Q: A 150.0 g sample of an alloy is heated from 298 K to 398 K, requiring 59.3 kJ of energy. What is the specific heat capacity ($$C_s) of $$the alloy in J/g·K?

$$C_s = \frac{q}{m \Delta T} = \frac{59300\ \text{J}}{150.0\ \text{g} \times 100\ \text{K}} = 3.95\ \text{J/g·K}$$

Q: 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°C to 62.3°C. Given $$\Delta H^\circ_{rxn} = -1235 kJ $$for $$\mathrm{C_2H_5OH(l) + 3 O_2$(g) \rightarrow 2 CO_2$(g) + 3 H_2O(g)}$$, what is the heat capacity ($$C_{cal}) of $$the calorimeter in J/°C?

$$C_{cal} = \frac{q_{rxn}}{\Delta T} = \frac{(-1235\ \text{kJ}) \times \frac{21.8}{46.07}}{62.3 - 25.0} \times 1000 = 155.6\ \text{J/°C}$$

Q: How much energy is required to decompose 612 g of $$\mathrm{$$PCl_3$$}$$ according to $$4\ \mathrm{$$PCl_3$$(g)} \rightarrow \mathrm{P_4$(s)} + 6\ \mathrm{Cl_2$(g)}$$, $$\Delta H^\circ_{rxn} = +1207 kJ$$? (Molar mass $$\mathrm{$$PCl_3$$} = 137.32 g/$$mol)

$$\text{Energy} = \frac{612\ \text{g}}{137.32\ \text{g/mol}} \times \frac{1207\ \text{kJ}}{4} = 1346\ \text{kJ}$$

Q: A 100.0 mL sample of 0.300 M NaOH is mixed with 100.0 mL of 0.300 M HCl at 35.00°C. The final temperature is 37.00°C. Assuming density and heat capacity are the same as water ($$4.184\ \text{J/g}^\circ\text{C}$$), what is $$\Delta H^\circ_{rxn} in kJ/$$mol NaOH?

$$\Delta H^\circ_{rxn} = \frac{q}{\text{mol NaOH}} = \frac{(200\ \text{g}) \times 4.184\ \text{J/g}^\circ\text{C} \times 2.00^\circ\text{C}}{0.0300\ \text{mol}} \times \frac{1}{1000} = -55.8\ \text{kJ/mol}$$

Q: Using the following data, calculate $$\Delta H^\circ_{rxn}$$ for $$\mathrm{P_4$(g) + 10\ Cl_2$(g) \rightarrow 4\ $$PCl_5$$(s)}$$: $$\mathrm{$$PCl_5$$(s) \rightarrow $$PCl_3$$(g) + Cl_2$(g)}$$ $$\Delta H^\circ_{rxn} = +157 kJ$$ $$\mathrm{P_4$(g) + 6\ Cl_2$(g) \rightarrow 4\ $$PCl_3$$(g)}$$ $$\Delta H^\circ_{rxn} = -1207 kJ$$

$$\Delta H^\circ_{rxn} = -1207\ \text{kJ} + 4 \times (+157\ \text{kJ}) = -1207\ \text{kJ} + 628\ \text{kJ} = -579\ \text{kJ}$$

Q: Electromagnetic radiation with a wavelength of 525 nm appears as green light. What is the energy of one photon of this light in J?

$$E = \frac{hc}{\lambda} = \frac{6.626 \times 10$$^{-34}$$\ \text{J·s} \times 3.00 \times 10^8$\ \text{m/s}}{525 \times 10$$^{-9}$$\ \text{m}} = 3.79 \times 10$$^{-19}$$\ \text{J}$$

Q: Calculate the wavelength (in nm) of blue light emitted by a mercury lamp with a frequency of $$6.88 \times 10$$^{14}$$ Hz.

$$\lambda = \frac{c}{v} = \frac{3.00 \times 10^8$\ \text{m/s}}{6.88 \times 10$$^{14}$$\ \text{Hz}} = 4.36 \times 10$$^{-7}$$\ \text{m} = 436\ \text{nm}$$

Q: Determine the velocity of a medicine ball ($$m = 10.0 kg) $$with a wavelength of $$1.33 \times 10$$^{-35}$$ m using the de Broglie relation.

