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14–17C Express Dalton’s law of additive pressures. Does this law hold exactly for ideal-gas mixtures? How about nonideal-gas mixtures?

Answer :

Dalton's Law of Partial Pressures, also known as Dalton's Law of Additive Pressures, is a principle in chemistry that deals with the pressure of gases. It states that the total pressure exerted by a mixture of non-reacting gases in a closed system is equal to the sum of the partial pressures of each individual gas in the mixture.

In mathematical terms, Dalton's Law can be expressed as:

[tex]P_{\text{total}} = P_1 + P_2 + P_3 + \ldots + P_n[/tex]

Where:

  • [tex]P_{\text{total}}[/tex] is the total pressure of the gas mixture.
  • [tex]P_1, P_2, P_3, \ldots, P_n[/tex] are the partial pressures of gases 1, 2, 3, ..., n respectively.

Ideal-Gas Mixtures:

Dalton's Law holds exactly for ideal-gas mixtures. Ideal gases are hypothetical gases that perfectly follow the gas laws without any interactions between the molecules other than collisions. In ideal conditions, the behavior described by Dalton's Law is exactly accurate because there are no forces acting between the gas molecules, so the gases act independently of each other.

Nonideal-Gas Mixtures:

However, for nonideal-gas mixtures, Dalton's Law may not hold precisely. Nonideal, or real, gases deviate from ideal behavior due to interactions between gas molecules. In real gases, factors like van der Waals forces (attractive or repulsive forces between molecules) can affect the pressure exerted by a gas mixture. These deviations become significant at high pressures or low temperatures where the volume of the gas particles is no longer negligible, and intermolecular forces cannot be ignored.

In reality, corrections are often applied for nonideal-gas behavior using more complex models, such as the van der Waals equation, to adjust for these interactions and better predict the behavior of gas mixtures under nonideal conditions.

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