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Making connections: take-home experiment—refrigerating a balloon

Inflate a balloon at room temperature. Leave the inflated balloon in the refrigerator overnight. What happens to the balloon, and why?

Calculating the number of molecules in a cubic meter of gas

How many molecules are in a typical object, such as gas in a tire or water in a drink? We can use the ideal gas law to give us an idea of how large N size 12{N} {} typically is.

Calculate the number of molecules in a cubic meter of gas at standard temperature and pressure (STP), which is defined to be 0 º C size 12{0°C} {} and atmospheric pressure.

Strategy

Because pressure, volume, and temperature are all specified, we can use the ideal gas law PV = NkT size 12{ ital "PV"= ital "NkT"} {} , to find N size 12{N} {} .

Solution

1. Identify the knowns.

T = 0 º C = 273 K P = 1 . 01 × 10 5 Pa V = 1 . 00 m 3 k = 1 . 38 × 10 23 J/K

2. Identify the unknown: number of molecules, N size 12{N} {} .

3. Rearrange the ideal gas law to solve for N size 12{N} {} .

PV = NkT N = PV kT alignl { stack { size 12{ ital "PV"= ital "NkT"} {} #size 12{N= { { ital "PV"} over { ital "kT"} } } {} } } {}

4. Substitute the known values into the equation and solve for N size 12{N} {} .

N = PV kT = 1 . 01 × 10 5 Pa 1 . 00 m 3 1 . 38 × 10 23 J/K 273 K = 2 . 68 × 10 25 molecules size 12{N= { { ital "PV"} over { ital "kT"} } = { { left (1 "." "01" times "10" rSup { size 8{5} } " Pa" right ) left (1 "." "00 m" rSup { size 8{3} } right )} over { left (1 "." "38" times "10" rSup { size 8{ - "23"} } " J/K" right ) left ("273 K" right )} } =2 "." "68" times "10" rSup { size 8{"25"} } `"molecules"} {}

Discussion

This number is undeniably large, considering that a gas is mostly empty space. N size 12{N} {} is huge, even in small volumes. For example, 1 cm 3 size 12{1" cm" rSup { size 8{3} } } {} of a gas at STP has 2 . 68 × 10 19 size 12{2 "." "68"´"10" rSup { size 8{"19"} } } {} molecules in it. Once again, note that N size 12{N} {} is the same for all types or mixtures of gases.

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Moles and avogadro’s number

It is sometimes convenient to work with a unit other than molecules when measuring the amount of substance. A mole    (abbreviated mol) is defined to be the amount of a substance that contains as many atoms or molecules as there are atoms in exactly 12 grams (0.012 kg) of carbon-12. The actual number of atoms or molecules in one mole is called Avogadro’s number     ( N A ) size 12{ \( N rSub { size 8{A} } \) } {} , in recognition of Italian scientist Amedeo Avogadro (1776–1856). He developed the concept of the mole, based on the hypothesis that equal volumes of gas, at the same pressure and temperature, contain equal numbers of molecules. That is, the number is independent of the type of gas. This hypothesis has been confirmed, and the value of Avogadro’s number is

N A = 6 . 02 × 10 23 mol 1 . size 12{N rSub { size 8{A} } =6 "." "02" times "10" rSup { size 8{"23"} } `"mol" rSup { size 8{ - 1} } "." } {}

Avogadro’s number

One mole always contains 6 . 02 × 10 23 size 12{6 "." "02"´"10" rSup { size 8{"23"} } } {} particles (atoms or molecules), independent of the element or substance. A mole of any substance has a mass in grams equal to its molecular mass, which can be calculated from the atomic masses given in the periodic table of elements.

N A = 6 . 02 × 10 23 mol 1 size 12{N rSub { size 8{A} } =6 "." "02" times "10" rSup { size 8{"23"} } `"mol" rSup { size 8{ - 1} } } {}
The illustration shows relatively flat land with a solitary mountain, labeled Mt. Everest, and blue sky above. A double-headed vertical arrow stretches between the land and a point in the sky that is well above the peak of the mountain. The arrow, labeled table tennis balls, serves to indicate that a column of one mole of table tennis balls would reach a point in the sky that is much higher than the peak of Mt. Everest.
How big is a mole? On a macroscopic level, one mole of table tennis balls would cover the Earth to a depth of about 40 km.

