Question 1

Boltzmann's constant,k,has a value of 1.381 $\times$ 10^-23 J/K.What is the significance of the constant? A)It defines a characteristic energy at the microscopic level given the temperature in kelvins. B)It allows the pressure of the gas to be calculated given the volume and temperature. C)It measures the average kinetic energy of a molecule at a given temperature for each degree of freedom. D)(A)and (B) E)(A)and (C)

Accepted Answer

Boltzmann's constant relates the average kinetic energy of a molecule to the temperature and determines the characteristic energy at the microscopic level for each degree of freedom. Thus, it measures the amount of energy required for a molecule to change its state, and it is closely related to the entropy, which is a measure of disorder in a system. Therefore, option (C) is correct, as well as (A), since Boltzmann's constant allows calculating the energy at the microscopic level given the temperature. Option (B) is incorrect because pressure depends on other factors such as the number of molecules and their interactions, and Boltzmann's constant does not play a direct role in this calculation.

Question 2

In a vacuum system,a container is pumped down to a pressure of 1.33 $\times$ 10^-6 Pa at 20ºC.How many molecules of gas are there in 1 cm³ of this container? (Boltzmann's constant k = 1.38 $\times$ 10^-23 J/K) A)3.3 $\times$ 10⁸ B)4.8 $\times$ 10⁹ C)3.3 $\times$ 10¹⁴ D)7.9 $\times$ 10¹² E)4.8 $\times$ 10¹²

Accepted Answer

The number of molecules can be calculated using the ideal gas law in the form: $ n = \frac{P \cdot V}{k \cdot T} $. Substituting the given values: $ P = 1.33 \times 10^{-6} \, \text{Pa} $, $ V = 1 \times 10^{-6} \, \text{m}^3 $, $ k = 1.38 \times 10^{-23} \, \text{J/K} $, and $ T = 293 \, \text{K} $, we find $ n \approx 3.3 \times 10^8 $ molecules.

Question 3

The relationship between the pressure and the volume of a gas expressed by Boyle's law holds true
A)for some gases under any conditions.
B)if the density is constant.
C)if the container of the gas can expand with increasing pressure.
D)if the temperature is constant.
E)for all gases under any conditions.

Accepted Answer

Boyle's law states that at constant temperature, the volume of a given amount of gas is inversely proportional to its pressure. Therefore, the law holds true only if the temperature is kept constant. The other choices are not relevant to Boyle's law.

Question 4

You can double both the pressure and the volume of an ideal gas if you change the temperature of the gas by
A)reducing it to one-quarter of its original value.
B)doubling it.
C)reducing it to one-half of its original value.
D)quadrupling it.
E)doing none of these

Accepted Answer

Doubling both the pressure and volume of an ideal gas implies that the final state has four times the initial energy (since PV = nRT, and both P and V are doubled, the left side of the equation becomes 4PV). To achieve this, the temperature must also be quadrupled, as temperature is directly proportional to the energy of the gas.

Question 5

The air around us has 78% nitrogen and 21% oxygen.If the pressure is 1 atm,the pressure due to oxygen is
A)0.21 atm
B)0.78 atm
C)1 atm
D)0.5 atm
E)0.67 atm

Accepted Answer

The pressure due to oxygen in the air can be calculated using Dalton's Law of Partial Pressures, which states that the total pressure of a mixture of gases is equal to the sum of the partial pressures of the individual gases. Given that oxygen makes up 21% of the air and the total pressure is 1 atm, the pressure due to oxygen is 0.21 atm (21% of 1 atm).

Question 6

Inside a sphere of radius 12 cm are 8.0 $\times$ 10²³ gas molecules at a temperature of 50S1U1P1$\circ$S1S1P0C.What pressure do the gas molecules exert on the inside of the sphere? A)650 $\times$ 10³ Pa B)370 $\times$ 10³ Pa C)76.0 $\times$ 10³ Pa D)160 $\times$ 10³ Pa E)490 $\times$ 10³ Pa

Accepted Answer

The answer of Inside a sphere of radius 12 cm...

