Chapter 6

Describe the difference between force and pressure.

Describe the role of collisions in generating pressure.

How does Torricelli's barometer measure atmospheric pressure?

What is the relationship between torr and atmospberes of pressure?

What is the relationship between millibars and pascals of pressure?

Three barometers based on Torricelli's design are constructed using water \((d=1.00 \mathrm{g} / \mathrm{mL}),\) ethanol \((d=0.789 \mathrm{g} / \mathrm{mL}),\) and mercury \((d=13.546 \mathrm{g} / \mathrm{mL}) .\) Which barometer contains the tallest column of liquid?

Why does an ice skater exert more pressure on ice when wearing newly sharpened skates than when wearing skates with dull blades?

Why does atmospheric pressure decrease with increasing elevation?

Pieces of different metals have the same mass but different densities. Could these objects ever exert the same pressure?

Calculate the downward pressure due to gravity exerted by the bottom face of a \(1.00 \mathrm{kg}\) cube of iron that is \(5.00 \mathrm{cm}\) on a side.

Convert the following pressures into atmospheres: (a) \(2.0 \mathrm{kPa}\) (b) \(562 \mathrm{mmHg}\).

Convert the following pressures into millimeters of mercury: (a) 0.541 atm; (b) \(2.8 \mathrm{kPa}\).

Which is the larger pressure: 10 torr or 10 atm?

Which helium balloon has more collisions at room temperature: a 1 L helium balloon at 0.1 atm or a \(1 \mathrm{L}\) helium balloon at 455 mm Hg?

The highest atmospheric pressure recorded on Earth was measured at Tosontsengel, Mongolia, on December \(19,2001,\) when the barometer read \(108.6 \mathrm{kP}\) a. Express this pressure in (a) millimeters of mercury, (b) atmospheres, and (c) millibars.

Hurricane Irene registered an atmospheric pressure of 982 mbar in August 2011\. Hurricane Katrina registered an atmospheric pressure of \(86.2 \mathrm{kPa}\) in September \(2005 .\) What was the difference in pressure between the two hurricanes in (a) millimeters of mercury, (b) atmospheres, and (c) millibars?

Venus is similar to Earth in size and distance from the Sun but has an atmosphere inhospitable for human life that consists of \(96.5 \% \mathrm{CO}_{2}\) and \(3.5 \% \mathrm{N}_{2}\) by mass. a. Calculate the atmospheric pressure on Venus given the mass of the Venusian atmosphere \(\left(4.8 \times 10^{20} \mathrm{kg}\right),\) the surface area \(\left(4.6 \times 10^{14} \mathrm{m}^{2}\right)\), and the acceleration due to gravity \(\left(8.87 \mathrm{m} / \mathrm{s}^{2}\right)\) "b. Given the similarity between Venus and Earth in surface area, why do you suppose atmospheric pressure on Venus is so much higher than on Earth?

Uranus is much larger than Earth, with a surface area of \(8.1 \times 10^{15} \mathrm{m}^{2}\) with an atmosphere composed of low-density gases: \(82.5 \%\) H \(_{2}, 15.2 \%\) He, and \(2.3 \% \mathrm{CH}_{4} .\) The acceleration due to gravity is similar to that on Earth, \(8.7 \mathrm{m} / \mathrm{s}^{2}\), yet the atmospheric pressure on Uranus is estimated to exceed \(10^{8} \mathrm{Pa}\). What is the mass of the atmosphere on Uranus?

From the molecular perspective, why is pressure directly proportional to temperature at fixed volume (Amontons's law)?

How do we explain Boyle's law on a molecular basis?

A balloonist is rising too fast for her taste. Should she increase the temperature of the gas in the balloon or decrease it?

If the volume of gasoline vapor and air in an automobile engine cylinder is reduced to \(1 / 10\) of its original volume before ignition, by what factor does the pressure in the cylinder increase? (Assume there is no change in temperature.)

What is the final pressure of 1.00 mol of ammonia gas, initially at 1.00 atm, if the volume is a. gradually decreased from \(78.0 \mathrm{mL}\) to \(39.0 \mathrm{mL}\) at constant temperature? b. increased from \(43.5 \mathrm{mL}\) to \(65.5 \mathrm{mL}\) at constant temperature? c. decreased by \(40 \%\) at constant temperature?

The behavior of \(485 \mathrm{mL}\) of an ideal gas in response to pressure is studied in a vessel with a movable piston. What is the final volume of the gas if the pressure on the sample is a. increased from \(715 \mathrm{mmHg}\) to 3.55 atm at constant temperature? b. decreased from 1.15 atm to \(520 \mathrm{mmHg}\) at constant temperature? c. increased by \(26 \%\) at constant temperature?

Underwater Archeology \(\mathrm{A}\) scuba diver releases a balloon containing \(153 \mathrm{L}\) of helium attached to a tray of artifacts at an underwater archaeological site (Figure \(\mathrm{P} 6.51\) ). When the balloon reaches the surface, it has expanded to a volume of 352 L. The pressure at the surface is 1.00 atm; what is the pressure at the underwater site? Pressure increases by 1.0 atm for every \(10 \mathrm{m}\) of depth; at what depth was the diver working? Assume the temperature remains constant.

