Q: A 750.0 mL gas cylinder contains a gas at 840.0 mm Hg. If the pressure is reduced to 360.0 mm Hg at constant temperature, what is the final volume of the gas?

$$V_2$$ = \frac{$$P_1$$ $$V_1$$}{$$P_2$$} = \frac{840.0 \times 750.0}{360.0} = 1750\ \text{mL}$$

Q: A 5.00 L balloon of gas at $$25^\circC is $$cooled to $$0^\circC at $$constant pressure. What is the new volume of the balloon?

$$V_2$$ = $$V_1$$ \frac{$$T_2$$}{$$T_1$$} = 5.00 \times \frac{273}{298} = 4.58\ \text{L}$$

Q: A 500.0 mL balloon at $$25^\circC is $$heated to $$50^\circC at $$constant pressure. What is the final volume?

$$V_2$$ = $$V_1$$ \frac{$$T_2$$}{$$T_1$$} = 500.0 \times \frac{323}{298} = 542\ \text{mL}$$

Q: A sample of 0.255 mol of gas has a volume of 748 mL at $$28^\circC. $$Calculate the pressure of this gas. ($$R = 0.08206\ \text{L} \cdot \text{atm} / \text{mol} \cdot \text{K})$$

$$P = \frac{nRT}{V} = \frac{0.255 \times 0.08206 \times 301}{0.748} = 0.842\ \text{atm}$$

Q: A mixture of gases contains 78% nitrogen at a pressure of 984 torr and 22% carbon dioxide at 345 torr. What is the total pressure of the system?

$$P_{total} = 984 + 345 = 1329\ \text{torr}$$

Q: Hydrogen gas is collected over water at $$25^\circC. $$The barometric pressure is 742.5 mm Hg and the vapor pressure of water at $$25^\circC is 23.8 mm Hg. $$What is the pressure of dry hydrogen gas?

$$P_{H_2$} = P_{total} - P_{H_2O} = 742.5 - 23.8 = 718.7\ \text{mm Hg}$$

Q: Ammonia gas decomposes according to $$2NH_3(g) \rightarrow N_2$(g) + 3H_2(g). If 15.0 L of $$nitrogen is formed at STP, how many liters of hydrogen will be produced (also measured at STP)?

$$3 \times 15.0 = 45.0\ \text{L}$$

Q: Water can be formed according to $$2H_2(g) + O_2$(g) \rightarrow 2H_2O(g). If 8.0 L of $$hydrogen is reacted at STP, exactly how many liters of oxygen at STP would be needed to allow complete reaction?

$$O_2 = 8.0$$ \times \frac{1}{2} = 4.0\ \text{L}$$

Question 1

A 750.0 mL gas cylinder contains a gas at 840.0 mm Hg. If the pressure is reduced to 360.0 mm Hg at constant temperature, what is the final volume of the gas?

Accepted Answer

$$V_2$$ = \frac{$$P_1$$ $$V_1$$}{$$P_2$$} = \frac{840.0 	imes 750.0}{360.0} = 1750\ 	ext{mL}$$

Question 2

A 5.00 L balloon of gas at $$25^\circC is $$cooled to $$0^\circC at $$constant pressure. What is the new volume of the balloon?

Accepted Answer

$$V_2$$ = $$V_1$$ \frac{$$T_2$$}{$$T_1$$} = 5.00 	imes \frac{273}{298} = 4.58\ 	ext{L}$$

Question 3

A 500.0 mL balloon at $$25^\circC is $$heated to $$50^\circC at $$constant pressure. What is the final volume?

Accepted Answer

$$V_2$$ = $$V_1$$ \frac{$$T_2$$}{$$T_1$$} = 500.0 	imes \frac{323}{298} = 542\ 	ext{mL}$$

Question 4

A sample of helium gas initially at $$37.0^\circC$$, 785 torr, and 2.01 L is heated to $$58.0^\circC $$and expands to 3.24 L. What is the final pressure in atm?

Accepted Answer

$$P_2$$ = $$P_1$$ \frac{$$V_1$$}{$$V_2$$} \frac{$$T_2$$}{$$T_1$$} = 785 	imes \frac{2.01}{3.24} 	imes \frac{331}{310} = 509\ 	ext{torr} = 0.670\ 	ext{atm}$$

Question 5

A sample of 0.255 mol of gas has a volume of 748 mL at $$28^\circC. $$Calculate the pressure of this gas. ($$R = 0.08206\ 	ext{L} \cdot 	ext{atm} / 	ext{mol} \cdot 	ext{K})$$

Accepted Answer

$$P = \frac{nRT}{V} = \frac{0.255 	imes 0.08206 	imes 301}{0.748} = 0.842\ 	ext{atm}$$

Question 6

A 3.76 g sample of a noble gas is stored in a 2.00 L vessel at 874 torr and $$25^\circC. $$What is the noble gas?

