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)?

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

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

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

Q: Which of the following equations represents the standard enthalpy of formation ($$\Delta H^\circ_f) $$for $$\text{Li}_2\text{SO}_4 (s$$), given that sulfur occurs as $$\text{S}_8$$ under standard conditions?

$$2\ \text{Li}(s) + \frac{1}{8}\ \text{S}_8(s) + 2\ \text{O}_2(g) \rightarrow \text{Li}_2\text{SO}_4(s)$$

Q: A 21.8 g sample of ethanol ($$\text{C}_2\text{H}_5\text{OH}$$, molar mass = 46.07 g/mol) is burned in a bomb calorimeter. The temperature rises from 25.0°C to 62.3°C. Given $$\Delta H^\circ_{rxn} = -1235\ \text{kJ}$$ for $$\text{C}_2\text{H}_5\text{OH}(l) + 3\ \text{O}_2(g) \rightarrow 2\ \text{CO}_2(g) + 3\ \text{H}_2\text{O}(g)$$, what is the heat capacity of the calorimeter ($$C_{cal}) in J$$/°C?

$$C_{cal} = \frac{q_{rxn}}{\Delta T} = \frac{(-1235\ \text{kJ}) \times \frac{21.8}{46.07}}{62.3 - 25.0} \times 1000 = \frac{-585.0\ \text{kJ}}{37.3\ ^\circ\text{C}} \times 1000 = 15680\ \text{J}/^\circ\text{C}$$

Q: Calculate the energy required to decompose 612 g of $$\text{PCl}_3$$ according to $$4\ \text{PCl}_3(g) \rightarrow \text{P}_4(s) + 6\ \text{Cl}_2(g)$$, $$\Delta H^\circ_{rxn} = +1207\ \text{kJ}. ($$Molar mass $$\text{PCl}_3 = 137.32\ \text{g/mol})$$

$$\text{moles} = \frac{612}{137.32} = 4.46\ \text{mol}$$; $$\text{energy} = \frac{4.46}{4} \times 1207 = 1346\ \text{kJ}$$

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?

$$q = m C_s \Delta T = 200\ \text{g} \times 4.184\ \text{J/g}^\circ\text{C} \times 2.00^\circ\text{C} = 1674\ \text{J}$$; $$\text{moles NaOH} = 0.100\ \text{L} \times 0.300\ \text{mol/L} = 0.0300\ \text{mol}$$; $$\Delta H^\circ_{rxn} = \frac{-1674}{0.0300} = -55.8\ \text{kJ/mol}$$

Q: Using the following data, calculate $$\Delta H^\circ_{rxn}$$ for $$\text{SO}_2\text{Cl}_2(g) + 2\ \text{H}_2\text{O}(l) \rightarrow 2\ \text{HCl}(g) + \text{H}_2\text{SO}_4(l)$$: $$\Delta H^\circ_f (kJ/$$mol): $$\text{SO}_2\text{Cl}_2(g) = -364$$, $$\text{H}_2\text{O}(l) = -286$$, $$\text{HCl}(g) = -92$$, $$\text{H}_2\text{SO}_4(l) = -814$$

$$\Delta H^\circ_{rxn} = [2 \times (-92) + (-814)] - [(-364) + 2 \times (-286)] = [-184 - 814] - [-364 - 572] = -998 - (-936) = -62\ \text{kJ}$$

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

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

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

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

Q: Determine the mass of a ball with a wavelength of $$3.45 \times 10$$^{-34}$$\ \text{m}$$ and a velocity of $$6.55\ \text{m/s}$$ using the de Broglie relation ($$h = 6.626 \times 10$$^{-34}$$\ \text{J·s}).$$

$$m = \frac{h}{\lambda v} = \frac{6.626 \times 10$$^{-34}$$}{3.45 \times 10$$^{-34}$$ \times 6.55} = 0.294\ \text{kg}$$

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

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

Question 2

Which equation correctly represents the relationship between internal energy ($$\Delta E$$), heat ($$q$$), and work ($$w) $$for a system?

Accepted Answer

$$\Delta E = q + w$$

Question 3

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

Accepted Answer

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

Question 4

Which of the following equations represents the standard enthalpy of formation ($$\Delta H^\circ_f) $$for $$	ext{Li}_2	ext{SO}_4 (s$$), given that sulfur occurs as $$	ext{S}_8$$ under standard conditions?