Use the following data to draw a graph of the volume of He as a function of temperature for 1.0 mol of He gas at a constant pressure of 1.00 atm: (TABLE CAN'T COPY) How would the graph change if the amount of gas were halved?

A cylinder with a piston (Figure \(\mathrm{P} 6.57\) ) contains a sample of gas at \(25^{\circ} \mathrm{C} .\) The piston moves to keep the pressure constant inside the cylinder. At what gas temperature would the piston move so that the volume inside the cylinder doubled?

Calculate the temperature of a \(5.6 \mathrm{L}\) sample of gas in the cylinder in Figure \(\mathrm{P} 6.57\) after it is subjected to the following changes in conditions: a. The gas, at constant pressure, is cooled from \(78^{\circ} \mathrm{C}\) to a temperature at which its volume is \(4.3 \mathrm{L}\) b. The external pressure is doubled at constant volume. c. The number of molecules in the cylinder is increased by \(15 \%\) at constant pressure and volume.

A student holding a 50.0 L balloon containing 800 mmHg of hydrogen at \(19^{\circ} \mathrm{C}\) lets go of the balloon, allowing the gas to escape. How many moles of gas did the balloon contain and how much work was done on the surroundings if the temperature remains constant?

Which of the following actions would produce the greater increase in the volume of a gas sample: (a) lowering the pressure from \(760 \mathrm{mmHg}\) to \(720 \mathrm{mmHg}\) at constant temperature or (b) raising the temperature from \(10^{\circ} \mathrm{C}\) to \(40^{\circ} \mathrm{C}\) at constant pressure?

Which of the following actions would produce the greater increase in the volume of a gas sample: (a) doubling the amount of gas in the sample at constant temperature and pressure or (b) raising the temperature from \(244^{\circ} \mathrm{C}\) to \(1100^{\circ} \mathrm{C}\) at constant pressure?

What happens to the volume of gas in a cylinder with a movable piston under the following conditions? a. Both the absolute temperature and the external pressure on the piston double. b. The absolute temperature is halved, and the external pressure on the piston doubles. c. The absolute temperature increases by \(75 \%,\) and the external pressure on the piston increases by \(50 \%\).

What happens to the pressure of a gas under the following conditions? a. The absolute temperature is halved and the volume doubles. b. Both the absolute temperature and the volume double. c. The absolute temperature increases by \(75 \%,\) and the volume decreases by \(50 \%\).

A sample of a gas enclosed in a cylinder with a piston has a volume of \(500.0 \mathrm{mL}\) at \(30.0^{\circ} \mathrm{C} .\) What is the sample volume at \(100.0^{\circ} \mathrm{C} ?\)

A tank containing 5.00 L of nitrogen at 75.0 atm pressure and \(28^{\circ} \mathrm{C}\) is left standing in sunlight. Its temperature rises to \(50.0^{\circ} \mathrm{C} .\) What is the gas pressure at this higher temperature?

Temperature Effects on Bicycle Tires A bicycle racer inflates his tires to 7.1 atm on a warm autumn afternoon when temperatures reached \(27^{\circ} \mathrm{C} .\) By morning the temperature has dropped to \(5.0^{\circ} \mathrm{C} .\) What is the pressure in the tires if we assume that the volume of the tire does not change significantly?

A balloon vendor at a street fair is using a tank of helium to fill her balloons. The tank has a volume of \(145 \mathrm{L}\) and a pressure of 136 atm at \(25^{\circ} \mathrm{C}\). After a while she notices that the valve has not been closed properly, and the pressure has dropped to 94 atm. How many moles of gas have been lost?

What is meant by standard temperature and pressure (STP)? What is the volume of 1 mole of an ideal gas at STP?

Which of the following are not characteristics of an ideal gas? a. The molecules of gas have little volume compared with the volume that they occupy. b. Its volume is independent of temperature. c. The density of all ideal gases is the same. d. Gas atoms or molecules do not interact with one another.

What does the slope represent in a graph of pressure as a function of \(1 / V\) at constant temperature for an ideal gas?

At what temperature will 1.00 mole of an ideal gas in a \(1.00 \mathrm{L}\) container exert a pressure of a. 1.00 atm? b. 2.00 atm? c. 0.75 atm?

Hyperbaric Oxygen Therapy Hyperbaric oxygen chambers are used to treat divers suffering from decompression sickness (the "bends") with pure oxygen at greater than atmospheric pressure. Other clinical uses include treatment of patients with thermal burns, necrotizing fasciitis, and CO poisoning. What is the pressure in a chamber with a volume of \(2.36 \times 10^{3} \mathrm{L}\) that contains \(4635 \mathrm{g}\) of \(\mathrm{O}_{2}(g)\) at a temperature of \(298 \mathrm{K} ?\)

Hydrogen holds promise as an "environment friendly" fuel. How many grams of \(\mathrm{H}_{2}\) gas are present in a \(50.0 \mathrm{L}\) fuel tank at a pressure of \(2850 \mathrm{lb} / \mathrm{in}^{2}(\mathrm{psi})\) at \(20^{\circ} \mathrm{C} ?\) Assume that \(1 \mathrm{atm}=14.7 \mathrm{psi}\).

