Q: A fluorescent tube light with a length of 4.00 ft and a diameter of 1.5 inches contains mercury vapor and argon. A specific bulb contains 0.263% mercury and has a total pressure of 304 Pa. How many argon atoms are present in the lamp? (Assume ideal gas behavior and neglect mercury vapor pressure.)

$$1.58 \times 10$$^{21}$$ atoms

Q: Calculate the molar mass of an unknown liquid using the Dumas method: mass of vapor = 1.3214 g, volume of flask = 500 mL, pressure = 754.3 torr, temperature = 99.43°C.

$$M = \frac{mRT}{PV}$$ $$M = \frac{1.3214 \times 0.08206 \times 372.58}{0.993 \times 0.500} = 76.95 g/$$mol

Q: A sample of phosgene gas (COCl$$_2) is $$kept at 850 torr and 35.0°C. Determine its density in g/L.

$$d = \frac{PM}{RT}$$ $$d = \frac{1.118 \times 99.0}{0.08206 \times 308.15} = 3.15 g/L$$

Q: A 135 mL sample of butane gas is collected over water at 28°C and 742 torr. Calculate the number of moles of butane in the collected sample.

$$n = \frac{PV}{RT}$$ $$n = \frac{0.976 \times 0.135}{0.08206 \times 301} = 0.00552$$ mol

Question 1

A gas has a volume of 43.0 L at 18°C and a pressure of 765 torr. If the volume changes to 26.0 L and the temperature changes to 86°C, what is the new pressure (in torr) if the amount of gas remains constant? Use three significant figures.

Accepted Answer

$$P_2$$ = \frac{$$P_1$$ $$V_1$$ $$T_2$$}{$$V_2$$ $$T_1$$}$$
P_2$ = \frac{765 	imes 43.0 	imes (86+273)}{26.0 	imes (18+273)} = 1.56 	imes 10^3$ torr$

Question 2

A vessel contains CO, H$$_2$$, and O$$_2. $$The mole fractions of H$$_2$$ and O$$_2$$ are 0.17 and 0.62, respectively. What is the mole fraction of CO?

Accepted Answer

$$0.21$$

Question 3

A fluorescent tube light with a length of 4.00 ft and a diameter of 1.5 inches contains mercury vapor and argon. A specific bulb contains 0.263% mercury and has a total pressure of 304 Pa. How many argon atoms are present in the lamp? (Assume ideal gas behavior and neglect mercury vapor pressure.)

Accepted Answer

$$1.58 	imes 10$$^{21}$$ atoms

Question 4

Calculate the molar mass of an unknown liquid using the Dumas method: mass of vapor = 1.3214 g, volume of flask = 500 mL, pressure = 754.3 torr, temperature = 99.43°C.

Accepted Answer

$$M = \frac{mRT}{PV}$$
$$M = \frac{1.3214 	imes 0.08206 	imes 372.58}{0.993 	imes 0.500} = 76.95 g/$$mol

Question 5

A sample of phosgene gas (COCl$$_2) is $$kept at 850 torr and 35.0°C. Determine its density in g/L.

Accepted Answer

$$d = \frac{PM}{RT}$$
$$d = \frac{1.118 	imes 99.0}{0.08206 	imes 308.15} = 3.15 g/L$$

Question 6

A 135 mL sample of butane gas is collected over water at 28°C and 742 torr. Calculate the number of moles of butane in the collected sample.

Accepted Answer

$$n = \frac{PV}{RT}$$
$$n = \frac{0.976 	imes 0.135}{0.08206 	imes 301} = 0.00552$$ mol

Question 7

What would be the density of oxygen, O$$_2$$, at the following conditions?
(a) STP
(b) 1.56 atm and 66.0°C
Answer in g/L.

Accepted Answer

a) $$1.43 g/L$$; b) $$1.79 g/L$$

Question 8

A Kr gas was allowed to effuse through a small hole under constant pressure. The 2 L sample of Kr took 96.0 s to effuse. Another gas of unknown identity took 55.5 s to effuse for a 2 L sample. Calculate the molar mass of the unknown gas.

Accepted Answer

$$M_{unk} = M_{Kr} \left(\frac{t_{unk}}{t_{Kr}}\$$right)^2$$
M$$_{unk} = 83.8 \left(\frac{55.5}{96.0}\$$right)^2 = 20.2$ g/mol

Question 9

Explain how the following changes affect the root-mean-square speed ($$v_{rms}) of a $$gas:
(a) increasing pressure
(b) decreasing volume
(c) decreasing temperature

Accepted Answer

(a) no effect; (b) no effect; (c) decrease

Question 10

At STP, consider three separate 10-L samples of He, O$$_2$$, and Cl$$_2$$ behaving ideally. Rank them in order of increasing average kinetic energy and increasing average velocity.

Accepted Answer

All gases will have the same kinetic energy; He \u003c O$$_2$$ \u003c Cl$$_2$$ for increasing average velocity.

Question 11

Which of the following statements is true for the image shown where gas A and B are different gases?
[Graph: Molecular velocity distribution curves for A and B]

Accepted Answer

The root-mean-square speed is the highest speed for both gas A and B.

Question 12

Identify which molecule has the higher molar mass and which has the higher rate of effusion based on the molecular velocity distribution shown below.
Legend: Molecule X → blue, Molecule Y → yellow

Accepted Answer

Higher MM: Y, Higher rate of effusion: X

Question 13

Two containers with a volume of 150 L are filled with gas at 350 K. One container holds 5 moles of Ar, while another holds 5 moles of CO. Based on kinetic molecular theory, which gas has a faster average speed?

Accepted Answer

CO has a faster average speed than Ar.

Question 14

Determine the pressure exerted by a 1.50 mol sample of NH$$_3$$ gas at 60.0°C that occupies a volume of 56.8 L considering that (a) it behaves as an ideal gas (b) it behaves as a real gas (using the van der Waals equation: $$a = 4.17 L$^2$$·atm/mol$$^2$$, $$b = 0.0371 L/$$mol).

Accepted Answer

(a) $$P = 0.722$$ atm; (b) $$P = 0.720$$ atm

Question 15

On average, a television consumes 107 kWh of electricity per year. Calculate the kilojoules of electricity consumed in three years.

Accepted Answer

$$107 	ext{ kWh} 	imes 3 	imes 3600 	ext{ kJ/kWh} = 1.16 	imes 10^6$ kJ

Question 16

Determine the potential energy of a 48 kg swimmer at the apex of his dive from an 8.0 m platform if the apex of the dive is 8.6 m relative to the surface of the water.

Accepted Answer

$$PE = mgh = 48 	imes 9.8 	imes 8.6 = 4.0 	imes 10^3$ J

Question 17

Which of the following statements is true based on the first law of thermodynamics?

Accepted Answer

Energy is conserved.

Question 18

The internal energy ($$\Delta E) $$and the enthalpy change ($$\Delta H) $$are the same for a reaction and both are measured at constant pressure. Is this statement true or false?

Accepted Answer

False

Question 19

Why do the surroundings feel colder during an endothermic reaction?

Accepted Answer

The reaction absorbs heat from the surroundings.

Question 20

Suppose that 0.130 kg of a substance is initially at 25.0°C. What is the final temperature of the substance upon absorbing 2.35 kJ of heat if its specific heat capacity is 0.456 J/g°C?

Accepted Answer

$$q = mc\Delta T ightarrow \Delta T = \frac{q}{mc}$$
$$\Delta T = \frac{2350}{130 	imes 0.456} = 39.4$$°C; $$T_f = 25.0 + 39.4 = 64.4$$°C

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