Question 1

An ideal gas occupies 12 liters at 293 K and 1 atm (76 cm Hg).Its temperature is now raised to 373 K and its pressure increased to 215 cm Hg.The new volume is:

Accepted Answer

We can use the combined gas law to solve for the new volume:

(P₁V₁/T₁) = (P₂V₂/T₂)

We can convert the initial pressure to atm:

1 atm = 76 cm Hg * (1 atm / 760 cm Hg) = 0.1 atm

Similarly, we can convert the final pressure to atm:

215 cm Hg * (1 atm / 760 cm Hg) = 0.283 atm

Now we can plug in the values:

(0.1 L) / (293 K) = (0.283 atm * V₂) / (373 K)

Solving for V₂:

V₂ = (0.1 L * 373 K * 0.283 atm) / (293 K * 1)

V₂ = 5.4 L

Therefore, the new volume is 5.4 liters.

Question 2

A 2.0-m³ weather balloon is loosely filled with helium at 1 atm (76 cm Hg)and at 27 $\degree$C.At an elevation of 20,000 ft, the atmospheric pressure is down to 38 cm Hg and the helium has expanded, being under no constraint from the confining bag.If the temperature at this elevation is -48 $\degree$C, the gas volume is:

Accepted Answer

Using the combined gas law (PV/T = constant), we can calculate the final volume of the helium at the higher elevation:

(P1V1/T1) = (P2V2/T2)

where P1 = 76 cm Hg, V1 = 2.0 m^3 (assuming the balloon is completely filled), T1 = 27°F + 460 (converting to Rankine scale), P2 = 38 cm Hg, V2 = ?, and T2 = -48°F + 460. Solving for V2, we get:

V2 = (P1/P2)*(T2/T1)*V1
   = (76/38)*(460-48)/(460+27)*2.0
   = 3.0 m^3

Therefore, the best choice is C, which gives the calculated volume of the helium at the higher elevation.

Question 3

Evidence that a gas consists mostly of empty space is the fact that:

Accepted Answer

The fact that the density of a gas becomes much greater when it is liquefied suggests that gases consist mostly of empty space. When a gas is liquefied, its molecules are brought closer together, occupying less volume and increasing the density.

Question 4

Over 1 cycle of a cyclic process in which a system does net work on its environment:

Accepted Answer

In a cyclic process, the system returns to its initial state at the end of the cycle. This means that all state functions, including pressure, volume, temperature, and internal energy, return to their initial values. Therefore, the changes in these properties over one complete cycle are zero.

Question 5

In order that a single process be both isothermal and occur at constant pressure:

Accepted Answer

A change of phase (such as evaporation or condensation) is necessary for a process to be both isothermal and occur at constant pressure. This is because during a phase change, the temperature remains constant while the pressure is able to change.

Question 6

An air bubble doubles in volume as it rises from the bottom of a lake (1000 kg/m³).Ignoring any temperature changes, the depth of the lake is:

Accepted Answer

The answer of An air bubble doubles in volume as...

Question 7

It is known that 28 grams of a certain ideal gas occupy 22.4 liters at standard conditions (0 $\degree$C, 1 atm).The volume occupied by 42 grams of this gas at standard conditions is:

Accepted Answer

The ideal gas law, PV = nRT, tells us that the volume of a gas is directly proportional to the number of moles of gas present. Since the temperature, pressure, and gas type are constant at standard conditions, we can use the ratio of the number of moles of gas to find the ratio of volumes.

28 g of gas is equivalent to 1 mole of gas (using the molar mass of the gas). 
42 g of gas is equivalent to 1.5 moles of gas (using the molar mass of the gas).

Since the ratio of moles of gas is 1:1.5, the ratio of volumes will also be 1:1.5. Therefore, the volume occupied by 42 g of gas at standard conditions will be:

1.5 x 22.4 L = 33.6 L

So, the correct answer is choice C.

Question 8

Air enters a hot-air furnace at 7 $\degree$C and leaves at 77 $\degree$C.If the pressure does not change each entering cubic meter of air expands to:

Accepted Answer

According to the problem, the volume remains constant since the pressure is constant. We can use the formula:
P1V1/T1 = P2V2/T2
Where P1 and T1 are the initial pressure and temperature, and P2 and T2 are the final pressure and temperature.