The active ingredient in a Tylenol pill is 325 mg of acetaminophen ( C 8 H 9 NO 2 ) size 12{ \( C rSub { size 8{8} } H rSub { size 8{9} } "NO" rSub { size 8{2} } \) } {} . Find the number of active molecules of acetaminophen in a single pill.

We first need to calculate the molar mass (the mass of one mole) of acetaminophen. To do this, we need to multiply the number of atoms of each element by the element’s atomic mass.

( 8 moles of carbon ) ( 12 grams/mole ) + ( 9 moles hydrogen ) ( 1 gram/mole ) + ( 1 mole nitrogen ) ( 14 grams/mole ) + ( 2 moles oxygen ) ( 16 grams/mole ) = 151 g

Then we need to calculate the number of moles in 325 mg.

325 mg 151 grams/mole 1 gram 1000 mg = 2.15 × 10 3 moles

Then use Avogadro’s number to calculate the number of molecules.

N = 2.15 × 10 3 moles 6.02 × 10 23 molecules/mole = 1.30 × 10 21 molecules size 12{N= left (2 "." "15" times "10" rSup { size 8{ - 3} } `"moles" right ) left (6 "." "02" times "10" rSup { size 8{"23"} } `"molecules/mole" right )=1 "." "30" times "10" rSup { size 8{"21"} } `"molecules"} {}
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Questions & Answers

where Newton second law applies
Latief Reply
A soccer player kicked off a ball at velocity of 62 ft/s at angle 45°. A goal keeper is 43 yard away from the direction in which ball kicked off. At what minimum velocity he runs to meet the ball?
Ram Reply
A soccer player kicked off the ball at the velocity of 62 ft/s at 45° with horizontal.A goal keeper is 43 yard away from the ball kicked position.At what minimum velocity he runs to meet the ball?
Ram
what is torque
Deepak Reply
The turning effect of force is called torque.
Uzair
What is the effect of static electricity
Ruth
what there factors affect the surface tension of a liquid
Promise Reply
formula for impedance
muyiwa Reply
ehat is central forces
Nita Reply
what is distance?
Jonathan Reply
What does mean ohms law imply
Victoria Reply
ohms law state that the electricity passing through a metallic conductor is directly proportional to the potential difference across its end
muyiwa
what is matter
folajin Reply
Anything that occupies space
Kevin
Any thing that has weight and occupies space
Victoria
Anything which we can feel by any of our 5 sense organs
Suraj
Right
Roben
thanks
Suraj
what is a sulphate
Alo
any answers
Alo
the time rate of increase in velocity is called
Blessing Reply
acceleration
Emma
What is uniform velocity
Victoria
Greetings,users of that wonderful app.
Frank Reply
how to solve pressure?
Cruz Reply
how do we calculate weight and eara eg an elefant that weight 2000kg has four fits or legs search of surface eara is 0.1m2(1metre square) incontact with the ground=10m2(g =10m2)
Cruz
P=F/A
Mira
can someone derive the formula a little bit deeper?
Bern
what is coplanar force?
OLADITI Reply
forces acting and lying on d same plane
Promise
what is accuracy and precision
Peace Reply
How does a current follow?
Vineeta Reply
follow?
akif
which one dc or ac current.
akif
how does a current following?
Vineeta
?
akif
AC current
Vineeta
AC current follows due to changing electric field and magnetic field.
akif
you guys are just saying follow is flow not follow please
Abubakar
ok bro thanks
akif
flows
Abubakar
but i wanted to understand him/her in his own language
akif
but I think the statement is written in English not any other language
Abubakar
my mean that in which form he/she written this,will understand better in this form, i write.
akif
ok
Abubakar
ok thanks bro. my mistake
Vineeta
u are welcome
Abubakar
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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