A weather balloon with a volume of \(200.0 \mathrm{L}\) is launched at \(20^{\circ} \mathrm{C}\) at sea level, where the atmospheric pressure is 1.00 atm. a. What is the volume of the balloon at 20,000 m where atmospheric pressure is \(63 \mathrm{mmHg}\) and the temperature is \(220 \mathrm{K} ?\) b. At even higher elevations (the stratosphere, up to \(50,000 \mathrm{m}),\) the temperature of the atmosphere increases to \(270 \mathrm{K}\) but the pressure decreases to \(0.80 \mathrm{mmHg} .\) What is the volume of the balloon under these conditions? c. If the balloon is designed to rupture when the volume exceeds \(400.0 \mathrm{L},\) will the balloon break under either of these sets of conditions?

A sealed, flexible foil bag of potato chips, containing \(0.500 \mathrm{L}\) of air, is carried from Boston \(\left(P_{\mathrm{atm}}=1.0 \mathrm{atm}\right)\) to Denver \(\left(P_{\text {atm }}=0.83 \mathrm{atm}\right)\) a. What would the volume of the bag be upon arrival in Denver? b. If the structural limitations of the bag allow for only a \(10 \%\) expansion in the volume of the bag, what is the pressure in the bag? c. If the bag is placed in checked luggage, the pressure and temperature in the hold will decrease considerably during flight to \(T=210 \mathrm{K}\) and \(P=126\) torr. Calculate the pressure in the bag during flight.

Miners' Lamps Before the development of reliable batteries, miners' lamps burned acetylene produced by the reaction of calcium carbide with water: $$ \mathrm{CaC}_{2}(s)+\mathrm{H}_{2} \mathrm{O}(\ell) \rightarrow \mathrm{C}_{2} \mathrm{H}_{2}(g)+\mathrm{CaO}(s) $$ A lamp uses \(1.00 \mathrm{L}\) of acetylene per hour at 1.00 atm pressure and \(18^{\circ} \mathrm{C}\) a. How many moles of \(\mathrm{C}_{2} \mathrm{H}_{2}\) are used per hour? b. How many grams of calcium carbide must be in the lamp for a 4 -h shift?

Acid precipitation dripping on limestone produces carbon dioxide by the following reaction: \(\mathrm{CaCO}_{3}(s)+2 \mathrm{H}_{3} \mathrm{O}^{+}(a q) \rightarrow \mathrm{Ca}^{2+}(a q)+\mathrm{CO}_{2}(g)+3 \mathrm{H}_{2} \mathrm{O}(\ell)\) If \(15.0 \mathrm{mL}\) of \(\mathrm{CO}_{2}\) was produced at \(25^{\circ} \mathrm{C}\) and \(760 \mathrm{mmHg}\), then a. how many moles of \(\mathrm{CO}_{2}\) were produced? b. how many milligrams of \(\mathrm{CaCO}_{3}\) were consumed?

Air is about \(78 \%\) nitrogen by volume and \(21 \%\) oxygen. Pure nitrogen can be produced by the decomposition of ammonium dichromate: $$ \left(\mathrm{NH}_{4}\right)_{2} \mathrm{Cr}_{2} \mathrm{O}_{7}(s) \rightarrow \mathrm{N}_{2}(g)+\mathrm{Cr}_{2} \mathrm{O}_{3}(s)+4 \mathrm{H}_{2} \mathrm{O}(g) $$ Oxygen can be generated by the thermal decomposition of potassium chlorate: $$ 2 \mathrm{KClO}_{3}(s) \rightarrow 2 \mathrm{KCl}(s)+3 \mathrm{O}_{2}(g) $$ How many grams of ammonium dichromate and how many grams of potassium chlorate would be needed to make \(200.0 \mathrm{L}\) of \(^{\mathrm{u}}\) air" at 0.85 atm and \(273 \mathrm{K} ?\)

The CO \(_{2}\) that builds up in the air of a submerged submarine can be removed by reacting it with sodium peroxide: $$ 2 \mathrm{Na}_{2} \mathrm{O}_{2}(s)+2 \mathrm{CO}_{2}(g) \rightarrow 2 \mathrm{Na}_{2} \mathrm{CO}_{3}(s)+\mathrm{O}_{2}(g) $$ If a sailor exhales \(150.0 \mathrm{mL}\) of \(\mathrm{CO}_{2}\) per minute at \(20^{\circ} \mathrm{C}\) and 1.02 atm, how much sodium peroxide is needed per sailor in a 24 -hr period?

Do all gases at the same pressure and temperature have the same density? Explain your answer.