Let's assume that one cubic meter of air enters the furnace. Then we can find the volume of air leaving the furnace using the formula:
V2 = V1(T2/T1)(P1/P2)
We can plug in the given values to get:
V2 = 1(350/280)(1/1) = 1.25 cubic meters

Therefore, each cubic meter of air expands to 1.25 cubic meters. The answer is B.

Question 9

What is the relationship between the ideal gas constant R and the Boltzmann constant k?

Accepted Answer

R = Nk, where N is Avogadro's number and k is the Boltzmann constant. This relationship connects the macroscopic and microscopic worlds, linking the ideal gas constant to the energy scale of individual molecules.

Question 10

Use R = 8.2* 10^-5 m³ .atm/mol . K and N_A = 6.02 *10²³ mol^-1.The approximate number of air molecules in a 1 m³ volume at room temperature (300 K)and atmospheric pressure is:

Accepted Answer

Using the ideal gas law, we can find the number of moles of air present in a 1 m3 volume at room temperature and atmospheric pressure: PV = nRT where P = 1 atm, V = 1 m3, n = ?, R = 8.2 atm/mol K, and T = 300 K. Solving for n, we get: n = PV/RT = (1 atm)(1 m3)/(8.2 atm/mol K)(300 K) = 0.0408 mol Multiplying this by Avogadro's number (N_A), we can find the number of air molecules: (0.0408 mol)(6.02 F1F1F1S1F1F1F10 10²³ mol^-1) = 2.45 F1F1F1S1F1F1F10 10²⁵ Therefore, the answer is C, 2.4 F1F1F1S1F1F1F10 10²⁵.

Question 11

Two identical rooms in a house are connected by an open doorway.The temperatures in the two rooms are maintained at different values.Which room contains more air?

Accepted Answer

The answer of Two identical rooms in a house are...

Question 12

Avogadro's number is:

Accepted Answer

Avogadro's number, which is a fundamental constant in chemistry, is 6.02 x 10^23 mol^-1, representing the number of atoms, ions, or molecules in one mole of substance.

Question 13

Platinum has a molar mass of 195 g/mol.If you have a ring that contains 2.3 g of platinum, how many moles does it contain?

Accepted Answer

To find the number of moles, we need to divide the mass of platinum by its molar mass.

Number of moles = Mass of platinum / Molar mass of platinum 
Number of moles = 2.3 g / 195 g/mol 
Number of moles = 0.01179 mol which is approximately equal to 0.012 mol.

Therefore, the answer is A) 0.012 mol.

Question 14

An ideal gas undergoes an isothermal process starting with a pressure of 2 * 10⁵ Pa and a volume of 6 cm³.Which of the following might be the pressure and volume of the final state?

Accepted Answer

In an isothermal process, the temperature remains constant. Therefore, we can use the ideal gas law to find the final pressure and volume:

P1V1 = P2V2

where P1 = 2 x 10^5 Pa, V1 = 6 cm^3, and P2 and V2 are the final pressure and volume, respectively. Since the process is isothermal, we can also use the equation PV = nRT, where n is the number of moles of gas, R is the gas constant, and T is the temperature.

Setting the initial and final states equal, we have:

P1V1 = nRT

and

P2V2 = nRT

Dividing the second equation by the first, we get:

P2/P1 = V1/V2

Substituting the values we have:

P2/2 x 10^5 Pa = 6 cm^3/V2

P2V2 = 12 x 10^5 cm^3 Pa

Now, we can use the ideal gas law to find the final volume:

PV = nRT

Substituting P2 = 6 x 10^5 Pa, V2 = ?, and the other values:

6 x 10^5 Pa x V2 = n x R x T

Since the process is isothermal, T remains constant. Therefore, we can write:

6 x 10^5 Pa x V2 = n x R x T1

where T1 is the initial temperature.

We can simplify this equation using the fact that for an ideal gas, PV = nRT:

6 x 10^5 Pa x V2 = P1V1

Substituting the values we have:

6 x 10^5 Pa x V2 = 2 x 10^5 Pa x 6 cm^3

V2 = 2 cm^3

Therefore, the final state is:

Pressure = 6 x 10^5 Pa
Volume = 2 cm^3

The answer is choice D.

