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Relative humidity is related to the partial pressure of water vapor in the air. At 100% humidity, the partial pressure is equal to the vapor pressure, and no more water can enter the vapor phase. If the partial pressure is less than the vapor pressure, then evaporation will take place, as humidity is less than 100%. If the partial pressure is greater than the vapor pressure, condensation takes place. In everyday language, people sometimes refer to the capacity of air to “hold” water vapor, but this is not actually what happens. The water vapor is not held by the air. The amount of water in air is determined by the vapor pressure of water and has nothing to do with the properties of air.

Saturation vapor density of water
Temperature ( º C ) size 12{ \( °C \) } {} Vapor pressure (Pa) Saturation vapor density (g/m 3 )
−50 4.0 0.039
−20 1 . 04 × 10 2 size 12{1 "." "04" times "10" rSup { size 8{2} } } {} 0.89
−10 2 . 60 × 10 2 size 12{2 "." "60"´"10" rSup { size 8{2} } } {} 2.36
0 6 . 10 × 10 2 size 12{6 "." "10"´"10" rSup { size 8{2} } } {} 4.84
5 8 . 68 × 10 2 size 12{8 "." "68"´"10" rSup { size 8{2} } } {} 6.80
10 1 . 19 × 10 3 size 12{1 "." "19"´"10" rSup { size 8{3} } } {} 9.40
15 1 . 69 × 10 3 size 12{1 "." "69"´"10" rSup { size 8{3} } } {} 12.8
20 2 . 33 × 10 3 size 12{2 "." "33"´"10" rSup { size 8{3} } } {} 17.2
25 3 . 17 × 10 3 size 12{3 "." "17"´"10" rSup { size 8{3} } } {} 23.0
30 4 . 24 × 10 3 size 12{4 "." "24"´"10" rSup { size 8{3} } } {} 30.4
37 6 . 31 × 10 3 size 12{6 "." "31"´"10" rSup { size 8{3} } } {} 44.0
40 7 . 34 × 10 3 size 12{7 "." "34"´"10" rSup { size 8{3} } } {} 51.1
50 1 . 23 × 10 4 size 12{1 "." "23" times "10" rSup { size 8{4} } } {} 82.4
60 1 . 99 × 10 4 size 12{1 "." "99"´"10" rSup { size 8{4} } } {} 130
70 3 . 12 × 10 4 size 12{3 "." "12"´"10" rSup { size 8{4} } } {} 197
80 4 . 73 × 10 4 size 12{4 "." "73"´"10" rSup { size 8{4} } } {} 294
90 7 . 01 × 10 4 size 12{7 "." "01"´"10" rSup { size 8{4} } } {} 418
95 8 . 59 × 10 4 size 12{8 "." "59"´"10" rSup { size 8{4} } } {} 505
100 1 . 01 × 10 5 size 12{1 "." "99"´"10" rSup { size 8{5} } } {} 598
120 1 . 99 × 10 5 size 12{1 "." "99"´"10" rSup { size 8{5} } } {} 1095
150 4 . 76 × 10 5 size 12{4 "." "76"´"10" rSup { size 8{5} } } {} 2430
200 1 . 55 × 10 6 size 12{1 "." "55"´"10" rSup { size 8{6} } } {} 7090
220 2 . 32 × 10 6 size 12{2 "." "32"´"10" rSup { size 8{6} } } {} 10,200

Calculating density using vapor pressure

[link] gives the vapor pressure of water at 20 . 0 º C size 12{"20" "." 0°C} {} as 2 . 33 × 10 3 Pa . size 12{2 "." "33"´"10" rSup { size 8{3} } " Pa" "." } {} Use the ideal gas law to calculate the density of water vapor in g / m 3 size 12{g/m rSup { size 8{3} } } {} that would create a partial pressure equal to this vapor pressure. Compare the result with the saturation vapor density given in the table.

Strategy

To solve this problem, we need to break it down into a two steps. The partial pressure follows the ideal gas law,

PV = nRT, size 12{ size 11{ ital "PV"= ital "nRT"}} {}

where n size 12{n} {} is the number of moles. If we solve this equation for n / V size 12{n/V} {} to calculate the number of moles per cubic meter, we can then convert this quantity to grams per cubic meter as requested. To do this, we need to use the molecular mass of water, which is given in the periodic table.

