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In the text, it was shown that N / V = 2 . 68 × 10 25 m 3 size 12{N/V=2 "." "68" times "10" rSup { size 8{"25"} } `m rSup { size 8{ - 3} } } {} for gas at STP. (a) Show that this quantity is equivalent to N / V = 2 . 68 × 10 19 cm 3 , size 12{N/V=2 "." "68" times "10" rSup { size 8{"19"} } `"cm" rSup { size 8{ - 3} } ,} {} as stated. (b) About how many atoms are there in one μm 3 size 12{"μm" rSup { size 8{3} } } {} (a cubic micrometer) at STP? (c) What does your answer to part (b) imply about the separation of atoms and molecules?

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Calculate the number of moles in the 2.00-L volume of air in the lungs of the average person. Note that the air is at 37 . 0 º C size 12{"37" "." 0°C} {} (body temperature).

7 . 86 × 10 2 mol size 12{7 "." "86" times "10" rSup { size 8{ - 2} } `"mol"} {}

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An airplane passenger has 100 cm 3 size 12{"100"" cm" rSup { size 8{3} } } {} of air in his stomach just before the plane takes off from a sea-level airport. What volume will the air have at cruising altitude if cabin pressure drops to 7 . 50 × 10 4 N/m 2 ? size 12{7 "." "50"´"10" rSup { size 8{4} } " N/m" rSup { size 8{2} } } {}

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(a) What is the volume (in km 3 size 12{"km" rSup { size 8{3} } } {} ) of Avogadro’s number of sand grains if each grain is a cube and has sides that are 1.0 mm long? (b) How many kilometers of beaches in length would this cover if the beach averages 100 m in width and 10.0 m in depth? Neglect air spaces between grains.

(a) 6 . 02 × 10 5 km 3 size 12{6 "." "02" times "10" rSup { size 8{5} } `"km" rSup { size 8{3} } } {}

(b) 6 . 02 × 10 8 km size 12{6 "." "02" times "10" rSup { size 8{8} } `"km"} {}

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An expensive vacuum system can achieve a pressure as low as 1 . 00 × 10 7 N/m 2 size 12{1 "." "00"´"10" rSup { size 8{ +- 7} } " N/m" rSup { size 8{2} } } {} at 20 º C size 12{"20"°C} {} . How many atoms are there in a cubic centimeter at this pressure and temperature?

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The number density of gas atoms at a certain location in the space above our planet is about 1 . 00 × 10 11 m 3 , size 12{1 "." "00" times "10" rSup { size 8{"11"} } `m rSup { size 8{ - 3} } ,} {} and the pressure is 2 . 75 × 10 10 N/m 2 size 12{2 "." "75"´"10" rSup { size 8{ +- "10"} } " N/m" rSup { size 8{2} } } {} in this space. What is the temperature there?

73 . 9 º C size 12{ - "73" "." 9°C} {}

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A bicycle tire has a pressure of 7 . 00 × 10 5 N/m 2 size 12{7 "." "00"´"10" rSup { size 8{5} } " N/m" rSup { size 8{2} } } {} at a temperature of 18 . 0 º C size 12{"18" "." 0°C} {} and contains 2.00 L of gas. What will its pressure be if you let out an amount of air that has a volume of 100 cm 3 size 12{"100"" cm" rSup { size 8{3} } } {} at atmospheric pressure? Assume tire temperature and volume remain constant.

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A high-pressure gas cylinder contains 50.0 L of toxic gas at a pressure of 1 . 40 × 10 7 N/m 2 size 12{1 "." "40"´"10" rSup { size 8{7} } " N/m" rSup { size 8{2} } } {} and a temperature of 25 . 0 º C size 12{"25" "." 0°C} {} . Its valve leaks after the cylinder is dropped. The cylinder is cooled to dry ice temperature ( 78 . 5 º C ) size 12{ \( –"78" "." 5°C \) } {} to reduce the leak rate and pressure so that it can be safely repaired. (a) What is the final pressure in the tank, assuming a negligible amount of gas leaks while being cooled and that there is no phase change? (b) What is the final pressure if one-tenth of the gas escapes? (c) To what temperature must the tank be cooled to reduce the pressure to 1.00 atm (assuming the gas does not change phase and that there is no leakage during cooling)? (d) Does cooling the tank appear to be a practical solution?