Accepted Answer

$$2\ 	ext{Li}(s) + \frac{1}{8}\ 	ext{S}_8(s) + 2\ 	ext{O}_2(g) ightarrow 	ext{Li}_2	ext{SO}_4(s)$$

Question 5

A 21.8 g sample of ethanol ($$	ext{C}_2	ext{H}_5	ext{OH}$$, molar mass = 46.07 g/mol) is burned in a bomb calorimeter. The temperature rises from 25.0°C to 62.3°C. Given $$\Delta H^\circ_{rxn} = -1235\ 	ext{kJ}$$ for $$	ext{C}_2	ext{H}_5	ext{OH}(l) + 3\ 	ext{O}_2(g) ightarrow 2\ 	ext{CO}_2(g) + 3\ 	ext{H}_2	ext{O}(g)$$, what is the heat capacity of the calorimeter ($$C_{cal}) in J$$/°C?

Accepted Answer

$$C_{cal} = \frac{q_{rxn}}{\Delta T} = \frac{(-1235\ 	ext{kJ}) 	imes \frac{21.8}{46.07}}{62.3 - 25.0} 	imes 1000 = \frac{-585.0\ 	ext{kJ}}{37.3\ ^\circ	ext{C}} 	imes 1000 = 15680\ 	ext{J}/^\circ	ext{C}$$

Question 6

Calculate the energy required to decompose 612 g of $$	ext{PCl}_3$$ according to $$4\ 	ext{PCl}_3(g) ightarrow 	ext{P}_4(s) + 6\ 	ext{Cl}_2(g)$$, $$\Delta H^\circ_{rxn} = +1207\ 	ext{kJ}. ($$Molar mass $$	ext{PCl}_3 = 137.32\ 	ext{g/mol})$$

Accepted Answer

$$	ext{moles} = \frac{612}{137.32} = 4.46\ 	ext{mol}$$; $$	ext{energy} = \frac{4.46}{4} 	imes 1207 = 1346\ 	ext{kJ}$$

Question 7

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

$$q = m C_s \Delta T = 200\ 	ext{g} 	imes 4.184\ 	ext{J/g}^\circ	ext{C} 	imes 2.00^\circ	ext{C} = 1674\ 	ext{J}$$; $$	ext{moles NaOH} = 0.100\ 	ext{L} 	imes 0.300\ 	ext{mol/L} = 0.0300\ 	ext{mol}$$; $$\Delta H^\circ_{rxn} = \frac{-1674}{0.0300} = -55.8\ 	ext{kJ/mol}$$

Question 8

Using the following data, calculate $$\Delta H^\circ_{rxn}$$ for $$	ext{SO}_2	ext{Cl}_2(g) + 2\ 	ext{H}_2	ext{O}(l) ightarrow 2\ 	ext{HCl}(g) + 	ext{H}_2	ext{SO}_4(l)$$:
$$\Delta H^\circ_f (kJ/$$mol): $$	ext{SO}_2	ext{Cl}_2(g) = -364$$, $$	ext{H}_2	ext{O}(l) = -286$$, $$	ext{HCl}(g) = -92$$, $$	ext{H}_2	ext{SO}_4(l) = -814$$

Accepted Answer

$$\Delta H^\circ_{rxn} = [2 	imes (-92) + (-814)] - [(-364) + 2 	imes (-286)] = [-184 - 814] - [-364 - 572] = -998 - (-936) = -62\ 	ext{kJ}$$

Question 9

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

Accepted Answer

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

Question 10

Which color of visible light has the highest frequency?

Accepted Answer

blue

Question 11

Which color of visible light has the longest wavelength?

Accepted Answer

red

Question 12

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

Accepted Answer

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

Question 13

Determine the mass of a ball with a wavelength of $$3.45 	imes 10$$^{-34}$$\ 	ext{m}$$ and a velocity of $$6.55\ 	ext{m/s}$$ using the de Broglie relation ($$h = 6.626 	imes 10$$^{-34}$$\ 	ext{J·s}).$$

Accepted Answer

$$m = \frac{h}{\lambda v} = \frac{6.626 	imes 10$$^{-34}$$}{3.45 	imes 10$$^{-34}$$ 	imes 6.55} = 0.294\ 	ext{kg}$$

Question 14

What are the possible values for the magnetic quantum number $$m_l$$ for a d orbital?

Accepted Answer

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

Question 15

What are the possible values for the magnetic quantum number $$m_l$$ for a p orbital?

Accepted Answer

$$-1, 0, 1$$

Question 16

What are the possible values for the magnetic quantum number $$m_l$$ for an f orbital?

Accepted Answer

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

Question 17

Describe the shape of a p orbital.

Accepted Answer

dumbbell shaped

Question 18

Describe the shape of an s orbital.

Accepted Answer

spherical

Question 19

Electromagnetic radiation with a wavelength of 525 nm appears as green light. What is the energy of one photon of this light in J? ($$h = 6.626 	imes 10$$^{-34}$$\ 	ext{J·s}$$, $$c = 3.00 	imes 10^8$\ 	ext{m/s})$$

Accepted Answer

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

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