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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 is math number
Tric Reply
x-2y+3z=-3 2x-y+z=7 -x+3y-z=6
Sidiki Reply
Need help solving this problem (2/7)^-2
Simone Reply
x+2y-z=7
Sidiki
what is the coefficient of -4×
Mehri Reply
-1
Shedrak
the operation * is x * y =x + y/ 1+(x × y) show if the operation is commutative if x × y is not equal to -1
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An investment account was opened with an initial deposit of $9,600 and earns 7.4% interest, compounded continuously. How much will the account be worth after 15 years?
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lim x to infinity e^1-e^-1/log(1+x)
given eccentricity and a point find the equiation
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12, 17, 22.... 25th term
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12, 17, 22.... 25th term
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Carole
I'm 13 and I understand it great
AJ
I am 1 year old but I can do it! 1+1=2 proof very hard for me though.
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Not really they are just easy concepts which can be understood if you have great basics. I am 14 I understood them easily.
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Solomon
find the 15th term of the geometric sequince whose first is 18 and last term of 387
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I know this work
salma
The given of f(x=x-2. then what is the value of this f(3) 5f(x+1)
virgelyn Reply
hmm well what is the answer
Abhi
If f(x) = x-2 then, f(3) when 5f(x+1) 5((3-2)+1) 5(1+1) 5(2) 10
Augustine
how do they get the third part x = (32)5/4
kinnecy Reply
make 5/4 into a mixed number, make that a decimal, and then multiply 32 by the decimal 5/4 turns out to be
AJ
how
Sheref
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
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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
hmm
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is it a question of log
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Commplementary angles
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Nharnhar
A soccer field is a rectangle 130 meters wide and 110 meters long. The coach asks players to run from one corner to the other corner diagonally across. What is that distance, to the nearest tenths place.
Kimberly Reply
Jeannette has $5 and $10 bills in her wallet. The number of fives is three more than six times the number of tens. Let t represent the number of tens. Write an expression for the number of fives.
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What is the expressiin for seven less than four times the number of nickels
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How do i figure this problem out.
how do you translate this in Algebraic Expressions
linda Reply
why surface tension is zero at critical temperature
Shanjida
I think if critical temperature denote high temperature then a liquid stats boils that time the water stats to evaporate so some moles of h2o to up and due to high temp the bonding break they have low density so it can be a reason
s.
Need to simplify the expresin. 3/7 (x+y)-1/7 (x-1)=
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. After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight?
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Source:  OpenStax, College physics: physics of california. OpenStax CNX. Sep 30, 2013 Download for free at http://legacy.cnx.org/content/col11577/1.1
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