Question 7

Which of the following statements about the ideal gas law,PV = nRT,is NOT true?
A)When the temperature of two low density gases,which are initially at the same temperature,pressure and volume,is increased by the same amount,the volume increases by the same amount.
B)When the volume of two low density gases,which are initially at the same temperature,pressure and volume,is compressed by the same amount,the temperature increases by the same amount.
C)A P-T plot of any gas at low density intercept the T-axis at the same point.
D)The intercept at the ordinate for PV/nT vs P plot of any gas is the gas constant.
E)The ideal gas law is valid for high density of all gases.

Accepted Answer

The ideal gas law is not valid for high density gases because at high densities, the intermolecular forces between gas molecules become significant and the gas behaves less like an ideal gas. Therefore, statement E is not true.

Question 8

A collection of oxygen molecules occupies a volume V at standard temperature and pressure.What is the new volume if the amount of oxygen is doubled and the pressure is tripled?
A)V
B)(2/3)V
C)(3/2)V
D)6V
E)(5/9)V

Accepted Answer

The answer of A collection of oxygen molecules occupies a...

Question 9

Assume that helium is a perfect gas and that the volume of a cylinder containing helium is independent of temperature.A cylinder of helium at +85ºC has a pressure of 208 atm.The pressure of the helium when it is cooled to -55ºC is
A)-132 atm
B)127 atm
C)335 atm
D)132 atm
E)204 atm

Accepted Answer

The pressure of a gas related to temperature can be described by the ideal gas law, $P_1/T_1 = P_2/T_2$, assuming the volume and the amount of gas remain constant. Convert temperatures to Kelvin: $T_1 = 85 + 273 = 358K$ and $T_2 = -55 + 273 = 218K$. Solve for $P_2$: $P_2 = P_1 \times (T_2/T_1) = 208 \times (218/358) \approx 127 atm$.

Question 10

What mass of He gas occupies 8.5 liters at 0S1U1P1$\circ$S1S1P0C and 1 atmosphere? (The molar mass of He = 4.00 g/mol.)
A)10.5 g
B)0.66 g
C)2.6 g
D)0.38 g
E)1.52 g

Accepted Answer

To find the mass of He gas, we can use the ideal gas law equation PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature in Kelvin. Given that the volume V = 8.5 liters, P = 1 atmosphere, and T = 0°C (which is 273.15 K), we can solve for n, the number of moles of He. The ideal gas constant R = 0.0821 L·atm/(mol·K). Rearranging the ideal gas law to solve for n gives n = PV/(RT). Substituting the given values, n = (1 atm * 8.5 L) / (0.0821 L·atm/(mol·K) * 273.15 K) = 0.379 moles of He. The mass of He can then be found by multiplying the number of moles by the molar mass of He (4.00 g/mol), so the mass = 0.379 moles * 4.00 g/mol = 1.52 g.

Question 11

A cylinder of volume 50 L contains oxygen gas at a pressure of 2 atm.If nitrogen gas of volume 25 L and at pressure 1 atm is added to the oxygen cylinder,the new pressure is
A)2 atm
B)3 atm
C)2.5 atm
D)3.5 atm
E)4 atm

Accepted Answer

Using the combined gas law, we can find the new pressure:
(P1V1)/T1 = (P2V2)/T2
Assuming constant temperature and solving for P2:
P2 = (P1V1 + P2V2)/ (V1 + V2)
P2 = (2 atm * 50 L + 1 atm * 25 L) / (50 L + 25 L) = 2.33 atm
Rounding to the nearest tenth, the new pressure is approximately 2.5 atm. Therefore, the correct answer is C) 2.5 atm.

Question 12

A large balloon is being filled with He from gas cylinders.The temperature is 25S1U1P1$\circ$S1S1P0C and the pressure is 1 atmosphere.The volume of the inflated balloon is 2500 m³.What was the volume of He in the cylinders if the gas was under a pressure of 110 atmospheres and at a temperature of 12S1U1P1$\circ$S1S1P0C when in the gas cylinders? A)11 m³ B)22 m³ C)24 m³ D)15 m³ E)23 m³

Accepted Answer

Using the ideal gas law and the combined gas law, the volume of He in the cylinders can be calculated as 22 m³.