Solution

1. Identify the knowns and convert them to the proper units:

  1. temperature T = 20 º C=293 K size 12{T="20"°"C=293 K"} {}
  2. vapor pressure P size 12{P} {} of water at 20 º C size 12{"20"°C} {} is 2 . 33 × 10 3 Pa size 12{2 "." "33" times "10" rSup { size 8{3} } " Pa"} {}
  3. molecular mass of water is 18 . 0 g/mol size 12{"18" "." 0" g/mol"} {}

2. Solve the ideal gas law for n / V size 12{n/V} {} .

n V = P RT size 12{ { { size 11{n}} over { size 11{V}} } = { { size 11{P}} over { size 11{ ital "RT"}} } } {}

3. Substitute known values into the equation and solve for n / V size 12{n/V} {} .

n V = P RT = 2 . 33 × 10 3 Pa 8 . 31 J/mol K 293 K = 0 . 957 mol/m 3 size 12{ { { size 11{n}} over { size 11{V}} } = { { size 11{P}} over { size 11{ ital "RT"}} } = { { size 11{2 "." "33" times "10" rSup { size 8{3} } `"Pa"}} over { size 12{ left (8 "." "31"`"J/mol" cdot K right ) left ("293"`K right )} } } =0 "." "957"`"mol/m" rSup { size 8{3} } } {}

4. Convert the density in moles per cubic meter to grams per cubic meter.

ρ = 0 . 957 mol m 3 18 . 0 g mol = 17 . 2 g/m 3 size 12{ size 11{ρ= left ( size 11{0 "." "957" { { size 11{"mol"}} over { size 11{m rSup { size 8{3} } }} } } right ) left ( size 12{ { {"18" "." "0 g"} over { size 12{"mol"} } } } right )="17" "." 2" g/m" rSup { size 8{3} } }} {}

Discussion

The density is obtained by assuming a pressure equal to the vapor pressure of water at 20 . 0 º C size 12{"20" "." 0°C} {} . The density found is identical to the value in [link] , which means that a vapor density of 17 . 2 g/m 3 size 12{"17" "." 2" g/m" rSup { size 8{3} } } {} at 20 . 0 º C size 12{"20" "." 0°C} {} creates a partial pressure of 2 . 33 × 10 3 Pa, size 12{2 "." "33"´"10" rSup { size 8{3} } " Pa,"} {} equal to the vapor pressure of water at that temperature. If the partial pressure is equal to the vapor pressure, then the liquid and vapor phases are in equilibrium, and the relative humidity is 100%. Thus, there can be no more than 17.2 g of water vapor per m 3 size 12{m rSup { size 8{3} } } {} at 20 . 0 º C size 12{"20" "." 0°C} {} , so that this value is the saturation vapor density at that temperature. This example illustrates how water vapor behaves like an ideal gas: the pressure and density are consistent with the ideal gas law (assuming the density in the table is correct). The saturation vapor densities listed in [link] are the maximum amounts of water vapor that air can hold at various temperatures.

Questions & Answers

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
what is a semiconductor
Vineeta Reply
substances having lower forbidden gap between valence band and conduction band
akif
what is a conductor?
Vineeta
replace lower by higher only
akif
convert 56°c to kelvin
Abubakar
How does a current follow?
Vineeta
A semiconductor is any material whose conduction lies between that of a conductor and an insulator.
AKOWUAH
what is Atom? what is molecules? what is ions?
Abubakar Reply
atoms are the smallest unit of an element which is capable of behaving as a single unit
Promise
a molecule is d smallest unit of a substances capable of independent existence and can also retain the chemical proper ties of that substance
Promise
an ion is referred to as freely moving charged particles
Promise
What is a molecule
Samuel Reply
Is a unit of a compound that has two or more atoms either of the same or different atoms
Justice
A molecule is the smallest indivisible unit of a compound, Just like the atom is the smallest indivisible unit of an element.
Rachel
what is a molecule?
Vineeta
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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