Question

At \(620 \mathrm{~K}\), the vapor density of ammonium chloride relative to hydrogen \(\left(\mathrm{H}_{2}\right)\) under the same conditions of temperature and pressure is \(14.5,\) although, according to its formula mass, it should have a vapor density of 26.8 . How would you account for this discrepancy?

Short answer

The discrepancy is due to ammonium chloride decomposing into NH_3 and HCl , lowering the vapor density.

Step-by-step solution

Understanding Vapor Density

The vapor density of a substance in relation to hydrogen ( H_2 ) is defined as the ratio of the mass of a certain volume of gas to the mass of an equal volume of hydrogen at the same temperature and pressure. Vapor density is numerically equal to half the molar mass of the gas.

Calculating Expected Vapor Density

For ammonium chloride ( NH_4Cl ), we first calculate the expected vapor density using its formula mass. The molar mass of NH_4Cl is calculated by adding the molar masses of its constituent elements: N (14.01 g/mol), H_4 (4×1.01 g/mol), Cl (35.45 g/mol). This gives a total molar mass of 53.5 g/mol, and the expected vapor density is 53.5 / 2 = 26.8 .

Given Observed Vapor Density

The observed vapor density is given as 14.5, which is much lower than the expected 26.8. This discrepancy suggests that the actual molecular weight of the gas in vapor form might be lower than expected.

Considering Decomposition

Ammonium chloride ( NH_4Cl ) likely decomposes upon vaporization. In the gas phase, it can dissociate into ammonia ( NH_3 ) and hydrogen chloride ( HCl ). Let's calculate the weighted average of these vapors considering they're present in equal amounts.

Calculating Decomposition Impact

The molecular masses of ammonia ( NH_3 ) and hydrogen chloride ( HCl ) are 17.03 g/mol and 36.46 g/mol, respectively. The average molecular mass of the gaseous products is (17.03 + 36.46) / 2 = 26.75 g/mol, yielding a vapor density 26.75 / 2 = 13.375 , close to the observed 14.5 when considering experimental conditions.

Conclusion on Discrepancy

The discrepancy in vapor density for ammonium chloride is due to its dissociation into ammonia and hydrogen chloride upon heating, explaining why the observed value (14.5) is significantly lower than the calculated value without dissociation (26.8).

Key concepts

Ammonium Chloride

Ammonium chloride, with the chemical formula \( \text{NH}_4\text{Cl} \), is a compound commonly known for its role in various industries. It consists of ammonium ions \((\text{NH}_4^+)\) and chloride ions \((\text{Cl}^-)\). When analyzed in terms of vapor density, it presents some intriguing behaviors due to its tendency to dissociate during heating.

In its solid form, ammonium chloride looks like a white crystalline salt. It's often used as a nitrogen source in fertilizers, a flavoring agent in licorices, and a part of the Galvanizing process. However, what's particularly interesting is what happens when it is heated.

• Upon heating, ammonium chloride sublimates, meaning it transitions directly from a solid to a gas.
• In its gaseous state, the compound has shown unexpected behaviors in experiments measuring its vapor density.

These behaviors are crucial for understanding the discrepancy in its expected vapor density and its actual observed values.

Molecular Mass

Molecular mass is the mass of a molecule based on the sum of the atomic masses of all atoms in the molecule. For ammonium chloride, we calculate the molecular mass by adding up the molar masses of its constituents: one nitrogen atom, four hydrogen atoms, and one chlorine atom.

• Nitrogen: \( 14.01 \, \text{g/mol} \)
• Hydrogen: \( 4 \times 1.01 \, \text{g/mol} = 4.04 \, \text{g/mol} \)
• Chlorine: \( 35.45 \, \text{g/mol} \)

The total molecular mass of ammonium chloride is therefore \( 53.5 \, \text{g/mol} \). As molecular mass is directly related to vapor density, which is half the molar mass, we would expect the vapor density of ammonium chloride to be \( 26.8 \) under normal conditions. Yet, discrepancies arise from other chemical phenomena.

Decomposition

Decomposition involves breaking down a compound into its constituent elements or simpler compounds. For ammonium chloride, this occurs when it is heated and transitions into a gaseous state.

During decomposition, ammonium chloride breaks down into ammonia \((\text{NH}_3)\) and hydrogen chloride \((\text{HCl})\). This molecular breakdown significantly affects the overall molecular mass.

• Ammonia has a molecular mass of \( 17.03 \, \text{g/mol} \).
• Hydrogen chloride has a molecular mass of \( 36.46 \, \text{g/mol} \).

In the gas phase, these products are formed in equal amounts, leading to an average molecular mass calculation of \( \frac{17.03 + 36.46}{2} = 26.75 \, \text{g/mol} \). This decomposition explains the lower experimental vapor density of \( 14.5 \) observed for ammonium chloride, aligning closely with the calculated vapor density when its dissociation is considered.

Gas Laws

The behavior and properties of gases, including those of decomposed ammonium chloride in its vapor form, can be better understood by applying gas laws. These laws help predict how gases will behave under different physical conditions such as pressure and temperature.

Key gas laws that apply include:

• Boyle's Law: States that pressure of a gas decreases as the volume increases, provided the temperature remains constant.
• Charles's Law: Demonstrates that the volume of a gas increases with an increase in temperature, assuming constant pressure.
• Ideal Gas Law: Combines several gas laws into the equation \( PV = nRT \), relating the pressure \(P\), volume \(V\), and temperature \(T\) of a gas to the amount of substance \(n\) and the gas constant \(R\).

Understanding these principles helps explain why experimentally observed vapor behavior might deviate from theoretical predictions. When ammonium chloride is heated to high temperatures (like \( 620 \, K \)), these gas laws guide our understanding of why the observed data (vapor density) might differ from what is expected in a closed system.