$$v = \frac{h}{m\lambda} = \frac{6.626 \times 10$$^{-34}$$\ \text{J·s}}{10.0\ \text{kg} \times 1.33 \times 10$$^{-35}$$\ \text{m}} = 4.98 \times 10^2$\ \text{m/s}$$

Q: Determine the mass of a ball with a wavelength of $$3.45 \times 10$$^{-34}$$ m and a velocity of 6.55$ m/s using the de Broglie relation.

$$m = \frac{h}{v\lambda} = \frac{6.626 \times 10$$^{-34}$$\ \text{J·s}}{6.55\ \text{m/s} \times 3.45 \times 10$$^{-34}$$\ \text{m}} = 0.29\ \text{kg}$$

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

$$\Delta E = q + w = 35.8\ \text{kJ} + [-(1.00\ \text{atm}) \times (24.0 - 8.00)\ \text{L} \times 101.3\ \text{J/L·atm} \times \frac{1}{1000}] = 35.8\ \text{kJ} - 1.62\ \text{kJ} = 34.2\ \text{kJ}$$

Question 1

A 150.0 g sample of an alloy is heated from 298 K to 398 K, requiring 59.3 kJ of energy. What is the specific heat capacity ($$C_s) of $$the alloy in J/g·K?

Accepted Answer

$$C_s = \frac{q}{m \Delta T} = \frac{59300\ 	ext{J}}{150.0\ 	ext{g} 	imes 100\ 	ext{K}} = 3.95\ 	ext{J/g·K}$$

Question 2

Which equation correctly represents the change in internal energy ($$\Delta E) $$for a system that does work on the surroundings and loses heat?

Accepted Answer

$$\Delta E = -q - w$$

Question 3

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°C to 62.3°C. Given $$\Delta H^\circ_{rxn} = -1235 kJ $$for $$\mathrm{C_2H_5OH(l) + 3 O_2$(g) \rightarrow 2 CO_2$(g) + 3 H_2O(g)}$$, what is the heat capacity ($$C_{cal}) of $$the calorimeter in J/°C?

Accepted Answer

$$C_{cal} = \frac{q_{rxn}}{\Delta T} = \frac{(-1235\ 	ext{kJ}) 	imes \frac{21.8}{46.07}}{62.3 - 25.0} 	imes 1000 = 155.6\ 	ext{J/°C}$$

Question 4

How much energy is required to decompose 612 g of $$\mathrm{$$PCl_3$$}$$ according to $$4\ \mathrm{$$PCl_3$$(g)} \rightarrow \mathrm{P_4$(s)} + 6\ \mathrm{Cl_2$(g)}$$, $$\Delta H^\circ_{rxn} = +1207 kJ$$? (Molar mass $$\mathrm{$$PCl_3$$} = 137.32 g/$$mol)

Accepted Answer

$$	ext{Energy} = \frac{612\ 	ext{g}}{137.32\ 	ext{g/mol}} 	imes \frac{1207\ 	ext{kJ}}{4} = 1346\ 	ext{kJ}$$

Question 5

A 100.0 mL sample of 0.300 M NaOH is mixed with 100.0 mL of 0.300 M HCl at 35.00°C. The final temperature is 37.00°C. Assuming density and heat capacity are the same as water ($$4.184\ 	ext{J/g}^\circ	ext{C}$$), what is $$\Delta H^\circ_{rxn} in kJ/$$mol NaOH?

Accepted Answer

$$\Delta H^\circ_{rxn} = \frac{q}{	ext{mol NaOH}} = \frac{(200\ 	ext{g}) 	imes 4.184\ 	ext{J/g}^\circ	ext{C} 	imes 2.00^\circ	ext{C}}{0.0300\ 	ext{mol}} 	imes \frac{1}{1000} = -55.8\ 	ext{kJ/mol}$$

Question 6

Using the following data, calculate $$\Delta H^\circ_{rxn}$$ for $$\mathrm{P_4$(g) + 10\ Cl_2$(g) \rightarrow 4\ $$PCl_5$$(s)}$$:
$$\mathrm{$$PCl_5$$(s) \rightarrow $$PCl_3$$(g) + Cl_2$(g)}$$ $$\Delta H^\circ_{rxn} = +157 kJ$$
$$\mathrm{P_4$(g) + 6\ Cl_2$(g) \rightarrow 4\ $$PCl_3$$(g)}$$ $$\Delta H^\circ_{rxn} = -1207 kJ$$

Accepted Answer

$$\Delta H^\circ_{rxn} = -1207\ 	ext{kJ} + 4 	imes (+157\ 	ext{kJ}) = -1207\ 	ext{kJ} + 628\ 	ext{kJ} = -579\ 	ext{kJ}$$

Question 7

Electromagnetic radiation with a wavelength of 525 nm appears as green light. What is the energy of one photon of this light in J?

