Question

Which of the following mixture of gases does not obey Dalton's law of partial pressure? (a) \(\mathrm{O}_{2}\) and \(\mathrm{CO}_{2}\) (b) \(\mathrm{N}_{2}\) and \(\mathrm{O}_{2}\) (c) \(\mathrm{Cl}_{2}\) and \(\mathrm{SO}_{2}\) (d) \(\mathrm{NH}_{3}\) and \(\mathrm{HCl}\)

Short answer

The mixture \(\mathrm{NH}_3\) and \(\mathrm{HCl}\) does not obey Dalton's law of partial pressure.

Step-by-step solution

Understanding Dalton's Law of Partial Pressure

Dalton's Law of Partial Pressure states that the total pressure exerted by a mixture of non-reacting gases is equal to the sum of the partial pressures of individual gases. It's important to note that this law applies only to non-reacting gas mixtures.

Examine Each Choice

Examine the given options to determine if any of the gases react with each other.- (a) \(\mathrm{O}_2\) and \(\mathrm{CO}_2\): These are inert to each other and do not react.- (b) \(\mathrm{N}_2\) and \(\mathrm{O}_2\): These gases do not react under normal conditions.- (c) \(\mathrm{Cl}_2\) and \(\mathrm{SO}_2\): These gases can react under certain conditions, forming sulfuryl chloride (\(\mathrm{SO}_2\mathrm{Cl}_2\)), but are often considered unreactive in atmospheric conditions.- (d) \(\mathrm{NH}_3\) and \(\mathrm{HCl}\): These gases react readily to form ammonium chloride (\(\mathrm{NH}_4\mathrm{Cl}\)).

Identifying the Exception

From the examination, option (d) \(\mathrm{NH}_3\) and \(\mathrm{HCl}\) are the gases that react with each other, violating Dalton's Law since a new substance (ammonium chloride) forms instead of the gases existing independently as a mixture.

Key concepts

Reactive and Non-Reactive Gas Mixtures

When discussing gas mixtures, understanding the difference between reactive and non-reactive gases is crucial. Non-reactive or inert gases do not change chemically when mixed under normal conditions. This is why Dalton's Law applies to them. In a non-reactive gas mixture, each gas maintains its unique partial pressure independent of others. Examples include mixtures like

• Oxygen ( \(\mathrm{O}_2\) ) and Carbon Dioxide ( \(\mathrm{CO}_2\) )
• Nitrogen ( \(\mathrm{N}_2\) ) and Oxygen

These consist of gases that do not react with each other chemically. Reactive gas mixtures, on the other hand, undergo chemical reactions when combined. In such cases, new compounds form, and Dalton's Law does not apply. A classic example of reactive gas mixtures is Ammonia (\(\mathrm{NH}_3\) ) and Hydrochloric Acid (\(\mathrm{HCl}\)). These two gases promptly combine to create solid Ammonium Chloride (\(\mathrm{NH}_4\mathrm{Cl}\)), indicating a chemical reaction has occurred.

Chemical Reactions in Gas Mixtures

Chemical reactions in gas mixtures involve the forming of new chemical substances. When reactive gases are combined, they may interact at the molecular level, leading to new products. This can be visualized as: \[\text{Reactant 1} + \text{Reactant 2} \rightarrow \text{Product}\]In the exercise example involving \(\mathrm{NH}_3\) Ammonia and \(\mathrm{HCl}\) Hydrochloric Acid:\[\mathrm{NH}_3 (g) + \mathrm{HCl} (g) \rightarrow \mathrm{NH}_4\mathrm{Cl} (s)\]A chemical reaction occurs because these two gaseous reactants form a solid compound, indicating a significant change from the initial gaseous state. The transformation invalidates the application of Dalton’s Law, which assumes no chemical interaction between gases.

Partial Pressure Calculations

Dalton's Law simplifies calculating the individual pressures of gases in a non-reactive mixture. It can be defined by the equation: \[P_{total} = P_1 + P_2 + P_3 + \ldots\]Where \(P_{total}\) is the total pressure of the gas mixture and \(P_1, P_2, P_3, \ldots\) represent the partial pressures of each individual gas in the mixture. Each partial pressure corresponds to what each gas would exert if it occupied the container alone. This approach works beautifully provided no chemical reactions occur between the gases.Partial pressure is directly proportional to the mole fraction, which can be calculated using: \[P_i = \chi_i \cdot P_{total}\]Here,

• \(P_i\) is the partial pressure of gas \(i\)
• \(\chi_i\) is the mole fraction of gas

Partial pressures allow us to understand how individual gases contribute to a gas mixture's total pressure, especially in controlled environments where no reactive substances are present.