亨利定理和道尔顿定理

亨利定理和道尔顿定理

2007年05月29日 星期二 15:01

亨利定律Henry's law

在一定温度下，气体在液体中的饱和浓度与液面上该气体的平衡分压成正比。它是英国的W.亨利于1803年在实验基础上发现的经验规律。实验表明，只有当气体在液体中的溶解度不很高时该定律才是正确的，此时的气体实际上是稀溶液中的挥发性溶质，气体压力则是溶质的蒸气压。所以亨利定律还可表述为：在一定温度下，稀薄溶液中溶质的蒸气分压与溶液浓度成正比：

pB＝kxB

式中pB是稀薄溶液中溶质的蒸气分压；xB是溶质的物质的量分数； k为亨利常数，其值与温度、压力以及溶质和溶剂的本性有关。由于在稀薄溶液中各种浓度成正比，所以上式中的xB还可以是mB（质量摩尔浓度）或cB（物质的量浓度）等，此时的k值将随之变化。

只有溶质在气相中和液相中的分子状态相同时，亨利定律才能适用。若溶质分子在溶液中有离解、缔合等，则上式中的

xB（或mB、cB等）应是指与气相中分子状态相同的那一部分的含量；在总压力不大时，若多种气体同时溶于同一个液体中，亨利定律可分别适用于其中的任一种气体；一般来说，溶液越稀,亨利定律愈准确，在xB→0时溶质能严格服从定律。

道尔顿气体分压定律

在任何容器内的气体混合物中，如果各组分之间不发生化学反应，则每一种气体都均匀地分布在整个容器内，它所产生的压强和它单独占有整个容器时所产生的压强相同。也就是说，一定量的气体在一定容积的容器中的压强仅与温度有关。例如，零摄氏度时，1mol 氧气在 22.4L 体积内的压强是 101.3kPa 。如果向容器内加入 1mol 氮气并保持容器体积不变，则氧气的压强还是 101.3kPa，但容器内的总压强增大一倍。可见， 1mol 氮气在这种状态下产生的压强也是

101.3kPa 。

道尔顿（Dalton）总结了这些实验事实，得出下列结论：某一气体在气体混合物中产生的分压等于它单独占有整个容

器时所产生的压力；而气体混合物的总压强等于其中各气体分压之和，这就是气体分压定律（law of partial pressure）。

Henry's law

In chemistry, Henry's law is one of the gas laws, formulated by

William Henry. It states that: At a constant temperature, the

amount of a given gas dissolved in a given type and volume of

liquid is directly proportional to the partial pressure of that gas

in equilibrium with that liquid.

Dalton's law

In chemistry and physics, Dalton's law (also called Dalton's law

of partial pressures) states that the total pressure exerted by a

gaseous mixture is equal to the sum of the partial pressures of

each individual component in a gas mixture. This empirical law

was observed by John Dalton in 1801 and is related to the ideal

gas laws.

Mathematically, the pressure of a mixture of gases can be

defined as the summation

P total =P1+P2+…+Pn

Where P1, P2, Pn represent the partial pressure of each

component.

It is assumed that the gases do not react with each other.

Pi=P total Xi

Where Xi = the mole fraction of the i-th component in the total

mixture of m components.

The relationship below provides a way to determine the volume

based concentration of any individual gaseous component.

Pi=P total Ci/1000000

Where, Ci is the concentration of the i-th component expressed

in ppm.

Dalton's law is not exactly followed by real gases. Those

deviations are considerably large at high pressures. In such

conditions, the volume occupied by the molecules can become

significant compared to the free space between them. Moreover,

the short average distance between molecules raises the intensity

of intermolecular forces between gas molecules enough to

substantially change the pressure exerted by them. Neither of

those effects are considered by the ideal gas model.

Henry's law

In chemistry, Henry's law is one of the gas laws, formulated by William Henry. It

states that:

At a constant temperature, the amount of a given gas dissolved in a given type and

volume of liquid is directly proportional to the partial pressure of that gas in equilibrium

with that liquid.

Formula and Henry constant

A formula for Henry's Law is:

where:

is approximately 2.7182818, the base of the natural logarithm (also called Euler's number)

is the partial pressure of the solute above the solution

is the concentration of the solute in the solution (in one of its many units)

is the Henry's Law constant, which has units such as L·atm/mol, atm/(mol fraction) or

Pa·m3/mol.

Taking the natural logarithm of the formula, gives us the more commonly used

formula:[1]

Some values for k include:

oxygen (O2) : 769.2 L·atm/mol

carbon dioxide (CO2) : 29.4 L·atm/mol

hydrogen (H2) : 1282.1 L·atm/mol

when these gases are dissolved in water at 298 kelvins.

Note that in the above, the unit of concentration was chosen to be molarity. Hence the

dimensional units: L is liters of solution, atm is the partial pressure of the gaseous

solute above the solution (in atmospheres of absolute pressure), and mol is the moles

of the gaseous solute in the solution. Also note that the Henry's Law constant, k,

varies with the solvent and the temperature.

As discussed in the next section, there are other forms of Henry's Law each of

which defines the constant k differently and requires different dimensional

units.[2] The form of the equation presented above is consistent with the given

example numerical values for oxygen, carbon dioxide and hydrogen and with

their corresponding dimensional units.

