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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.

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"} {}

Questions & Answers

Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
why?
Adin
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
Maciej
characteristics of micro business
Abigail
for teaching engĺish at school how nano technology help us
Anassong
Do somebody tell me a best nano engineering book for beginners?
s. Reply
there is no specific books for beginners but there is book called principle of nanotechnology
NANO
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
s.
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
NANO
so some one know about replacing silicon atom with phosphorous in semiconductors device?
s. Reply
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
SUYASH Reply
for screen printed electrodes ?
SUYASH
What is lattice structure?
s. Reply
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
what is biological synthesis of nanoparticles
Sanket Reply
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Source:  OpenStax, Concepts of physics. OpenStax CNX. Aug 25, 2015 Download for free at https://legacy.cnx.org/content/col11738/1.5
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