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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

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Chovwe Reply
is the meaning of phrase in physics
Chovwe
write an expression for a plane progressive wave moving from left to right along x axis and having amplitude 0.02m, frequency of 650Hz and speed if 680ms-¹
Gabriel Reply
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Friday Reply
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Ridwan Reply
Vector quality have both direction and magnitude, such as Force, displacement, acceleration and etc.
Besmellah
Is the force attractive or repulsive between the hot and neutral lines hung from power poles? Why?
Jack Reply
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Chinaza Reply
electromagnetic induction is a process in which conductor is put in a particular position and magnetic field keeps varying.
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Salaudeen
what is mutual induction?
je
mutual induction can be define as the current flowing in one coil that induces a voltage in an adjacent coil.
Johnson
how to undergo polarization
Ajayi Reply
show that a particle moving under the influence of an attractive force mu/y³ towards the axis x. show that if it be projected from the point (0,k) with the component velocities U and V parallel to the axis of x and y, it will not strike the axis of x unless u>v²k² and distance uk²/√u-vk as origin
Gabriel Reply
show that a particle moving under the influence of an attractive force mu/y^3 towards the axis x. show that if it be projected from the point (0,k) with the component velocities U and V parallel to the axis of x and y, it will not strike the axis of x unless u>v^2k^2 and distance uk^2/√u-k as origin
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Mavis
I can't even understand the question
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An engineer builds two simple pendula. Both are suspended from small wires secured to the ceiling of a room. Each pendulum hovers 2 cm above the floor. Pendulum 1 has a bob with a mass of 10kg . Pendulum 2 has a bob with a mass of 100 kg . Describe how the motion of the pendula will differ if the bobs are both displaced by 12º .
Imtiaz Reply
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Augstine
if u at an angle of 12 degrees their period will be same so as their velocity, that means they both move simultaneously since both both hovers at same length meaning they have the same length
Ademiye
Modern cars are made of materials that make them collapsible upon collision. Explain using physics concept (Force and impulse), how these car designs help with the safety of passengers.
Isaac Reply
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Mildred Reply
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Ademiye
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Ajayi
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Makperr Reply
The number of protons in the nucleus of an atom
Deborah
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Yinka Reply
oxygen gas contained in a ccylinder of volume has a temp of 300k and pressure 2.5×10Nm
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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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