# 13.3 The ideal gas law  (Page 7/11)

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In the text, it was shown that $N/V=2\text{.}\text{68}×{\text{10}}^{\text{25}}\phantom{\rule{0.25em}{0ex}}{\text{m}}^{-3}$ for gas at STP. (a) Show that this quantity is equivalent to $N/V=2\text{.}\text{68}×{\text{10}}^{\text{19}}\phantom{\rule{0.25em}{0ex}}{\text{cm}}^{-3},$ as stated. (b) About how many atoms are there in one ${\text{μm}}^{3}$ (a cubic micrometer) at STP? (c) What does your answer to part (b) imply about the separation of atoms and molecules?

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 $\text{37}\text{.}0\text{º}\text{C}$ (body temperature).

$7\text{.}\text{86}×{\text{10}}^{-2}\phantom{\rule{0.25em}{0ex}}\text{mol}$

An airplane passenger has $\text{100}\phantom{\rule{0.25em}{0ex}}{\text{cm}}^{3}$ 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 $7\text{.}\text{50}×{\text{10}}^{4}\phantom{\rule{0.25em}{0ex}}{\text{N/m}}^{2}?$

(a) What is the volume (in ${\text{km}}^{3}$ ) 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) $6\text{.}\text{02}×{\text{10}}^{5}\phantom{\rule{0.25em}{0ex}}{\text{km}}^{3}$

(b) $6\text{.}\text{02}×{\text{10}}^{8}\phantom{\rule{0.25em}{0ex}}\text{km}$

An expensive vacuum system can achieve a pressure as low as $1\text{.}\text{00}×{\text{10}}^{–7}\phantom{\rule{0.25em}{0ex}}{\text{N/m}}^{2}$ at $\text{20}\text{º}\text{C}$ . How many atoms are there in a cubic centimeter at this pressure and temperature?

The number density of gas atoms at a certain location in the space above our planet is about $1\text{.}\text{00}×{\text{10}}^{\text{11}}\phantom{\rule{0.25em}{0ex}}{\text{m}}^{-3},$ and the pressure is $2\text{.}\text{75}×{\text{10}}^{–\text{10}}\phantom{\rule{0.25em}{0ex}}{\text{N/m}}^{2}$ in this space. What is the temperature there?

$-\text{73}\text{.}9\text{º}\text{C}$

A bicycle tire has a pressure of $7\text{.}\text{00}×{\text{10}}^{5}\phantom{\rule{0.25em}{0ex}}{\text{N/m}}^{2}$ at a temperature of $\text{18}\text{.}0\text{º}\text{C}$ 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 $\text{100}\phantom{\rule{0.25em}{0ex}}{\text{cm}}^{3}$ at atmospheric pressure? Assume tire temperature and volume remain constant.

A high-pressure gas cylinder contains 50.0 L of toxic gas at a pressure of $1\text{.}\text{40}×{\text{10}}^{7}\phantom{\rule{0.25em}{0ex}}{\text{N/m}}^{2}$ and a temperature of $\text{25}\text{.}0\text{º}\text{C}$ . Its valve leaks after the cylinder is dropped. The cylinder is cooled to dry ice temperature $\left(–\text{78}\text{.}5\text{º}\text{C}\right)$ 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) $9\text{.}\text{14}×{\text{10}}^{6}\phantom{\rule{0.25em}{0ex}}{\text{N/m}}^{2}$

(b) $8\text{.}\text{23}×{\text{10}}^{6}\phantom{\rule{0.25em}{0ex}}{\text{N/m}}^{2}$

(c) 2.16 K

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

Find the number of moles in 2.00 L of gas at $\text{35}\text{.}0\text{º}\text{C}$ and under $7\text{.}\text{41}×{\text{10}}^{7}\phantom{\rule{0.25em}{0ex}}{\text{N/m}}^{2}$ of pressure.

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

(a) What is the gauge pressure in a $\text{25}\text{.}0\text{º}\text{C}$ 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 $\text{25}\text{.}0\text{º}\text{C}$ ? Assume the temperature returns to $\text{25}\text{.}0\text{º}\text{C}$ and the volume remains constant.

(a) In the deep space between galaxies, the density of atoms is as low as ${\text{10}}^{6}\phantom{\rule{0.25em}{0ex}}{\text{atoms/m}}^{3},$ and the temperature is a frigid 2.7 K. What is the pressure? (b) What volume (in ${\text{m}}^{3}$ ) is occupied by 1 mol of gas? (c) If this volume is a cube, what is the length of its sides in kilometers?

