Partial Pressure

Partial pressure

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In a mixture of ideal gases, each gas has a partial pressure which is the pressure which the gas would have if it alone occupied the volume.[1] The total pressure of a gas mixture is the sum of the partial pressures of each individual gas in the mixture.

In chemistry, the partial pressure of a gas in a mixture of gases is defined as above. The partial pressure of a gas dissolved in a liquid is the partial pressure of that gas which would be generated in a gas phase in equilibrium with the liquid at the same temperature. The partial pressure of a gas is a measure of thermodynamic activity of the gas’s molecules. Gases will always flow from a region of higher partial pressure to one of lower pressure; the larger this difference, the faster the flow. Gases dissolve, diffuse, and react according to their partial pressures, and not necessarily according to their concentrations in a gas mixture.




[edit] Dalton’s law of partial pressures

Main article: Dalton’s law

The partial pressure of an ideal gas in a mixture is equal to the pressure it would exert if it occupied the same volume alone at the same temperature. This is because ideal gas molecules are so far apart that they don’t interfere with each other at all. Actual real-world gases come very close to this ideal.

A consequence of this is that the total pressure of a mixture of ideal gases is equal to the sum of the partial pressures of the individual gases in the mixture as stated by Dalton’s law.[2] For example, given an ideal gas mixture of nitrogen (N2), hydrogen (H2) and ammonia (NH3):

P = P_{{\mathrm{N}}_2} + P_{{\mathrm{H}}_2} + P_{{\mathrm{NH}}_3}
P \, = total pressure of the gas mixture
P_{{\mathrm{N}}_2} = partial pressure of nitrogen (N2)
P_{{\mathrm{H}}_2} = partial pressure of hydrogen (H2)
P_{{\mathrm{NH}}_3} = partial pressure of ammonia (NH3)

[edit] Ideal gas mixtures

The mole fraction of an individual gas component in an ideal gas mixture can be expressed in terms of the component’s partial pressure or the moles of the component:

x_{\mathrm{i}} = \frac{P_{\mathrm{i}}}{P} = \frac{n_{\mathrm{i}}}{n}

and the partial pressure of an individual gas component in an ideal gas can be obtained using this expression:

P_{\mathrm{i}} = x_{\mathrm{i}} \cdot P
xi = mole fraction of any individual gas component in a gas mixture
Pi = partial pressure of any individual gas component in a gas mixture
ni = moles of any individual gas component in a gas mixture
n = total moles of the gas mixture
P = total pressure of the gas mixture

The mole fraction of a gas component in a gas mixture is equal to the volumetric fraction of that component in a gas mixture.[3]

[edit] Vapor pressure

Main article: Vapor pressure

A typical vapor pressure chart for various liquids

Vapor pressure is the pressure of a vapor in equilibrium with its non-vapor phases (i.e., liquid or solid). Most often the term is used to describe a liquid‘s tendency to evaporate. It is a measure of the tendency of molecules and atoms to escape from a liquid or a solid. A liquid’s atmospheric pressure boiling point corresponds to the temperature at which its vapor pressure is equal to the surrounding atmospheric pressure and it is often called the normal boiling point.

The higher the vapor pressure of a liquid at a given temperature, the lower the normal boiling point of the liquid.

The vapor pressure chart to the right has graphs of the vapor pressures versus temperatures for a variety of liquids.[4] As can be seen in the chart, the liquids with the highest vapor pressures have the lowest normal boiling points.

For example, at any given temperature, propane has the highest vapor pressure of any of the liquids in the chart. It also has the lowest normal boiling point(-43.7 °C), which is where the vapor pressure curve of propane (the purple line) intersects the horizontal pressure line of one atmosphere (atm) of absolute vapor pressure.

[edit] Equilibrium constants of reactions involving gas mixtures

It is possible to work out the equilibrium constant for a chemical reaction involving a mixture of gases given the partial pressure of each gas and the overall reaction formula. For a reversible reaction involving gas reactants and gas products, such as:

a\,A + b\,B \leftrightarrow c\,C + d\,D

the equilibrium constant of the reaction would be:

K_P = \frac{P_C^c\, P_D^d} {P_A^a\, P_B^b}
KP =  the equilibrium constant of the reaction
a =  coefficient of reactant A
b =  coefficient of reactant B
c =  coefficient of product C
d =  coefficient of product D
P_C^c =  the partial pressure of C raised to the power of c
P_D^d =  the partial pressure of D raised to the power of d
P_A^a =  the partial pressure of A raised to the power of a
P_B^b =  the partial pressure of B raised to the power of b

For reversible reactions, changes in the total pressure, temperature or reactant concentrations will shift the equilibrium so as to favor either the right or left side of the reaction in accordance with Le Chatelier’s Principle. However, the reaction kinetics may either oppose or enhance the equilibrium shift. In some cases, the reaction kinetics may be the over-riding factor to consider.

