Gases and the Kinetic-Molecular Theory

How does a sample of gas differ in its behavior from a sample of liquid in each of the following situations?

(a) The sample is transferred from one container to a larger one.

(b) The sample is heated in an expandable container, but no change of state occurs.

(c) The sample is placed in a cylinder with a piston, and an external force is applied.

Are the particles in a gas farther apart or closer together than the particles in a liquid? Use your answer to explain each of the following general observations:

(a) Gases are more compressible than liquids.

(b) Gases have lower viscosities than liquids.

(c) After thorough stirring, all gas mixtures are solutions.

(d) The density of a substance in the gas state is lower than in the liquid state.

How does a barometer work? Is the column of mercury in a barometer shorter when it is on a mountaintop or at sea level? Explain.

How can a unit of length such as millimetre of mercury (mmHg) be used as a unit of pressure, which has the dimensions of force per unit area?

In a closed-end manometer, the mercury level in the arm attached to the flask can never be higher than the mercury level in the other arm, whereas in an open-end manometer, it can be higher. Explain.

On a cool, rainy day, the barometric pressure is 730 mmHg. Calculate the barometric pressure in centimeters of water (cmH₂O) (d of Hg = 13.5 g/mL; d of H₂O = 1.00 g/mL).

Convert the following:

(a) 0.745 atm to mmHg                  (b) 992 torr to bar

(c) 365 kPa to atm                           (d) 804 mmHg to kPa

Convert the following:

(a) 76.8 cmHg to atm          (b) 27.5 atm to kPa

(c) 6.50 atm to bar               (d) 0.937 kPa to torr

Convert each of the pressures described below to atm:

(a) At the peak of Mt. Everest, atmospheric pressure is only $2.75\times {10}^2 mmHg$ .

(b) A cyclist fills her bike tires to $86 psi$ .

(c) The surface of Venus has an atmospheric pressure of  $9.15\times {10}^6 Pa$.

(d) At 100 ft below sea level, a scuba diver experiences a pressure of $2.54\times {10}^4 torr$ .

The gravitational force exerted by an object is given by F = mg, where F is the force in Newtons, m is the mass in kilograms, and g is the acceleration due to gravity (9.81 m/s²).

(a) Use the definition of the pascal to calculate the mass (in kg) of the atmosphere above 1 m² of ocean.

(b) Osmium (Z = 76) is a transition metal in Group 8B(8) and has the highest density of any element (22.6 g/mL). If an osmium column is 1 m² in area, how high must it be for its pressure to equal atmospheric pressure? [Use the answer from part (a) in your calculation.]

A long glass tube, sealed at one end, has an inner diameter of 10.0 mm. The tube is filled with water and inverted into a pail of water. If the atmospheric pressure is 755 mmHg, how high (in mmH₂O) is the column of water in the tube (d of Hg = 13.5 g/mL; d of H₂O = 1.00 g/mL)?

In Figure P5.10, what is the pressure of the gas in the flask (in atm) if the barometer reads 738.5 torr?

In Figure P5.11, what is the pressure of the gas in the flask (in kPa) if the barometer reads 765.2 mmHg?

If the sample flask in Figure P5.12 is open to the air, what is the atmospheric pressure (in atm)?

What is the pressure (in Pa) of the gas in the flask in Figure P5.13?

A student states Boyle’s law as follows: “The volume of a gas is inversely proportional to its pressure.” How is this statement incomplete? Give a correct statement of Boyle’s law.

In preparation for a demonstration, your professor brings a 1.5-L bottle of sulfur dioxide into the lecture hall before class to allow the gas to reach room temperature. If the pressure gauge reads 85 psi and the temperature in the hall is $\mathbf{23}\mathbf{°}\mathbf{C}$ , how many moles of sulfur dioxide are in the bottle?

A 75.0-g sample of dinitrogen monoxide is confined in a 3.1-L vessel. What is the pressure (in atm) at $\mathbf{115}\mathbf{°}\mathit{C}$?

A gas-filled weather balloon with a volume of 65.0 L is released at sea-level conditions of 745 torr and $\mathbf{25}\mathbf{°}\mathbf{C}$ . The balloon can expand to a maximum volume of 835 L. When the balloon rises to an altitude at which the temperature is $\mathbf{-}\mathbf{5}\mathbf{°}\mathbf{C}$ and the pressure is 0.066 atm, will it reach its maximum volume?

Why is moist air less dense than dry air?

