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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

can someone help me with some logarithmic and exponential equations.
Jeffrey Reply
sure. what is your question?
ninjadapaul
20/(×-6^2)
Salomon
okay, so you have 6 raised to the power of 2. what is that part of your answer
ninjadapaul
I don't understand what the A with approx sign and the boxed x mean
ninjadapaul
it think it's written 20/(X-6)^2 so it's 20 divided by X-6 squared
Salomon
I'm not sure why it wrote it the other way
Salomon
I got X =-6
Salomon
ok. so take the square root of both sides, now you have plus or minus the square root of 20= x-6
ninjadapaul
oops. ignore that.
ninjadapaul
so you not have an equal sign anywhere in the original equation?
ninjadapaul
Commplementary angles
Idrissa Reply
hello
Sherica
im all ears I need to learn
Sherica
right! what he said ⤴⤴⤴
Tamia
what is a good calculator for all algebra; would a Casio fx 260 work with all algebra equations? please name the cheapest, thanks.
Kevin Reply
a perfect square v²+2v+_
Dearan Reply
kkk nice
Abdirahman Reply
algebra 2 Inequalities:If equation 2 = 0 it is an open set?
Kim Reply
or infinite solutions?
Kim
The answer is neither. The function, 2 = 0 cannot exist. Hence, the function is undefined.
Al
y=10×
Embra Reply
if |A| not equal to 0 and order of A is n prove that adj (adj A = |A|
Nancy Reply
rolling four fair dice and getting an even number an all four dice
ramon Reply
Kristine 2*2*2=8
Bridget Reply
Differences Between Laspeyres and Paasche Indices
Emedobi Reply
No. 7x -4y is simplified from 4x + (3y + 3x) -7y
Mary Reply
is it 3×y ?
Joan Reply
J, combine like terms 7x-4y
Bridget Reply
im not good at math so would this help me
Rachael Reply
yes
Asali
I'm not good at math so would you help me
Samantha
what is the problem that i will help you to self with?
Asali
how do you translate this in Algebraic Expressions
linda Reply
Need to simplify the expresin. 3/7 (x+y)-1/7 (x-1)=
Crystal Reply
. After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight?
Chris Reply
what's the easiest and fastest way to the synthesize AgNP?
Damian Reply
China
Cied
types of nano material
abeetha Reply
I start with an easy one. carbon nanotubes woven into a long filament like a string
Porter
many many of nanotubes
Porter
what is the k.e before it land
Yasmin
what is the function of carbon nanotubes?
Cesar
what is nanomaterials​ and their applications of sensors.
Ramkumar Reply
what is nano technology
Sravani Reply
what is system testing?
AMJAD
preparation of nanomaterial
Victor Reply
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
Himanshu Reply
good afternoon madam
AMJAD
what is system testing
AMJAD
what is the application of nanotechnology?
Stotaw
In this morden time nanotechnology used in many field . 1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc 2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc 3- Atomobile -MEMS, Coating on car etc. and may other field for details you can check at Google
Azam
anybody can imagine what will be happen after 100 years from now in nano tech world
Prasenjit
after 100 year this will be not nanotechnology maybe this technology name will be change . maybe aftet 100 year . we work on electron lable practically about its properties and behaviour by the different instruments
Azam
name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
Prasenjit
how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
Damian
silver nanoparticles could handle the job?
Damian
not now but maybe in future only AgNP maybe any other nanomaterials
Azam
can nanotechnology change the direction of the face of the world
Prasenjit Reply
At high concentrations (>0.01 M), the relation between absorptivity coefficient and absorbance is no longer linear. This is due to the electrostatic interactions between the quantum dots in close proximity. If the concentration of the solution is high, another effect that is seen is the scattering of light from the large number of quantum dots. This assumption only works at low concentrations of the analyte. Presence of stray light.
Ali Reply
the Beer law works very well for dilute solutions but fails for very high concentrations. why?
bamidele 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, College physics (engineering physics 2, tuas). OpenStax CNX. May 08, 2014 Download for free at http://legacy.cnx.org/content/col11649/1.2
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