[edit] Henry’s Law and the solubility of gases

Main article: Henry’s Law

Gases will dissolve in liquids to an extent that is determined by the equilibrium between the undissolved gas and the gas that has dissolved in the liquid (called the solvent).[5] The equilibrium constant for that equilibrium is:

(1)     k = \frac {P_X}{C_X}
k =  the equilibrium constant for the solvation process
PX =  partial pressure of gas X in equilibrium with a solution containing some of the gas
CX =  the concentration of gas X in the liquid solution

The form of the equilibrium constant shows that the concentration of a solute gas in a solution is directly proportional to the partial pressure of that gas above the solution. This statement is known as Henry’s Law and the equilibrium constant k is quite often referred to as the Henry’s Law constant.[5][6][7]

Henry’s Law is sometimes written as:[8]

(2)     k' = \frac {C_X}{P_X}

where k‘ is also referred to as the Henry’s Law constant.[8] As can be seen by comparing equations (1) and (2) above, k‘ is the reciprocal of k. Since both may be referred to as the Henry’s Law constant, readers of the technical literature must be quite careful to note which version of the Henry’s Law equation is being used.

Henry’s Law is an approximation that only applies for dilute, ideal solutions and for solutions where the liquid solvent does not react chemically with the gas being dissolved.

[edit] Partial pressure in diving breathing gases

In recreational diving and professional diving the richness of individual component gases of breathing gases is expressed by partial pressure.

Using diving terms, partial pressure is calculated as:

partial pressure = total absolute pressure x volume fraction of gas component

For the component gas “i”:

ppi = P x Fi

For example, at 50 metres (165 feet), the total absolute pressure is 6 bar (600 kPa) (i.e., 1 bar of atmospheric pressure + 5 bar of water pressure) and the partial pressures of the main components of air, oxygen 21% by volume and nitrogen 79% by volume are:

ppN2 = 6 bar x 0.79 = 4.7 bar absolute
ppO2 = 6 bar x 0.21 = 1.3 bar absolute
ppi = partial pressure of gas component i  = Pi in the terms used in this article
P = total pressure = P in the terms used in this article
Fi = volume fraction of gas component i  =  mole fraction, xi, in the terms used in this article
ppN2 = partial pressure of nitrogen  = P_{{\mathrm{N}}_2} in the terms used in this article
ppO2 = partial pressure of oxygen  = P_{{\mathrm{O}}_2} in the terms used in this article

The minimum safe lower limit for the partial pressures of oxygen in a gas mixture is 0.16 bar (16 kPa) absolute. Hypoxia and sudden unconsciousness becomes a problem with an oxygen partial pressure of less than 0.16 bar absolute. Oxygen toxicity, involving convulsions, becomes a problem when oxygen partial pressure is too high. The NOAA Diving Manual recommends a maximum single exposure of 45 minutes at 1.6 bar absolute, of 120 minutes at 1.5 bar absolute, of 150 minutes at 1.4 bar absolute, of 180 minutes at 1.3 bar absolute and of 210 minutes at 1.2 bar absolute. Oxygen toxicity becomes a risk when these oxygen partial pressures and exposures are exceeded. The partial pressure of oxygen determines the maximum operating depth of a gas mixture.

Nitrogen narcosis is a problem when breathing gases at high pressure. Typically, the maximum total partial pressure of narcotic gases used when planning for technical diving is 4.5 bar absolute, based on an equivalent narcotic depth of 35 metres (110 ft).