(a) $3\text{.}7×{\text{10}}^{-\text{17}}\phantom{\rule{0.25em}{0ex}}\text{Pa}$

(b) $6\text{.}0×{\text{10}}^{\text{17}}\phantom{\rule{0.25em}{0ex}}{\text{m}}^{3}$

(c) $8\text{.}4×{\text{10}}^{2}\phantom{\rule{0.25em}{0ex}}\text{km}$

what is a wave
wave means. A field of study
aondohemba
what are Atoms
aondohemba
is the movement back and front or up and down
sani
how ?
aondohemba
wave is a disturbance that transfers energy through matter or space with little or no associated mass.
lots
A wave is a motion of particles in disturbed medium that carry energy from one midium to another
conist
an atom is the smallest unit( particle) of an element that bares it's chemical properties
conist
what is electromagnetic induction?
conist
How is the de Broglie wavelength of electrons related to the quantization of their orbits in atoms and molecules?
How do you convert 0.0045kgcmÂ³ to the si unit?
how many state of matter do we really have like I mean... is there any newly discovered state of matter?
I only know 5: •Solids •Liquids •Gases •Plasma •Bose-Einstein condensate
Thapelo
Alright Thank you
Falana
Which one is the Bose-Einstein
James
can you explain what plasma and the I her one you mentioned
Olatunde
u can say sun or stars are just the state of plasma
Mohit
but the are more than seven
Issa
list it out I wanna know
Cristal
what the meaning of continuum
What state of matter is fire
fire is not in any state of matter...fire is rather a form of energy produced from an oxidising reaction.
Xenda
Isn`t fire the plasma state of matter?
Walter
all this while I taught it was plasma
Victor
How can you define time?
Time can be defined as a continuous , dynamic , irreversible , unpredictable quantity .
Tanaya
unpredictable? but I can say after one o'clock its going to be two o'clock predictably!
Victor
how can we define vector
mahmud
I would define it as having a magnitude (size)with a direction. An example I can think of is a car traveling at 50m/s (magnitude) going North (direction)
Hanzo
as for me guys u would say time is quantity that measures how long it takes for a specific condition to happen e.g how long it takes for the day to end or how it takes for the travelling car to cover a km.
conist
what is the relativity of physics
How do you convert 0.0045kgcm³ to the si unit?
flint
What is the formula for motion
V=u+at V²=u²-2as
flint
S=ut+½at
flint
they are eqns of linear motion
King
S=Vt
Thapelo
v=u+at s=ut+at^\2 v^=u^+2as where ^=2
King
hi
hello
King
Explain dopplers effect
Not yet learnt
Bob
Explain motion with types
Bob
Acceleration is the change in velocity over time. Given this information, is acceleration a vector or a scalar quantity? Explain.
Scalar quantity Because acceleration has only magnitude
Bob
acleration is vectr quatity it is found in a spefied direction and it is product of displcemnt
bhat
its a scalar quantity
Paul
velocity is speed and direction. since velocity is a part of acceleration that makes acceleration a vector quantity. an example of this is centripetal acceleration. when you're moving in a circular patter at a constant speed, you are still accelerating because your direction is constantly changing.
Josh
acceleration is a vector quantity. As explained by Josh Thompson, even in circular motion, bodies undergoing circular motion only accelerate because on the constantly changing direction of their constant speed. also retardation and acceleration are differentiated by virtue of their direction in
fitzgerald
respect to prevailing force
fitzgerald
What is the difference between impulse and momentum?
Manyo
Momentum is the product of the mass of a body and the change in velocity of its motion. ie P=m(v-u)/t (SI unit is kgm/s). it is literally the impact of collision from a moving body. While Impulse is the product of momentum and time. I = Pt (SI unit is kgm) or it is literally the change in momentum
fitzgerald
Or I = m(v-u)
fitzgerald
the tendency of a body to maintain it's inertia motion is called momentum( I believe you know what inertia means) so for a body to be in momentum it will be really hard to stop such body or object..... this is where impulse comes in.. the force applied to stop the momentum of such body is impulse..
Pelumi
Calculation of kinetic and potential energy
K.e=mv² P.e=mgh
Malia
K is actually 1/2 mv^2
Josh
what impulse is given to an a-particle of mass 6.7*10^-27 kg if it is ejected from a stationary nucleus at a speed of 3.2*10^-6ms²? what average force is needed if it is ejected in approximately 10^-8 s?
John
speed=velocity÷time velocity=speed×time=3.2×10^-6×10^-8=32×10^-14m/s impulse [I]=∆momentum[P]=mass×velocity=6.7×10^-27×32×10^-14=214.4×10^-41kg/ms force=impulse÷time=214.4×10^-41÷10^-8=214.4×10^-33N. dats how I solved it.if wrong pls correct me.
Melody
what is sound wave
sound wave is a mechanical longitudinal wave that transfers energy from one point to another
Ogor
its a longitudnal wave which is associted wth compresion nad rearfractions
bhat
what is power
it's also a capability to do something or act in a particular way.
Kayode
Newton laws of motion
Mike
power also known as the rate of ability to do work
Slim
power means capabilty to do work p=w/t its unit is watt or j/s it also represents how much work is done fr evry second
bhat
what does fluorine do?
strengthen and whiten teeth.
Gia