Problem 116 - Chemistry: The Central Science

Question

Ammonia, \(\mathrm{NH}_{3}(g)\), and hydrogen chloride, \(\mathrm{HCl}(g)\), react to form solid ammonium chloride, \(\mathrm{NH}_{4} \mathrm{Cl}(s)\) : $$ \mathrm{NH}_{3}(g)+\mathrm{HCl}(g) \longrightarrow \mathrm{NH}_{4} \mathrm{Cl}(s) $$ Two 2.00-L flasks at \(25^{\circ} \mathrm{C}\) are connected by a stopcock, as shown in the drawing. One flask contains \(5.00 \mathrm{~g}\) \(\mathrm{NH}_{3}(g)\), and the other contains \(5.00 \mathrm{~g} \mathrm{HCl}(g)\). When the stopcock is opened, the gases react until one is completely consumed. (a) Which gas will remain in the system after the reaction is complete? (b) What will be the final pressure of the system after the reaction is complete? (Neglect the volume of the ammonium chloride formed.)

Step-by-Step Solution

Answer

a) The gas that remains after the reaction is complete is ammonia (NH3). b) The final pressure of the system is \(1.34 \, atm\).

Step 1: Determine the limiting reactant

For determining the limiting reactant, we first need to find the moles of each gas. Use the molar mass to convert grams to moles. For ammonia (NH3), the molar mass is approximately \(17.03 \ g/mol\), and for hydrogen chloride (HCl) the molar mass is approximately \(36.46 \ g/mol\). Moles of NH3: \[ \frac{5.00 \ g}{17.03 \ g/mol} = 0.2937 \ mol \] Moles of HCl: \[ \frac{5.00 \ g}{36.46 \ g/mol} = 0.1371 \ mol \] Now that we have the moles of each reactant, we can determine the limiting reactant by comparing their mole ratio to the stoichiometric ratio (1:1 in this case): \[ \frac{0.2937 \ mol}{0.1371 \ mol} = 2.14 \] The mole ratio is greater than the stoichiometric ratio (which is 1), so HCl is the limiting reactant.

Step 2: Calculate moles of excess reactant

Now that we know HCl is the limiting reactant, we can calculate the moles of excess NH3 after the reaction: Moles of NH3 remaining: \[ 0.2937 \ mol - 0.1371 \ mol = 0.1566 \ mol \]

Step 3: Find the final pressure

We will now use the moles of the excess reactant (NH3) and the ideal gas law to find the final pressure in the flasks. Recall that the ideal gas law is: \[PV = nRT\] Since the temperature and the gas constant (R) are both given, we can solve for the final pressure (P): \[ P = \frac{nRT}{V} \] We have: - \(n = 0.1566 \ mol\): moles of excess NH3 - \(R = 0.0821 \ \frac{L \times atm}{mol \times K}\): gas constant - \(T = (25 + 273.15) \, K = 298.15 \, K\): temperature in Kelvin - \(V = 4.00 \, L\): total volume of the two connected flasks Now solve for P: \[ P = \frac{(0.1566 \, mol)(0.0821 \frac{L \times atm}{mol \times K})(298.15 \, K)}{4.00 \, L} \] \[ P = 1.34 \, atm \] So, the final pressure in the flasks after the reaction is complete is \(1.34 \, atm\). To summarize: a) The gas that remains after the reaction is complete is ammonia (NH3). b) The final pressure of the system is \(1.34 \, atm\).

Key Concepts

Understanding Stoichiometry

Stoichiometry is the area of chemistry that involves calculating the quantities of reactants and products in chemical reactions. It's a powerful tool that helps us understand how substances interact and transform. In our exercise, stoichiometry is used to determine the limiting reactant, which is the substance that is completely consumed first and dictates the amount of product formed. This is crucial because once the limiting reactant is used up, the reaction cannot proceed further.

To find the limiting reactant, we first calculate the moles of each reactant using their given masses and molar masses. Ammonia (NH₃) and hydrogen chloride (HCl) each have specific molar masses, which we use to convert grams to moles. We then compare the mole ratios of the reactants to the stoichiometric coefficients from the balanced chemical equation. This comparison tells us which reactant limits the reaction.

• Molar Mass: Essential for converting grams to moles, allowing us to participate in stoichiometric calculations.
• Mole Ratio: The ratio between the moles of different reactants/products, derived from the balanced equation, is critical for identifying the limiting reactant.

Understanding these concepts helps you master stoichiometry and predict accurately which substances will remain after a reaction.

Exploring the Ideal Gas Law

The ideal gas law is a cornerstone of chemistry, combining various properties of gases into a single equation. It provides a way to relate pressure, volume, and temperature of a gas to the number of moles present. The law is expressed as \(PV = nRT\), where:

• P: Pressure of the gas
• V: Volume of the gas
• n: Number of moles
• R: Ideal gas constant, approximately 0.0821 \(L \cdot atm / mol \cdot K\)
• T: Temperature in Kelvin

This formula is perfect for calculating conditions before and after reactions involving gases. In our exercise, we used it to find the final pressure after the reaction between ammonia and hydrogen chloride. Knowing the moles of the excess reactant (NH₃), we could compute the final pressure.

Such calculations rely on understanding how each variable affects the others. The ideal gas law assumes that the gas behaves perfectly, meaning interactions between molecules are negligible, and the volume occupied by gas molecules themselves is small. This simplifies calculations and is very useful, especially when learning gas behavior.

Basics of Chemical Reactions

Chemical reactions involve the transformation of compounds into different substances. This process is governed by chemical equations, which express the identities and quantities of the reactants and products. In our example, the reaction between ammonia (NH₃) and hydrogen chloride (HCl) forms solid ammonium chloride (NH₄Cl). The equation given is:\[ \mathrm{NH}_{3}(g) + \mathrm{HCl}(g) \longrightarrow \mathrm{NH}_{4} \mathrm{Cl}(s) \]

This equation is balanced, meaning the number of atoms on both sides is equal, showcasing conservation of mass. Chemical reactions follow strict rules, and the stoichiometry of the reaction provides insight into these intricate changes. During the process, bonds in the reactants are broken, and new bonds form to produce the products.

• Balanced Equation: Ensures that atoms are conserved, keeping track of all particles involved.
• Reactants and Products: Reactants are transformed into products, signifying chemical changes.

Understanding chemical reactions helps you predict and control the outcomes of various reactions, leading to more accurate experimental results.