Accepted Answer

Xenon ($$Xe)$$

Question 7

A gas cylinder contains only radon, nitrogen, and helium. The radon has a pressure of 222 torr, nitrogen has 446 torr, and the total pressure is 771 torr. What is the pressure due to helium?

Accepted Answer

$$P_{He} = P_{total} - P_{Rn} - P_{N_2$} = 771 - 222 - 446 = 103\ 	ext{torr}$$

Question 8

A mixture of gases contains 78% nitrogen at a pressure of 984 torr and 22% carbon dioxide at 345 torr. What is the total pressure of the system?

Accepted Answer

$$P_{total} = 984 + 345 = 1329\ 	ext{torr}$$

Question 9

Hydrogen gas is collected over water at $$25^\circC. $$The barometric pressure is 742.5 mm Hg and the vapor pressure of water at $$25^\circC is 23.8 mm Hg. $$What is the pressure of dry hydrogen gas?

Accepted Answer

$$P_{H_2$} = P_{total} - P_{H_2O} = 742.5 - 23.8 = 718.7\ 	ext{mm Hg}$$

Question 10

Ammonia gas decomposes according to $$2NH_3(g) \rightarrow N_2$(g) + 3H_2(g). If 15.0 L of $$nitrogen is formed at STP, how many liters of hydrogen will be produced (also measured at STP)?

Accepted Answer

$$3 	imes 15.0 = 45.0\ 	ext{L}$$

Question 11

Water can be formed according to $$2H_2(g) + O_2$(g) \rightarrow 2H_2O(g). If 8.0 L of $$hydrogen is reacted at STP, exactly how many liters of oxygen at STP would be needed to allow complete reaction?

Accepted Answer

$$O_2 = 8.0$$ 	imes \frac{1}{2} = 4.0\ 	ext{L}$$

Question 12

How many liters of $$O_2$$ are needed to react completely with 56.0 L of $$CH_4 at $$STP to produce $$CO_2$$ and $$H_2O$$? (Given: $$CH_4(g) + 2O_2(g$$) \rightarrow $$CO_2(g) + 2H_2O(g$$)$$)

Accepted Answer

$$O_2 = 56.0$$ 	imes 2 = 112\ 	ext{L}$$

Question 13

Calculate the volume of $$H_2(g$$)$$ at 273 K and 2.00 atm that will be formed when 275 mL of 0.725 M HCl solution reacts with 50.0 g Zn to give hydrogen gas and aqueous zinc chloride. (R = 0.08206$$\ 	ext{L} \cdot 	ext{atm} / 	ext{mol} \cdot 	ext{K}$$)

Accepted Answer

$$n_{HCl} = 0.275 	imes 0.725 = 0.199\ 	ext{mol}$$; $$n_{H_2$} = 0.0995\ 	ext{mol}$$; $$V = \frac{nRT}{P} = \frac{0.0995 	imes 0.08206 	imes 273}{2.00} = 1.12\ 	ext{L}$$

Question 14

A compound composed of carbon, hydrogen, and chlorine effuses through a pinhole 0.411 times as fast as neon. What is the molecular formula of the compound?

Accepted Answer

$$	ext{C}_2	ext{H}_2	ext{Cl}_2$$

Question 15

Calculate the density, in g/L, of $$SF_6$$ gas at $$27^\circC $$and 0.500 atm pressure.

Accepted Answer

$$d = \frac{PM}{RT} = \frac{0.500 	imes 146.06}{0.08206 	imes 300} = 2.97\ 	ext{g/L}$$

Question 16

A 1.325 g sample of an unknown vapor occupies 368 mL at $$114^\circC $$and 946 mm Hg. The empirical formula is $$NO_2. $$What is the molecular formula of the compound?

Accepted Answer

$$N_2O_4$$

Question 17

A gas is compressed to a volume of 286 mL and the pressure increases to 901 torr. If the initial temperature is $$32^\circC$$, what is the new temperature of the gas (in $$^\circC) if $$the initial pressure was 760 torr and the initial volume was 500 mL?

Accepted Answer

$$T_2$$ = \frac{$$P_2$$ $$V_2$$ $$T_1$$}{$$P_1$$ $$V_1$$} = \frac{901 	imes 286 	imes 305}{760 	imes 500} = 206\ 	ext{K} = -67^\circ	ext{C}$$

General Chemistry Study Notes: Gases, Gas Laws, and Related Calculations

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