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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

how do you calculate the 5% uncertainty of 4cm?
melia Reply
4cm/100×5= 0.2cm
haider
how do you calculate the 5% absolute uncertainty of a 200g mass?
melia Reply
= 200g±(5%)10g
haider
use the 10g as the uncertainty?
melia
which topic u discussing about?
haider
topic of question?
haider
the relationship between the applied force and the deflection
melia
sorry wrong question i meant the 5% uncertainty of 4cm?
melia
its 0.2 cm or 2mm
haider
thank you
melia
Hello group...
Chioma
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haider
well hello there
sean
the meaning of phrase in physics
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
how does a model differ from a theory
Friday Reply
To use the vocabulary of model theory and meta-logic, a theory is a set of sentences which can be derived from a formal model using some rule of inference (usually just modus ponens). So, for example, Number Theory is the set of sentences true about numbers. But the model is a structure together wit
Jesilda
with an iterpretation.
Jesilda
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Ridwan Reply
Vector quality have both direction and magnitude, such as Force, displacement, acceleration and etc.
Besmellah
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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.
Lukman
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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
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Ajayi Reply
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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
Gabriel Reply
No idea.... Are you even sure this question exist?
Mavis
I can't even understand the question
Ademiye
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Gabriel
mu/y³ u>v²k² uk²/√u-vk please help me out
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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
no ideas
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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find the time required for a train Half a Kilometre long to cross a bridge almost kilometre long racing at 100km/h
Ademiye
method of polarization
Ajayi
What is atomic number?
Makperr Reply
The number of protons in the nucleus of an atom
Deborah
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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