[edit] Other forms of Henry's law

There are various other forms Henry's Law which are discussed in the technical

literature.[3][4][2]

Table 1: Some forms of Henry's law and constants (gases in water at 298 K), derived from

[4]

equation:

dimension:

O2 769.23 1.3 E-3 4.259 E4 3.180 E-2

H2 1282.05 7.8 E-4 7.099 E4 1.907 E-2

CO2 29.41 3.4 E-2 0.163 E4 0.8317

N2 1639.34 6.1 E-4 9.077 E4 1.492 E-2

He 2702.7 3.7 E-4 14.97 E4 9.051 E-3

Ne 2222.22 4.5 E-4 12.30 E4 1.101 E-2

Ar 714.28 1.4 E-3 3.955 E4 3.425 E-2

CO 1052.63 9.5 E-4 5.828 E4 2.324 E-2

where:

= moles of gas per liter of solution

= liters of solution

= partial pressure of gas above the solution, in atmospheres of absolute pressure

= mole fraction of gas in solution = moles of gas per total moles ≈ moles of gas per mole

of water

= atmospheres of absolute pressure.

As can be seen by comparing the equations in the above table, the Henry's Law

constant kH,pc is simply the inverse of the constant kH,cp. Since all kH 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.[2]

It should also be noted the Henry's Law is a limiting law that only applies for dilute

enough solutions. The range of concentrations in which it applies becomes narrower

the more the system diverges from non-ideal behavior. Roughly speaking, that is the

more chemically different the solute is from the solvent.

It also only applies for solutions where the solvent does not react chemically with the

gas being dissolved. A common example of a gas that does react with the solvent is

carbon dioxide, which rapidly forms hydrated carbon dioxide and then carbonic acid

(H2CO3) with water.

[edit] Temperature dependence of the Henry constant

When the temperature of a system changes, the Henry constant will also change.[2]

This is why some people prefer to name it Henry coefficient. There are multiple

equations assessing the effect of temperature on the constant. This form of the van 't

Hoff equation is one example:[4]

where

k for a given temperature is the Henry's Law constant (as defined in the first section of

this article), identical with kH,pc defined in Table 1,

T is in Kelvin,

the index Θ (theta) refers to the standard temperature (298 K).

The above equation is an approximation only and should be used only when no better

experimentally derived formula for a given gas exists.

The following table lists some values for constant C (dimension of kelvins) in the

equation above:

Table 2: Values of C

Gas

O2 H2 CO2 N2 He Ne Ar CO

C 1700 500 2400 1300 230 490 1300 1300

Because solubility of gases is decreasing with increasing temperature, the partial

pressure a given gas concentration has in liquid must increase. While heating water

(saturated with nitrogen) from 25 °C to 95 °C the solubility will decrease to about

43% of its initial value. This can be verified when heating water in a pot. Small

bubbles evolve and rise, long before the water reaches boiling temperature. Similarly,

carbon dioxide from a carbonated drink escapes much faster when the drink is not

cooled because of the increased partial pressure of CO2 in higher temperatures. Partial

pressure of CO2 in seawater doubles with every 16 K increase in temperature.[5]

The constant C may be regarded as:

where

is the enthalpy of solution

R is the gas constant.

[edit] Henry's law in geophysics

In geophysics a version of Henry's law applies to the solubility of a noble gas in

contact with silicate melt. One equation used is

where:

subscript m = melt

subscript g = gas phase

ρ = the number densities of the solute gas in the melt and gas phase

β = 1 / kBT an inverse temperature scale

kB = the Boltzmann constant

μex,m and μex,g = the excess chemical potential of the solute in the two phases.

[edit] Henry's law versus Raoult's law

Both Henry's law and Raoult's law state that the vapor pressure of a component, p, is

proportional to its concentration.

Henry's law:

Raoult's law:

where:

is the mole fraction of the component;

is the Henry constant; (Note that the numerical value and dimensions of this constant

change when mole fractions are used rather than molarity, as seen in Table 1.)

is the equilibrium vapor pressure of the pure component.

If the solution is ideal, both components follow Raoult's law over the entire

composition range, but Henry noticed that at low concentrations of non-ideal

solutions, the constant of proportionality is not p*. Therefore Henry's law uses an

empirically-derived constant, k, based on an infinitely-dilute solution, i.e. x = 0, that is

specific to the components in the mixture and the temperature.

In most systems, the laws can only be applied over very limited concentrations at the

extreme ends of the mole-fraction range. Raoult's law, which uses the vapor pressure

of the pure component, is best used for the major component (solvent) and in

mixtures of similar components. Henry's law applies to the minor component (solute)

in dilute solutions.

In ideal-dilute solutions, the minor component follows Henry's law, while the solvent

obeys Raoult's law. This is proved by the Gibbs-Duhem equation.

Dalton's law

In chemistry and physics, Dalton's law (also called Dalton's law of partial

pressures) states that the total pressure exerted by a gaseous mixture is equal to the

sum of the partial pressures of each individual component in a gas mixture. This

empirical law was observed by John Dalton in 1801 and is related to the ideal gas

laws.

Mathematically, the pressure of a mixture of gases can be defined as the summation

P total =P1+P2+…+Pn

where P1, P2, Pn represent the partial pressure of each component.

It is assumed that the gases do not react with each other.

Pi=P total Xi

where Xi = the mole fraction of the i-th component in the total mixture of m

components .

The relationship below provides a way to determine the volume based concentration

of any individual gaseous component.

Pi=P total Ci/1000000

Where, Ci is the concentration of the i-th component expressed in ppm.

Dalton's law is not exactly followed by real gases. Those deviations are considerably

large at high pressures. In such conditions, the volume occupied by the molecules can

become significant compared to the free space between them. Moreover, the short

average distances between molecules raises the intensity of intermolecular forces

between gas molecules enough to substantially change the pressure exerted by them.

Neither of those effects are considered by the ideal gas model.