Question 13

A mass of He gas occupies a volume V at standard temperature and pressure.What volume is occupied if the mass is halved,the absolute temperature doubled,and the pressure increased by a third?
A)(3/16)V
B)(4/3)V
C)(3/4)V
D)(3/8)V
E)(1/3)V

Accepted Answer

We can use the combined gas law to solve this problem, which states that:

(P1V1)/T1 = (P2V2)/T2

where P is pressure, V is volume, and T is temperature.

Let's label the initial conditions as 1 and the final conditions as 2:

- Mass is halved, so the number of moles is halved. Since He gas is monatomic, its mass is directly proportional to the number of moles, so the mass of He is also halved. 
- Absolute temperature is doubled, which means T2 = 2T1. 
- Pressure is increased by a third, which means P2 = (4/3)P1.

Substituting these values into the combined gas law, we get:

(P1V1)/T1 = [(4/3)P1V2]/(2T1)

Simplifying, we get:

V2 = (3/4)V1

So the final volume is 3/4 of the initial volume, which means the best choice is C.

Question 14

A rigid container of air is at atmospheric pressure and 27ºC.To double the pressure in the container,heat it to
A)54ºC
B)300ºC
C)327ºC
D)600ºC
E)327 K

Accepted Answer

According to Charles's Law, at a constant pressure, the volume of a gas is directly proportional to its absolute temperature. Therefore, if we want to double the pressure in the container, we need to increase the temperature by a factor of 2 as well. To find the new temperature, we can use the formula:
(T2/T1) = (P2/P1) 
where T1 is the initial temperature, T2 is the final temperature, P1 is the initial pressure (atmospheric pressure), and P2 is the final pressure (twice the atmospheric pressure). Substituting the values, we get:
(T2/300K) = (2/1)
T2 = 600 K
However, we need to convert this to Celsius, so:
T2 = 327ºC
Therefore, the correct answer is C) 327ºC.

Question 15

The air in a balloon occupies a volume of 0.10 m³ when at a temperature of 27ºC and a pressure of 1.2 atm.What is the balloon's volume at 7ºC and 1.0 atm? (The amount of gas remains constant.) A)0.022 m³ B)0.078 m³ C)0.089 m³ D)0.11 m³ E)0.13 m³

Accepted Answer

To find the new volume, we can use the combined gas law: $ \frac{P_1V_1}{T_1} = \frac{P_2V_2}{T_2} $. Given $P_1 = 1.2 \, \text{atm}$, $V_1 = 0.10 \, \text{m}^3$, $T_1 = 27^\circ C = 300 \, K$, $P_2 = 1.0 \, \text{atm}$, and $T_2 = 7^\circ C = 280 \, K$, solving for $V_2$ gives a value close to $0.11 \, \text{m}^3$, considering the direct and inverse relationships between pressure, volume, and temperature.

Question 16

A gas has a density X at standard temperature and pressure.What is the new density when the absolute temperature is doubled and the pressure increased by a factor of 3?
A)(2/3)X
B)(4/3)X
C)(3/4)X
D)(6)X
E)(3/2)X

Accepted Answer

The density of a gas is directly proportional to its pressure and inversely proportional to its temperature (in Kelvin). When the temperature is doubled (T -> 2T) and the pressure is tripled (P -> 3P), the new density is (3P)/(2T) times the original density. Since the original density is proportional to P/T, the new density is (3/2) times the original density, hence (3/2)X.

Question 17

If a mass of oxygen gas occupies a volume of 8 L at standard temperature and pressure,what is the change in the volume if the temperature is reduced by one half and the pressure is doubled?
A)It increases to 12 L.
B)It decreases to 6 L.
C)It increases to 24 L.
D)It decreases to 2 L.
E)It does not change.

Accepted Answer

According to the combined gas law (P1V1/T1 = P2V2/T2), if the temperature is halved and the pressure is doubled, the volume will decrease to one-fourth of the original volume. Therefore, the volume changes from 8 L to 2 L.

Question 18

If the pressure and volume of an ideal gas are both reduced to half their original value,the absolute temperature of the gas is
A)unchanged.
B)doubled.
C)halved.
D)increased by a factor of 4.
E)decreased by a factor of 4.

Accepted Answer

The answer of If the pressure and volume of an...