(a) 9 . 14 × 10 6 N/m 2 size 12{9 "." "14" times "10" rSup { size 8{7} } `"N/m" rSup { size 8{2} } } {}

(b) 8 . 23 × 10 6 N/m 2 size 12{8 "." "23" times "10" rSup { size 8{7} } `"N/m" rSup { size 8{2} } } {}

(c) 2.16 K

(d) No. The final temperature needed is much too low to be easily achieved for a large object.

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Find the number of moles in 2.00 L of gas at 35 . 0 º C size 12{"35" "." 0°C} {} and under 7 . 41 × 10 7 N/m 2 size 12{7 "." "41"´"10" rSup { size 8{7} } " N/m" rSup { size 8{2} } } {} of pressure.

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Calculate the depth to which Avogadro’s number of table tennis balls would cover Earth. Each ball has a diameter of 3.75 cm. Assume the space between balls adds an extra 25.0% to their volume and assume they are not crushed by their own weight.

41 km

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(a) What is the gauge pressure in a 25 . 0 º C size 12{"25" "." 0°C} {} car tire containing 3.60 mol of gas in a 30.0 L volume? (b) What will its gauge pressure be if you add 1.00 L of gas originally at atmospheric pressure and 25 . 0 º C size 12{"25" "." 0°C} {} ? Assume the temperature returns to 25 . 0 º C size 12{"25" "." 0°C} {} and the volume remains constant.

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(a) In the deep space between galaxies, the density of atoms is as low as 10 6 atoms/m 3 , size 12{"10" rSup { size 8{6} } " atoms/m" rSup { size 8{3} } ,} {} and the temperature is a frigid 2.7 K. What is the pressure? (b) What volume (in m 3 size 12{m rSup { size 8{3} } } {} ) is occupied by 1 mol of gas? (c) If this volume is a cube, what is the length of its sides in kilometers?

(a) 3 . 7 × 10 17 Pa size 12{3 "." 7 times "10" rSup { size 8{ - "17"} } `"Pa"} {}

(b) 6 . 0 × 10 17 m 3 size 12{6 "." 0 times "10" rSup { size 8{"17"} } `m rSup { size 8{3} } } {}

(c) 8 . 4 × 10 2 km size 12{8 "." 4 times "10" rSup { size 8{2} } `"km"} {}

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Questions & Answers

full meaning of GPS system
Anaele Reply
how to prove that Newton's law of universal gravitation F = GmM ______ R²
Kaka Reply
sir dose it apply to the human system
Olubukola Reply
prove that the centrimental force Fc= M1V² _________ r
Kaka Reply
prove that centripetal force Fc = MV² ______ r
Kaka
how lesers can transmit information
mitul Reply
griffts bridge derivative
Ganesh Reply
below me
please explain; when a glass rod is rubbed with silk, it becomes positive and the silk becomes negative- yet both attracts dust. does dust have third types of charge that is attracted to both positive and negative
Timothy Reply
what is a conductor
Timothy
hello
Timothy
below me
why below you
Timothy
no....I said below me ...... nothing below .....ok?
dust particles contains both positive and negative charge particles
Mbutene
corona charge can verify
Stephen
when pressure increases the temperature remain what?
Ibrahim Reply
remains the temperature
betuel
what is frequency
Mbionyi Reply
define precision briefly
Sujitha Reply
CT scanners do not detect details smaller than about 0.5 mm. Is this limitation due to the wavelength of x rays? Explain.
MITHRA Reply
hope this helps
what's critical angle
Mahmud Reply
The Critical Angle Derivation So the critical angle is defined as the angle of incidence that provides an angle of refraction of 90-degrees. Make particular note that the critical angle is an angle of incidence value. For the water-air boundary, the critical angle is 48.6-degrees.
dude.....next time Google it
okay whatever
Chidalu
pls who can give the definition of relative density?
Temiloluwa
the ratio of the density of a substance to the density of a standard, usually water for a liquid or solid, and air for a gas.
Chidalu
What is momentum
aliyu Reply
mass ×velocity
Chidalu
it is the product of mass ×velocity of an object
Chidalu
how do I highlight a sentence]p? I select the sentence but get options like copy or web search but no highlight. tks. src
Sean Reply
then you can edit your work anyway you want
Wat is the relationship between Instataneous velocity
Oyinlusi Reply
Instantaneous velocity is defined as the rate of change of position for a time interval which is almost equal to zero
Astronomy
Practice Key Terms 4

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Source:  OpenStax, College physics. OpenStax CNX. Jul 27, 2015 Download for free at http://legacy.cnx.org/content/col11406/1.9
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