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The ideal gas law is a fundamental equation in chemistry that describes the behavior of an ideal gas. This law is expressed as \( PV = nRT \), where:

• \( P \) is the pressure of the gas,
• \( V \) is the volume of the gas,
• \( n \) is the number of moles,
• \( R \) is the ideal gas constant (0.0821 L·atm/mol·K), and
• \( T \) is the temperature in Kelvin.

To effectively use this law, we often need to convert pressure, volume, and temperature to the correct units. In this specific problem, we converted the pressure from torr to atm and the temperature from Celsius to Kelvin.

By rearranging the ideal gas law, \( n = \frac{PV}{RT} \), we calculated the number of moles of \( \text{NH}_3 \) present in the sample. This calculation is crucial for further determining the amount of \( \text{NH}_3 \) available for reacting with \( \text{HCl} \). Thus, understanding this equation allows you to predict how gases will behave under different conditions.

The concept of the limiting reactant is key in chemical reactions as it determines how much product can be formed. In a chemical reaction, the limiting reactant is the substance that is completely consumed first, preventing more products from forming.

In this case, both \( \text{NH}_3 \) and \( \text{HCl} \) react in a 1:1 mole ratio to form \( \text{NH}_4^+ \) and \( \text{Cl}^- \). By calculating the moles of each reactant, we found there were 0.303 moles of \( \text{NH}_3 \) and 0.20 moles of \( \text{HCl} \).

Since \( \text{HCl} \) has fewer moles, it is the limiting reactant. This means all of the \( \text{HCl} \) will react, leaving an excess of \( \text{NH}_3 \). Recognizing the limiting reactant helps predict the extent of the reaction and the composition of the resulting solution.

Calculating the \( \text{pH} \) of a solution is an important skill in chemistry, especially for acid-base reactions. The \( \text{pH} \) measures the concentration of hydrogen ions (\( \text{H}^+ \)) in a solution, where lower \( \text{pH} \) values represent acidic conditions and higher values indicate basic conditions. The reaction here leads to the formation of \( \text{NH}_4^+ \), which is a weak acid, capable of releasing \( \text{H}^+ \) in solution.

After the reaction, the concentration of \( \text{NH}_4^+ \) is determined to be 0.40 M. With the weak base dissociation constant \( K_b \) for ammonia known, we can calculate \( [\text{OH}^-] \) and subsequently \( \text{pOH} \). The relationship \( \text{pH} = 14 - \text{pOH} \) then allows us to find the \( \text{pH} \).

This process involves logarithms and equilibrium constants, granting insight into the acidity of weak acid solutions, which is central to chemistry studies.

Acid-base reactions are vital in chemistry and occur when an acid and a base react to form water and a salt. Here, ammonia (\( \text{NH}_3 \)) acts as a base and reacts with hydrochloric acid (\( \text{HCl} \)) to form ammonium chloride (\( \text{NH}_4^+ \) and \( \text{Cl}^- \)).

These reactions typically proceed through proton transfer, where the base accepts \( \text{H}^+ \) ions from the acid. In this case, \( \text{NH}_3 \) gains a proton from \( \text{HCl} \), transforming into \( \text{NH}_4^+ \). Understanding these reactions is crucial, as they underlie many processes in chemistry and biology.

Often, such reactions are central in buffer solutions, where weak acids/bases help maintain \( \text{pH} \) levels. Thus, knowledge of acid-base interactions expands your understanding of chemical behavior in various environments.