With the acceptance of ASHRAE (American Society of Heating, Refrigerating
and Air-Conditioning Engineers) Code 62 concerning indoor air quality, more
stringent reviews are required of an indoor pool’s air quality. This technical bulletin
summarizes the chemistry involved for pool water using chlorine and its effects
on air quality, and vice versa. It also reviews the impact of ventilation air on air
quality, as well as the use of special filters to remove airborne contaminants in
a pool facility.
Many detailed articles are available about this subject from other sources. This
bulletin summarizes only the basics about pool chemistry to provide an
overview. Contact the NSPI (National Spa and Pool Institute) for more information.
Chlorine is added to water to form hypochlorous acid (HClO), an excellent
bactericide. In this solution it is known as “free chlorine,” and is highly reactive.
The free chlorine reacts with organic wastes introduced into the pool water –
such as sweat, urine, perfumes and other ammonia-based impurities – to form
new “combined chlorine” compounds. These new compounds have very poor
bactericide properties. If enough free chlorine is present, it reacts with the
combined chlorine compounds to further break them down into basic
elements, such as H2O (water), CO2 (carbon dioxide gas), N2 (nitrogen gas)
and various salts. When this breakdown process occurs, the pool is deemed to
be safe for swimmers.
Whether or not the complete breakdown can occur, however,
is a function of the amount of free chlorine available as
compared to the amount of ammonia-containing wastes present.
Table 1 summarizes the pool conditions resulting from various
ratios of free chlorine to chlorine compounds.
Technical Bulletin 9
Figure 2 – Outdoor air changes equilibrium point.
(lower CL•A concentration yields higher ratio)
Figure 3 – Outdoor air and chlorine removal filters significantly
change equilibrium point for highest ratio.
Figure 1 – Pool facility at equilibrium.
(Note: CL•A = chloramine concentration)
Table 1
Ratio Compound Present Comments
<5:1 Mono-chloramines Quick reaction; very poor disinfecting capacity (100x less)
5:1 to 10:1 Di-chloramines “Chlorine” odor; poor disinfecting capacity
>10:1 Basic elements Properly treated pool
As Table 1 shows, a constant source of free chlorine is needed
to ensure the complete reaction. This is known as breakpoint
chlorination. If the combined chlorine compounds are not
eliminated, pool “shocking” is required: a larger dose of chlorine
is added to the water to complete the reaction and balance the pool.
118 10/06
The pool room odor commonly described as “chlorine”
(which, in fact, is the odor produced by chloramine compounds),
occurs when the pool water chemistry is improperly balanced.
The chloramines readily release into the air and reach a balance
based on a chemical law known as the partial pressure
law. In laymen’s terms, this law states how much chloramine
remains in the water and how much is released to the air
under various conditions.
The ASHRAE 62 ventilation code recognizes this “chlorine” smell
as a potential indoor air quality problem and offers specific
recommendations for the introduction of outdoor air based
on the size of the pool and deck. (Refer to Desert Aire’s
Technical Bulletin 5 – Ventilation Air for Indoor Pools, for
details on these recommendations.) The code attempts to
replace the indoor air once per hour to eliminate the odor.
Since nature requires a balance, removing some of the
chloramines from the air will cause more chloramines to be
released from the water. Table 1 shows that the release of more
chloramines to the air will improve the free chlorine ratio,
bringing the pool chemistry a step closer to proper balance.
The response of some pool designers is to go beyond
ASHRAE 62 air quality recommendations. That scenario,
however, can introduce other problems.
First, in cold climates, wintertime outdoor air must be heated.
For even the smallest pools, this adds up to thousands of dollars
per month in increased utility bills.
Second, the code requires that relative indoor humidity
remain below 60 percent. Summer conditions in most locales
add humidity to the space, so when an increased air volume
is introduced, the facility may no longer be compliant with the
indoor humidity code.
While this technical bulletin does not attempt to cover all
chemistry issues (for example, the influence of pH on free
chlorine), it does demonstrate the basic chemical interaction
occurring in an indoor pool facility.
The following design specifications are recommended:
1. Automatic chlorate control system. The chemical feed
pump must be sized to match worst case pool loading.
2. High water turnover to better mix the pool, to avoid
dead spots, and to provide better chlorine concentration
measurement and control.
3. Ensure ASHRAE 62 outdoor air compliance to aid in
breakpoint chlorination.
4. Add chlorine deactivating filters to help balance
energy, humidity and water chemistry demands.
Adding special chlorine deactivating filters to the pool room
results in additional chloramine removal, thereby decreasing
the amount of free chlorine required to reach breakpoint
chlorination. Using these types of filters in lieu of bringing in
more outdoor air avoids temperature and humidity problems
and treatment expense in a pool facility.
Chlorine deactivating filters are added to the dehumidification
air handler as an alternative to standard disposable filters.
Interaction of Pool Water and Air Chemistry
N120 W18485 Freistadt Road
Germantown, WI 53022
PH: (262) 946-7400
FAX: (262) 946-7401


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