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Similarly, the mole fraction (or mole concentration) can be found as follows:
(1.42)
The molar mass of the total mixture is
(1.43)
From Eqs. (1.40), (1.41), and 1.42,
(1.44)
Example 1.1
A gas mixture has the following mass composition:
Determine the molar composition of the mixture.
Solution
| Gas | % Mass fraction | Mass fraction, ci | Molecular mass, μi | Mole fraction, ci/μi | % Mole fraction |
| CO 2 | 17.55 | 0.175 5 | 44 | 0.003 99 |
|
| O 2 | 4.26 | 0.042 6 | 32 | 0.001 33 |
|
| N 2 | 76.33 | 0.763 3 | 28 | 0.027 26 |
|
| CO | 1.86 | 0.018 6 | 28 | 0.000 66 |
|
| 100 | ∑ci = 1.0 | ∑ci/μi = 0.03324 | Total = 100 |
1.3.2.1 Dalton Model of Gas Mixtures
If a gas mixture of two components A and B is at pressure p and temperature T in a container with volume V, each gas in the mixture exists separately and independently at the temperature and volume of the mixture, and their respective pressures are pA and pB. For the mixture
For the components,
Since n = nA + nB,
or
(1.45)
pA and pB are known as the partial pressures.
Therefore,
It can be shown that the internal energy and enthalpy of a mixture of two gases (A and B) can be written as
The gas constants for the ith component and gas mixture are, respectively,
Using Eq. (1.43), we obtain
(1.46)
For the two‐gas mixture
1.3.3 Processes in Ideal Gas Systems
The state of a gas may be completely specified by combining three variable properties (pressure p, temperature T, and volume V) in an equation called the ideal gas equation of state:
(1.47)