Question 15

How many molecules are in a sample of 10^-³ mol?

Accepted Answer

6.02 x 10^23 is Avogadro's number, which represents the number of molecules in one mole of a substance. The sample given in the question is already in the form of moles, so we can simply multiply it by Avogadro's number to get the number of molecules: 10^-³ mol x 6.02 x 10^23 molecules/mol = 6.02 x 10^23 x (10+1+1+1+1+13+1+1+0) molecules = 6.02 x 10^23 x 29 molecules = 1.748 x 10^25 molecules. However, this answer is not one of the choices. The closest choice is B, which is 6.02 x 10^23 x 30 molecules = 1.8076 x 10^25 molecules.

Question 16

273 cm³ of an ideal gas is at 0 $\degree$C.It is heated at constant pressure to 10 $\degree$C.It will now occupy:

Accepted Answer

The volume of an ideal gas at a constant pressure is directly proportional to its temperature in Kelvin. The initial temperature is 0°C, which is 273K, and the final temperature is 10°C, which is 283K. Since the volume is directly proportional to the temperature, increasing the temperature from 273K to 283K would also increase the volume by the same factor. Therefore, the volume increases to 283 cm³.

Question 17

An automobile tire is pumped up to a gauge pressure of 2.0 *10⁵ Pa when the temperature is 27 $\degree$C.What is its gauge pressure after the car has been running on a hot day so that the tire temperature is 77 $\degree$C? Assume that the volume remains fixed and take atmospheric pressure to be 1.013 *10⁵ Pa.

Accepted Answer

The answer of An automobile tire is pumped up to...

Question 18

A given mass of gas is enclosed in a suitable container so that it may be maintained at constant volume.Under these conditions, there can be no change in what property of the gas?

Accepted Answer

Since the volume is constant, the density of the gas cannot change. Pressure, molecular kinetic energy, internal energy, and temperature may all change depending on external factors or changes in the gas itself.

Question 19

The pressures p and volumes V of the five ideal gases, with the same number of molecules, are given below.Which has the highest temperature?

Accepted Answer

The answer of The pressures p and volumes V of...

Question 20

A sample of an ideal gas is compressed by a piston from 10 m³ to 5 m³ and simultaneously cooled from 273 $\degree$C to 0 $\degree$C.As a result there is:

Accepted Answer

The answer of A sample of an ideal gas is...

Quiz 19: The Kinetic Theory of Gases

An ideal gas occupies 12 liters at 293 K and 1 atm (76 cm Hg) .Its temperature is now raised to 373 K and its pressure increased to 215 cm Hg.The new volume is:

Evidence that a gas consists mostly of empty space is the fact that:

Over 1 cycle of a cyclic process in which a system does net work on its environment:

In order that a single process be both isothermal and occur at constant pressure:

An air bubble doubles in volume as it rises from the bottom of a lake (1000 kg/m³) .Ignoring any temperature changes, the depth of the lake is:

It is known that 28 grams of a certain ideal gas occupy 22.4 liters at standard conditions (0 $\degree$ C, 1 atm) .The volume occupied by 42 grams of this gas at standard conditions is:

Air enters a hot-air furnace at 7 $\degree$ C and leaves at 77 $\degree$ C.If the pressure does not change each entering cubic meter of air expands to:

What is the relationship between the ideal gas constant R and the Boltzmann constant k?

Use R = 8.2* 10^-5 m³ .atm/mol . K and N_A = 6.02 *10²³ mol^-1.The approximate number of air molecules in a 1 m³ volume at room temperature (300 K) and atmospheric pressure is:

Two identical rooms in a house are connected by an open doorway.The temperatures in the two rooms are maintained at different values.Which room contains more air?

Avogadro's number is:

Platinum has a molar mass of 195 g/mol.If you have a ring that contains 2.3 g of platinum, how many moles does it contain?

An ideal gas undergoes an isothermal process starting with a pressure of 2 * 10⁵ Pa and a volume of 6 cm³.Which of the following might be the pressure and volume of the final state?

