Q: A medical oxygen tank contains 2.0 moles of $O_2$ at a pressure of 3.0 atm and a temperature of 300 K. What is the volume of the tank? (Use $R = 0.0821 \ \text{L} \cdot \text{atm} / \text{mol} \cdot \text{K}$)

$V = \frac{nRT}{P} = \frac{2.0 \times 0.0821 \times 300}{3.0} = 16.42 \ \text{L}$

Q: A scuba diver uses a tank with a volume of 12 L at a pressure of 200 atm and a temperature of 300 K. How many moles of air are in the tank? ($R = 0.0821 \ \text{L} \cdot \text{atm} / \text{mol} \cdot \text{K}$)

$n = \frac{PV}{RT} = \frac{200 \times 12}{0.0821 \times 300} = 97.3$

Q: A tire contains 0.5 moles of air at a volume of 10 L and a temperature of 300 K. What is the pressure inside the tire? ($R = 0.0821 \ \text{L} \cdot \text{atm} / \text{mol} \cdot \text{K}$)

$P = \frac{nRT}{V} = \frac{0.5 \times 0.0821 \times 300}{10} = 1.23 \ \text{atm}$

Q: A gas sample at 2.0 atm and 250 K occupies 5.0 L. If the pressure is reduced to 1.0 atm and the temperature is increased to 500 K, what is the new volume?

$V_2 = V_1 \times \frac{P_1}{P_2} \times \frac{T_2}{T_1} = 5.0 \times \frac{2.0}{1.0} \times \frac{500}{250} = 20.0 \ \text{L}$

Question 1

According to the Ideal Gas Law, what is the mathematical relationship between pressure ($P$) and volume ($V$) when the number of moles ($n$) and temperature ($T$) are held constant?

Accepted Answer

They are inversely proportional: $P \propto \frac{1}{V}$

Question 2

If the temperature ($T$) of a gas is doubled while keeping the pressure ($P$) and number of moles ($n$) constant, what will happen to the volume ($V$)?

Accepted Answer

It will double.

Question 3

Which of the following equations correctly represents the Ideal Gas Law?

Accepted Answer

$PV = nRT$

Question 4

A medical oxygen tank contains 2.0 moles of $O_2$ at a pressure of 3.0 atm and a temperature of 300 K. What is the volume of the tank? (Use $R = 0.0821 \ 	ext{L} \cdot 	ext{atm} / 	ext{mol} \cdot 	ext{K}$)

Accepted Answer

$V = \frac{nRT}{P} = \frac{2.0 	imes 0.0821 	imes 300}{3.0} = 16.42 \ 	ext{L}$

Question 5

If the number of moles ($n$) in a container is tripled while keeping the pressure ($P$) constant, what happens to the volume ($V$)?

Accepted Answer

It will triple.

Question 6

Which graph best represents the relationship between the partial pressure of a gas ($P$) and the number of moles ($n$) at constant volume and temperature?

Accepted Answer

A curve that increases linearly: $P \propto n$

Question 7

A balloon is filled with 1.0 mole of gas at 1.0 atm and 273 K. If the temperature is increased to 546 K and the pressure remains constant, what will happen to the volume?

Accepted Answer

It will double.

Question 8

Which variable is directly proportional to the number of moles ($n$) in the Ideal Gas Law, assuming all other variables are constant?

Accepted Answer

Volume ($V$)

Question 9

A scuba diver uses a tank with a volume of 12 L at a pressure of 200 atm and a temperature of 300 K. How many moles of air are in the tank? ($R = 0.0821 \ 	ext{L} \cdot 	ext{atm} / 	ext{mol} \cdot 	ext{K}$)

Accepted Answer

$n = \frac{PV}{RT} = \frac{200 	imes 12}{0.0821 	imes 300} = 97.3$

Question 10

If the pressure ($P$) of a gas is increased while keeping the temperature ($T$) and number of moles ($n$) constant, what happens to the volume ($V$)?

Accepted Answer

It decreases.

Question 11

A patient receives a dose of anesthetic gas in a hospital room at 1.0 atm and 298 K. If the room pressure drops to 0.5 atm and the temperature remains constant, what happens to the volume of the gas?

Accepted Answer

It doubles.

Question 12

Which of the following best describes the relationship between volume ($V$) and temperature ($T$) for a fixed amount of gas at constant pressure?

Accepted Answer

Volume is directly proportional to temperature: $V \propto T$

Question 13

A tire contains 0.5 moles of air at a volume of 10 L and a temperature of 300 K. What is the pressure inside the tire? ($R = 0.0821 \ 	ext{L} \cdot 	ext{atm} / 	ext{mol} \cdot 	ext{K}$)

Accepted Answer

$P = \frac{nRT}{V} = \frac{0.5 	imes 0.0821 	imes 300}{10} = 1.23 \ 	ext{atm}$

Question 14

Which of the following changes will NOT affect the pressure of a gas in a sealed container?

Accepted Answer

Doubling the gas constant $R$.

Question 15

A gas sample at 2.0 atm and 250 K occupies 5.0 L. If the pressure is reduced to 1.0 atm and the temperature is increased to 500 K, what is the new volume?

Accepted Answer

$V_2 = V_1 	imes \frac{P_1}{P_2} 	imes \frac{T_2}{T_1} = 5.0 	imes \frac{2.0}{1.0} 	imes \frac{500}{250} = 20.0 \ 	ext{L}$

Ideal Gas Law Applications: Relationships and Graphs

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