Accepted Answer

$$E = \frac{hc}{\lambda} = \frac{6.626 	imes 10$$^{-34}$$\ 	ext{J·s} 	imes 3.00 	imes 10^8$\ 	ext{m/s}}{525 	imes 10$$^{-9}$$\ 	ext{m}} = 3.79 	imes 10$$^{-19}$$\ 	ext{J}$$

Question 8

Calculate the wavelength (in nm) of blue light emitted by a mercury lamp with a frequency of $$6.88 	imes 10$$^{14}$$ Hz.

Accepted Answer

$$\lambda = \frac{c}{v} = \frac{3.00 	imes 10^8$\ 	ext{m/s}}{6.88 	imes 10$$^{14}$$\ 	ext{Hz}} = 4.36 	imes 10$$^{-7}$$\ 	ext{m} = 436\ 	ext{nm}$$

Question 9

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

Accepted Answer

blue

Question 10

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

Accepted Answer

red

Question 11

Determine the velocity of a medicine ball ($$m = 10.0 kg) $$with a wavelength of $$1.33 	imes 10$$^{-35}$$ m using the de Broglie relation.

Accepted Answer

$$v = \frac{h}{m\lambda} = \frac{6.626 	imes 10$$^{-34}$$\ 	ext{J·s}}{10.0\ 	ext{kg} 	imes 1.33 	imes 10$$^{-35}$$\ 	ext{m}} = 4.98 	imes 10^2$\ 	ext{m/s}$$

Question 12

Determine the mass of a ball with a wavelength of $$3.45 	imes 10$$^{-34}$$ m and a velocity of 6.55$ m/s using the de Broglie relation.

Accepted Answer

$$m = \frac{h}{v\lambda} = \frac{6.626 	imes 10$$^{-34}$$\ 	ext{J·s}}{6.55\ 	ext{m/s} 	imes 3.45 	imes 10$$^{-34}$$\ 	ext{m}} = 0.29\ 	ext{kg}$$

Question 13

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

Accepted Answer

$$\Delta E = q + w = 35.8\ 	ext{kJ} + [-(1.00\ 	ext{atm}) 	imes (24.0 - 8.00)\ 	ext{L} 	imes 101.3\ 	ext{J/L·atm} 	imes \frac{1}{1000}] = 35.8\ 	ext{kJ} - 1.62\ 	ext{kJ} = 34.2\ 	ext{kJ}$$

Question 14

For a process at constant pressure, $$q = 145 kJ $$and $$w = -35 kJ. $$What are $$\Delta E$$ and $$\Delta H$$?

Accepted Answer

$$\Delta E = q + w = 145\ 	ext{kJ} + (-35\ 	ext{kJ}) = 110\ 	ext{kJ}$$, $$\Delta H = q = 145\ 	ext{kJ}$$

Question 15

Calculate the energy change associated with the transition from $$n = 2 to$$ $$n = 5 in $$the hydrogen atom.

Accepted Answer

$$\Delta E = -2.18 	imes 10$$^{-18}$$\ 	ext{J} \left( \frac{1}{n_f^2$} - \frac{1}{n_i^2$} ight) = -2.18 	imes 10$$^{-18}$$\ 	ext{J} \left( \frac{1}{25} - \frac{1}{4} ight) = +4.58 	imes 10$$^{-19}$$\ 	ext{J}$$

Question 16

Which set of $$m_l$$ values corresponds to a d orbital?

Accepted Answer

-2, -1, 0, 1, 2

Question 17

Which set of $$m_l$$ values corresponds to a p orbital?

Accepted Answer

-1, 0, 1

Question 18

Which set of $$m_l$$ values corresponds to an f orbital?

Accepted Answer

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

Question 19

Describe the shape of a p orbital.

Accepted Answer

dumbbell shaped

Question 20

Describe the shape of an s orbital.

Accepted Answer

spherical

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