How many molecules are in a sample of 10^-³ mol?

273 cm³ of an ideal gas is at 0 $\degree$ C.It is heated at constant pressure to 10 $\degree$ C.It will now occupy:

A given mass of gas is enclosed in a suitable container so that it may be maintained at constant volume.Under these conditions, there can be no change in what property of the gas?

The pressures p and volumes V of the five ideal gases, with the same number of molecules, are given below.Which has the highest temperature?

A sample of an ideal gas is compressed by a piston from 10 m³ to 5 m³ and simultaneously cooled from 273 $\degree$ C to 0 $\degree$ C.As a result there is:

Quiz 19: The Kinetic Theory of Gases

An ideal gas occupies 12 liters at 293 K and 1 atm (76 cm Hg) .Its temperature is now raised to 373 K and its pressure increased to 215 cm Hg.The new volume is:

Evidence that a gas consists mostly of empty space is the fact that:

Over 1 cycle of a cyclic process in which a system does net work on its environment:

In order that a single process be both isothermal and occur at constant pressure:

An air bubble doubles in volume as it rises from the bottom of a lake (1000 kg/m3) .Ignoring any temperature changes, the depth of the lake is:

It is known that 28 grams of a certain ideal gas occupy 22.4 liters at standard conditions (0 °\degree° C, 1 atm) .The volume occupied by 42 grams of this gas at standard conditions is:

Air enters a hot-air furnace at 7 °\degree° C and leaves at 77 °\degree° C.If the pressure does not change each entering cubic meter of air expands to:

What is the relationship between the ideal gas constant R and the Boltzmann constant k?

Use R = 8.2* 10-5 m3 .atm/mol . K and NA = 6.02 *1023 mol-1.The approximate number of air molecules in a 1 m3 volume at room temperature (300 K) and atmospheric pressure is:

Two identical rooms in a house are connected by an open doorway.The temperatures in the two rooms are maintained at different values.Which room contains more air?

Avogadro's number is:

Platinum has a molar mass of 195 g/mol.If you have a ring that contains 2.3 g of platinum, how many moles does it contain?

An ideal gas undergoes an isothermal process starting with a pressure of 2 * 105 Pa and a volume of 6 cm3.Which of the following might be the pressure and volume of the final state?

How many molecules are in a sample of 10-3 mol?

273 cm3 of an ideal gas is at 0 °\degree° C.It is heated at constant pressure to 10 °\degree° C.It will now occupy:

A given mass of gas is enclosed in a suitable container so that it may be maintained at constant volume.Under these conditions, there can be no change in what property of the gas?

The pressures p and volumes V of the five ideal gases, with the same number of molecules, are given below.Which has the highest temperature?

A sample of an ideal gas is compressed by a piston from 10 m3 to 5 m3 and simultaneously cooled from 273 °\degree° C to 0 °\degree° C.As a result there is:

An air bubble doubles in volume as it rises from the bottom of a lake (1000 kg/m³) .Ignoring any temperature changes, the depth of the lake is:

It is known that 28 grams of a certain ideal gas occupy 22.4 liters at standard conditions (0 $\degree$ C, 1 atm) .The volume occupied by 42 grams of this gas at standard conditions is:

Air enters a hot-air furnace at 7 $\degree$ C and leaves at 77 $\degree$ C.If the pressure does not change each entering cubic meter of air expands to:

Use R = 8.2* 10^-5 m³ .atm/mol . K and N_A = 6.02 *10²³ mol^-1.The approximate number of air molecules in a 1 m³ volume at room temperature (300 K) and atmospheric pressure is:

An ideal gas undergoes an isothermal process starting with a pressure of 2 * 10⁵ Pa and a volume of 6 cm³.Which of the following might be the pressure and volume of the final state?

How many molecules are in a sample of 10^-³ mol?

273 cm³ of an ideal gas is at 0 $\degree$ C.It is heated at constant pressure to 10 $\degree$ C.It will now occupy:

A sample of an ideal gas is compressed by a piston from 10 m³ to 5 m³ and simultaneously cooled from 273 $\degree$ C to 0 $\degree$ C.As a result there is: