Q: A 150.0 g sample of an alloy requires 59.3 kJ of heat to raise its temperature from 298 K to 398 K. What is the specific heat capacity $$C_s of $$the alloy in $$\mathrm{J/(g \cdot K)}$$?

$$C_s = \dfrac{59,300\ \mathrm{J}}{150.0\ \mathrm{g} \times (398\ \mathrm{K} - 298\ \mathrm{K})} = 3.95\ \mathrm{J/(g \cdot K)}$$

Q: Calculate the change in internal energy ($$\Delta E) $$for a system that absorbs $$35.8\ \mathrm{kJ} of $$heat and expands from $$8.00 to$$ $$24.0\ \mathrm{L} at$$ $$1.00\ \mathrm{atm}$$. ($$1\ \mathrm{L \cdot atm} = 101.3\ \mathrm{J})$$

$$\Delta E = 35.8\ \mathrm{kJ} - (1.00\ \mathrm{atm} \times 16.0\ \mathrm{L} \times 101.3\ \mathrm{J/L \cdot atm} \times 10$$^{-3}$$\ \mathrm{kJ/J}) = 35.8\ \mathrm{kJ} - 1.62\ \mathrm{kJ} = 34.2\ \mathrm{kJ}$$

Q: A 100.0 mL sample of $$0.300\ \mathrm{M}$$ NaOH is mixed with a 100.0 mL sample of $$0.300\ \mathrm{M}$$ HCl in a coffee cup calorimeter. The temperature rises from $$35.00^\circ\mathrm{C} to$$ $$37.00^\circ\mathrm{C}. $$Assuming the density and specific heat of the solution are the same as water ($$4.184\ \mathrm{J/g^\circ C}$$), what is $$\Delta H^\circ_{rxn} in$$ $$\mathrm{kJ/mol}$$ NaOH?

$$\Delta H^\circ_{rxn} = \dfrac{(200.0\ \mathrm{g}) \times 4.184\ \mathrm{J/g^\circ C} \times 2.00^\circ\mathrm{C}}{0.0300\ \mathrm{mol}} \times 10$$^{-3}$$ = -55.8\ \mathrm{kJ/mol}$$

Q: Calculate the wavelength (in nm) of blue light emitted by a mercury lamp with a frequency of $$6.88 \times 10$$^{14}$$\ \mathrm{Hz}$$. ($$c = 3.00 \times 10^8$\ \mathrm{m/s})$$

$$\lambda = \dfrac{3.00 \times 10^8$\ \mathrm{m/s}}{6.88 \times 10$$^{14}$$\ \mathrm{Hz}} = 4.36 \times 10$$^{-7}$$\ \mathrm{m} = 436\ \mathrm{nm}$$

Q: What is the energy of a single photon of green light with a wavelength of $$525\ \mathrm{nm}$$? ($$h = 6.626 \times 10$$^{-34}$$\ \mathrm{J \cdot s}$$, $$c = 3.00 \times 10^8$\ \mathrm{m/s})$$

$$E = \dfrac{6.626 \times 10$$^{-34}$$\ \mathrm{J \cdot s} \times 3.00 \times 10^8$\ \mathrm{m/s}}{525 \times 10$$^{-9}$$\ \mathrm{m}} = 3.79 \times 10$$^{-19}$$\ \mathrm{J}$$

Q: Determine the velocity of a medicine ball ($$m = 10.0\ \mathrm{kg}) $$with a de Broglie wavelength of $$1.33 \times 10$$^{-35}$$\ \mathrm{m}$$. ($$h = 6.626 \times 10$$^{-34}$$\ \mathrm{J \cdot s})$$

$$v = \dfrac{6.626 \times 10$$^{-34}$$\ \mathrm{J \cdot s}}{10.0\ \mathrm{kg} \times 1.33 \times 10$$^{-35}$$\ \mathrm{m}} = 4.98\ \mathrm{m/s}$$

Q: What is the energy change associated with the transition from $$n = 2 to$$ $$n = 5 in $$the hydrogen atom? ($$E_n = -2.18 \times 10$$^{-18}$$\ \mathrm{J}/n^2$)

$$\Delta E = -2.18 \times 10$$^{-18}$$\ \mathrm{J} \left( \dfrac{1}{5^2$} - \dfrac{1}{2^2$} \right ) = 4.58 \times 10$$^{-19}$$\ \mathrm{J}$$