You have 357 mL of chlorine trifluoride gas at 699 mmHg and $\mathbf{45}\mathbf{°}\mathit{C}$. What is the mass (in g) of the sample?

To collect a beaker of ${\mathbf{H}}_{\mathbf{2}}$   gas by displacing the air already in the beaker, would you hold the beaker upright or inverted? Why? How would you hold the beaker to collect ${\mathbf{CO}}_{\mathbf{2}}$ ?

Why can we use a gas mixture, such as air, to study the general behavior of an ideal gas under ordinary conditions?

If $\mathbf{1}\mathbf{.}\mathbf{47}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{3}}$ of argon occupies a 75.0-mL container at $\mathbf{26}\mathbf{.}\mathbf{°}\mathit{C}$, what is the pressure (in torr)?

A sample of chlorine gas is confined in a 5.0-L container at 328 torr and $\mathbf{37}\mathbf{°}\mathit{C}$. How many moles of gas are in the sample?

A sample of carbon monoxide occupies 3.65 L at 298 K and 745 torr. Find its volume at $\mathbf{-}\mathbf{14}\mathbf{°}\mathit{C}$ and 367 torr.

 A sample of Freon-12 ($\mathit{C}{\mathit{F}}_{\mathbf{2}}\mathit{C}{\mathit{I}}_{\mathbf{2}}$) occupies 25.5 L at 298 K and 153.3 kPa. Find its volume at STP.

A 93-L sample of dry air cools from $\mathbf{145}\mathbf{°}\mathit{C}$ to $\mathbf{-}\mathbf{22}\mathbf{°}\mathit{C}$ while the pressure is maintained at 2.85 atm. What is the final volume?

A sample of sulfur hexafluoride gas occupies 9.10 L at $\mathbf{198}\mathbf{°}\mathit{C}$. Assuming that the pressure remains constant, what temperature (in $\mathbf{°}\mathit{C}$) is needed to reduce the volume to 2.50 L?

What is the effect of the following on the volume of 1 mol of an ideal gas?

(a) Half the gas escapes (at constant P and T).

(b) The initial pressure is 722 torr, and the final pressure is 0.950 atm; the initial temperature is 32^oF, and the final temperature is 273 K.

(c) Both the pressure and temperature decrease to one-fourth of their initial values.

What is the effect of the following on the volume of 1 mol of an ideal gas?

(a) Temperature decreases from 800 K to 400 K (at constant P).

(b) Temperature increases from $\mathbf{250}\mathbf{°}\mathit{C}$ to $\mathbf{500}\mathbf{°}\mathit{C}$ (at constant P).

(c) Pressure increases from 2 atm to 6 atm (at constant T).

 What is the effect of the following on the volume of 1 mol of an ideal gas?

(a) The pressure is reduced by a factor of 4 (at constant T).

(b) The pressure changes from 760 torr to 202 kPa, and the temperature changes from $\mathbf{37}\mathbf{°}\mathit{C}$ to 155 K.

(c) The temperature changes from 305 K to $\mathbf{32}\mathbf{°}\mathit{C}$, and the pressure changes from 2 atm to 101 kPa.

 What is the effect of the following on the volume of 1 mol of an ideal gas?

(a) The pressure is tripled (at constant T).

(b) The absolute temperature is increased by a factor of 3.0 (at constant P).

(c) Three more moles of the gas are added (at constant P and T).

Each of the following processes caused the gas volume to double, as shown. For each process, state how the remaining gas variable changed or that it remained fixed:

(a) T doubles at fixed P.

(b) T and n are fixed.

(c) At fixed T, the reaction is $\mathit{C}{\mathit{D}}_{\mathbf{2}}\left(g\right)\mathbf{\to }\mathit{C}\left(g\right)\mathbf{+}{\mathit{D}}_{\mathbf{2}}\left(g\right)$

(d) At fixed P, the reaction is ${\mathit{A}}_{\mathbf{2}}\mathbf{\left(}\mathbf{g}\mathbf{\right)}\mathbf{+}{\mathit{B}}_{\mathbf{2}}\mathbf{\left(}\mathbf{g}\mathbf{\right)}\mathbf{\to }\mathbf{2}\mathit{A}\mathit{B}\mathbf{\left(}\mathbf{g}\mathbf{\right)}$

In the following relationships, which quantities are variables and which are fixed: (a) Charles’s law; (b) Avogadro’s law; (c) Amontons’s law?

Boyle’s law relates gas volume to pressure, and Avogadro’s law relates gas volume to number of moles. State a relationship between gas pressure and number of moles.