Question 19

If a mass of oxygen gas occupies a volume of 8 L at standard temperature and pressure,what is the change in the volume if the temperature is decreased to 136 K and the pressure remains constant?
A)It increases to 16 L.
B)It decreases to 12 L.
C)It increases to 24 L.
D)It decreases to 4 L.
E)It increases to 12 L.

Accepted Answer

The volume of a gas is directly proportional to the temperature if the pressure is constant. Therefore, if the temperature is decreased, the volume will also decrease. We can use the following formula:

V1/T1 = V2/T2

where V1 and T1 are the initial volume and temperature, and V2 and T2 are the final volume and temperature, respectively.

Plugging in the given values, we get:

8 L / 273 K = V2 / 136 K

Solving for V2, we get:

V2 = (8 L / 273 K) * 136 K = 2.35 L

Therefore, the change in volume is:

8 L - 2.35 L = 5.65 L

So, the final volume is:

8 L - 5.65 L = 2.35 L

which is less than the initial volume of 8 L. The closest answer choice is (D), which predicts that the volume decreases to 4 L.

Question 20

If both the temperature and the volume of an ideal gas are doubled,the pressure is
A)increased by a factor of 4.
B)doubled also.
C)unchanged.
D)diminished by a factor of ¼.
E)None of these is correct.

Accepted Answer

According to the ideal gas law (PV=nRT), if both the temperature (T) and volume (V) of an ideal gas are doubled, the pressure (P) remains unchanged because the increase in temperature is offset by the increase in volume.

Quiz 17: Temperature and the Kinetic Theory of Gases

Boltzmann's constant,k,has a value of 1.381 $\times$ 10^-23 J/K.What is the significance of the constant?

In a vacuum system,a container is pumped down to a pressure of 1.33 $\times$ 10^-6 Pa at 20ºC.How many molecules of gas are there in 1 cm³ of this container? (Boltzmann's constant k = 1.38 $\times$ 10^-23 J/K)

The relationship between the pressure and the volume of a gas expressed by Boyle's law holds true

You can double both the pressure and the volume of an ideal gas if you change the temperature of the gas by

The air around us has 78% nitrogen and 21% oxygen.If the pressure is 1 atm,the pressure due to oxygen is

Inside a sphere of radius 12 cm are 8.0 $\times$ 10²³ gas molecules at a temperature of 50^$\circ$C.What pressure do the gas molecules exert on the inside of the sphere?

Which of the following statements about the ideal gas law,PV = nRT,is NOT true?

A collection of oxygen molecules occupies a volume V at standard temperature and pressure.What is the new volume if the amount of oxygen is doubled and the pressure is tripled?

Assume that helium is a perfect gas and that the volume of a cylinder containing helium is independent of temperature.A cylinder of helium at +85ºC has a pressure of 208 atm.The pressure of the helium when it is cooled to -55ºC is

What mass of He gas occupies 8.5 liters at 0^$\circ$C and 1 atmosphere? (The molar mass of He = 4.00 g/mol.)

A cylinder of volume 50 L contains oxygen gas at a pressure of 2 atm.If nitrogen gas of volume 25 L and at pressure 1 atm is added to the oxygen cylinder,the new pressure is

A mass of He gas occupies a volume V at standard temperature and pressure.What volume is occupied if the mass is halved,the absolute temperature doubled,and the pressure increased by a third?

A rigid container of air is at atmospheric pressure and 27ºC.To double the pressure in the container,heat it to

The air in a balloon occupies a volume of 0.10 m³ when at a temperature of 27ºC and a pressure of 1.2 atm.What is the balloon's volume at 7ºC and 1.0 atm? (The amount of gas remains constant.)

A gas has a density X at standard temperature and pressure.What is the new density when the absolute temperature is doubled and the pressure increased by a factor of 3?

If a mass of oxygen gas occupies a volume of 8 L at standard temperature and pressure,what is the change in the volume if the temperature is reduced by one half and the pressure is doubled?

If the pressure and volume of an ideal gas are both reduced to half their original value,the absolute temperature of the gas is

If a mass of oxygen gas occupies a volume of 8 L at standard temperature and pressure,what is the change in the volume if the temperature is decreased to 136 K and the pressure remains constant?

If both the temperature and the volume of an ideal gas are doubled,the pressure is