Q: A laser emits $$1.3 \times 10$$^{-2}$$\ \mathrm{J} of $$energy in a pulse of green light ($$\lambda = 531\ \mathrm{nm}$$, $$E_{photon} = 3.74 \times 10$$^{-19}$$\ \mathrm{J}). $$How many photons are in each pulse?

$$\dfrac{1.3 \times 10$$^{-2}$$\ \mathrm{J}}{3.74 \times 10$$^{-19}$$\ \mathrm{J}} = 3.5 \times 10$$^{16}$$

Question 1

A 150.0 g sample of an alloy requires 59.3 kJ of heat to raise its temperature from 298 K to 398 K. What is the specific heat capacity $$C_s of $$the alloy in $$\mathrm{J/(g \cdot K)}$$?

Accepted Answer

$$C_s = \dfrac{59,300\ \mathrm{J}}{150.0\ \mathrm{g} 	imes (398\ \mathrm{K} - 298\ \mathrm{K})} = 3.95\ \mathrm{J/(g \cdot K)}$$

Question 2

A 21.8 g sample of ethanol ($$\mathrm{C_2H_5OH}$$, molar mass = 46.07 g/mol) is burned in a bomb calorimeter. The temperature rises from $$25.0^\circ\mathrm{C} to$$ $$62.3^\circ\mathrm{C}. $$Given $$\Delta H^\circ_{rxn} = -1235\ \mathrm{kJ}$$ for $$\mathrm{C_2H_5OH(l) + 3 O_2$(g) \rightarrow 2 CO_2$(g) + 3 H_2O(g)}$$, what is the heat capacity of the calorimeter ($$C_{cal}) in$$ $$\mathrm{kJ$$/^{\circ}$$C}$$?

Accepted Answer

$$C_{cal} = \dfrac{585.0\ \mathrm{kJ}}{37.3\ ^\circ\mathrm{C}} = 15.7\ \mathrm{kJ$$/^{\circ}$$C}$$

Question 3

Calculate the change in internal energy ($$\Delta E) $$for a system that absorbs $$35.8\ \mathrm{kJ} of $$heat and expands from $$8.00 to$$ $$24.0\ \mathrm{L} at$$ $$1.00\ \mathrm{atm}$$. ($$1\ \mathrm{L \cdot atm} = 101.3\ \mathrm{J})$$

Accepted Answer

$$\Delta E = 35.8\ \mathrm{kJ} - (1.00\ \mathrm{atm} 	imes 16.0\ \mathrm{L} 	imes 101.3\ \mathrm{J/L \cdot atm} 	imes 10$$^{-3}$$\ \mathrm{kJ/J}) = 35.8\ \mathrm{kJ} - 1.62\ \mathrm{kJ} = 34.2\ \mathrm{kJ}$$

Question 4

Which of the following equations correctly relates the change in internal energy ($$\Delta E) to $$heat ($$q) $$and work ($$w$$)?

Accepted Answer

$$\Delta E = q + w$$

Question 5

A 100.0 mL sample of $$0.300\ \mathrm{M}$$ NaOH is mixed with a 100.0 mL sample of $$0.300\ \mathrm{M}$$ HCl in a coffee cup calorimeter. The temperature rises from $$35.00^\circ\mathrm{C} to$$ $$37.00^\circ\mathrm{C}. $$Assuming the density and specific heat of the solution are the same as water ($$4.184\ \mathrm{J/g^\circ C}$$), what is $$\Delta H^\circ_{rxn} in$$ $$\mathrm{kJ/mol}$$ NaOH?

Accepted Answer

$$\Delta H^\circ_{rxn} = \dfrac{(200.0\ \mathrm{g}) 	imes 4.184\ \mathrm{J/g^\circ C} 	imes 2.00^\circ\mathrm{C}}{0.0300\ \mathrm{mol}} 	imes 10$$^{-3}$$ = -55.8\ \mathrm{kJ/mol}$$

Question 6

Which of the following visible colors of light has the highest frequency?

Accepted Answer

blue

Question 7

Which of the following visible colors of light has the longest wavelength?

Accepted Answer

red

Question 8

Calculate the wavelength (in nm) of blue light emitted by a mercury lamp with a frequency of $$6.88 	imes 10$$^{14}$$\ \mathrm{Hz}$$. ($$c = 3.00 	imes 10^8$\ \mathrm{m/s})$$

Accepted Answer

$$\lambda = \dfrac{3.00 	imes 10^8$\ \mathrm{m/s}}{6.88 	imes 10$$^{14}$$\ \mathrm{Hz}} = 4.36 	imes 10$$^{-7}$$\ \mathrm{m} = 436\ \mathrm{nm}$$

Question 9

What is the energy of a single photon of green light with a wavelength of $$525\ \mathrm{nm}$$? ($$h = 6.626 	imes 10$$^{-34}$$\ \mathrm{J \cdot s}$$, $$c = 3.00 	imes 10^8$\ \mathrm{m/s})$$

Accepted Answer

$$E = \dfrac{6.626 	imes 10$$^{-34}$$\ \mathrm{J \cdot s} 	imes 3.00 	imes 10^8$\ \mathrm{m/s}}{525 	imes 10$$^{-9}$$\ \mathrm{m}} = 3.79 	imes 10$$^{-19}$$\ \mathrm{J}$$

Question 10

Determine the velocity of a medicine ball ($$m = 10.0\ \mathrm{kg}) $$with a de Broglie wavelength of $$1.33 	imes 10$$^{-35}$$\ \mathrm{m}$$. ($$h = 6.626 	imes 10$$^{-34}$$\ \mathrm{J \cdot s})$$

Accepted Answer

$$v = \dfrac{6.626 	imes 10$$^{-34}$$\ \mathrm{J \cdot s}}{10.0\ \mathrm{kg} 	imes 1.33 	imes 10$$^{-35}$$\ \mathrm{m}} = 4.98\ \mathrm{m/s}$$

Question 11

Which of the following is the correct set of magnetic quantum numbers ($$m_l) $$for a d orbital?

Accepted Answer

$$-2, -1, 0, 1, 2$$

Question 12

Which equation correctly expresses the relationship between the speed of light ($$c$$), frequency ($$
u$$), and wavelength ($$\lambda$$)?

Accepted Answer

$$c = \lambda 
u$$

Question 13

What is the energy change associated with the transition from $$n = 2 to$$ $$n = 5 in $$the hydrogen atom? ($$E_n = -2.18 	imes 10$$^{-18}$$\ \mathrm{J}/n^2$)

Accepted Answer

$$\Delta E = -2.18 	imes 10$$^{-18}$$\ \mathrm{J} \left( \dfrac{1}{5^2$} - \dfrac{1}{2^2$} ight ) = 4.58 	imes 10$$^{-19}$$\ \mathrm{J}$$

Question 14

Which of the following best describes the shape of a p orbital?

Accepted Answer

dumbbell shaped

Question 15

Which of the following equations illustrates the standard enthalpy of formation ($$\Delta H^\circ_f) $$for $$\mathrm{Li_2SO_4(s)}$$? (Sulfur occurs as $$\mathrm{S_8$}$$ under standard conditions.)

Accepted Answer

$$2\ \mathrm{Li(s)} + \dfrac{1}{8}\ \mathrm{S_8$(s)} + 2\ \mathrm{O_2$(g)} \rightarrow \mathrm{Li_2SO_4(s)}$$

Question 16

A laser emits $$1.3 	imes 10$$^{-2}$$\ \mathrm{J} of $$energy in a pulse of green light ($$\lambda = 531\ \mathrm{nm}$$, $$E_{photon} = 3.74 	imes 10$$^{-19}$$\ \mathrm{J}). $$How many photons are in each pulse?

Accepted Answer

$$\dfrac{1.3 	imes 10$$^{-2}$$\ \mathrm{J}}{3.74 	imes 10$$^{-19}$$\ \mathrm{J}} = 3.5 	imes 10$$^{16}$$

Question 17

Which of the following transitions in a hydrogen atom represents the absorption of a photon?

Accepted Answer

$$n = 1 to$$ $$n = 2$$

Question 18

Which of the following best describes the shape of an s orbital?

Accepted Answer

spherical

Question 19

Which of the following is the correct set of magnetic quantum numbers ($$m_l) $$for a p orbital?

Accepted Answer

$$-1, 0, 1$$

Question 20

Which of the following is the correct set of magnetic quantum numbers ($$m_l) $$for an f orbital?

Accepted Answer

$$-3, -2, -1, 0, 1, 2, 3$$

Thermodynamics and Quantum Theory Study Guide (Chapters 6–7)

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