Summary

The change in internal energy for the combustion is determined. Thermodynamics, gases and temperatures are provided.

Thermodynamic of cyclic process of an ideal gas

An ideal gas described by T(initial)=300K,P(initial)=1 bar and V(i)=10 L is heated at constant volume until P=10 bar.It then undergoes a reversible isothermal expansion until P=1bar.It is then restored to its original state by the extraction of heat at constant pressure. Calculate w for each step.

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