Question

Ammonia and hydrogen chloride react to form solid ammonium chloride: $$\mathrm{NH}_{3}(g)+\mathrm{HCl}(g) \longrightarrow \mathrm{NH}_{4} \mathrm{Cl}(s)$$ Two 2.00 -L flasks at \(25^{\circ} \mathrm{C}\) are connected by a valve, as shown in the drawing. One flask contains 5.00 \(\mathrm{g}\) of \(\mathrm{NH}_{3}(g),\) and the other contains 5.00 \(\mathrm{g}\) of \(\mathrm{HCl}(g) .\) When the valve 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.) (c) What mass of ammonium chloride will be formed?

Short answer

a) Ammonia (\(NH_3\)) will remain in the system after the reaction is complete. b) The final pressure of the system after the reaction is complete is 0.968 atm. c) The mass of ammonium chloride formed is 7.34 g.

Step-by-step solution

Identify the limiting reactant

First, we need to determine which gas is the limiting reactant. We are given the mass of both gases and can use their molar mass to convert to moles. Moles of \(NH_3\): \(\frac{5.00 \mathrm{g}}{17.03 \mathrm{g/mol}}=0.2937 \mathrm{mol}\) Moles of \(HCl\): \(\frac{5.00 \mathrm{g}}{36.46 \mathrm{g/mol}}=0.1372 \mathrm{mol}\) The stoichiometry of the balanced equation is 1:1. Since there are more moles of \(NH_3\) than \(HCl\), \(HCl\) is the limiting reactant.

Calculate the moles of reactants after the reaction

Now, we need to determine the amount of each reactant left after the reaction is complete. Since \(HCl\) will be completely consumed, there will be no moles of \(HCl\) left. The moles of \(NH_3\) left can be calculated. Moles of \(NH_3\) left: \(0.2937 - 0.1372 = 0.1565 \mathrm{mol}\)

Calculate the final pressure of the system

The initial pressure of the system can be calculated using the ideal gas law, \(PV=nRT\), where \(P\) is pressure, \(V\) is volume, \(n\) is moles, \(R\) is the ideal gas constant, and \(T\) is temperature in Kelvin. The temperature is given as \(25^{\circ} \mathrm{C}\), which is equal to \(298.15 \mathrm{K}\). The ideal gas constant, \(R\), is \(0.0821 \mathrm{L \cdot atm/mol \cdot K}\). Initially, only \(NH_3\) is in the first flask, so: Initial pressure (both flasks): \(P_1=\frac{n_1 \cdot R \cdot T_1}{V_1}\) \(P_1=\frac{0.2937 \mathrm{mol} \cdot 0.0821 \mathrm{L \cdot atm/mol \cdot K} \cdot 298.15 \mathrm{K}}{2.00 \mathrm{L}}\) \(P_1=3.63 \mathrm{atm}\) After the reaction, the final pressure can be calculated using the moles of \(NH_3\) left: Final pressure (both flasks): \(P_2=\frac{n_2 \cdot R \cdot T_2}{V_2}\) \(P_2=\frac{0.1565 \mathrm{mol} \cdot 0.0821 \mathrm{L \cdot atm/mol \cdot K} \cdot 298.15 \mathrm{K}}{4.00 \mathrm{L}}\) \(P_2=0.968 \mathrm{atm}\)

Calculate the mass of ammonium chloride formed

Finally, we need to determine the mass of ammonium chloride formed from the reaction. Since \(HCl\) is the limiting reactant, the mass of ammonium chloride produced can be calculated using the stoichiometry of the balanced equation. Moles of \(NH_4Cl\) produced: \(0.1372 \mathrm{mol}\) Mass of \(NH_4Cl\) produced: \(0.1372 \mathrm{mol} \times 53.49 \mathrm{g/mol} = 7.34 \mathrm{g}\) In summary: a) The gas that will remain in the system after the reaction is complete is ammonia (\(NH_3\)). b) The final pressure of the system after the reaction is complete is 0.968 atm. c) The mass of ammonium chloride formed is 7.34 g.

Key concepts

Stoichiometry

Understanding stoichiometry is key to solving problems involving chemical reactions and their outcomes. It involves the quantitative relationships between reactants and products in a chemical reaction. To determine this, we need a balanced chemical equation. For the reaction between ammonia and hydrogen chloride to form ammonium chloride, the balanced equation is: \[ \mathrm{NH}_{3}(g) + \mathrm{HCl}(g) \rightarrow \mathrm{NH}_{4}\mathrm{Cl}(s) \] This equation shows a 1:1 molar ratio between ammonia and hydrogen chloride, meaning 1 mole of \( \mathrm{NH}_{3} \) reacts with 1 mole of \( \mathrm{HCl} \) to produce 1 mole of \( \mathrm{NH}_{4}\mathrm{Cl} \).
Using stoichiometry allows us to identify the limiting reactant—the substance that will be completely consumed first, limiting the amount of product formed. Here, hydrogen chloride is the limiting reactant because there are fewer moles of \( \mathrm{HCl} \) compared to \( \mathrm{NH}_{3} \). This concept helps us predict the amounts of remaining reactants and the mass of products formed as we saw with the mass of ammonium chloride calculated at 7.34 g.

Ideal Gas Law

The ideal gas law, expressed as \( PV = nRT \), is a fundamental equation that relates the pressure, volume, moles of gas, and temperature. In this formula:

• \( P \) is the pressure
• \( V \) is the volume
• \( n \) is the number of moles
• \( R \) is the ideal gas constant (0.0821 \( \mathrm{L \cdot atm/mol \cdot K} \))
• \( T \) is the temperature in Kelvin

The initial pressure was calculated before the reaction by applying this formula to both flasks considered as one system. Initially, 5 g of \( \mathrm{NH}_{3} \), equivalent to 0.2937 mol, gave an initial pressure of 3.63 atm in a single 2 L flask. After the valve opening, the systems combine into 4 L, and as \( \mathrm{HCl} \) fully reacts, the pressure decreases.
With ammonia left unreacted, a final pressure of 0.968 atm was computed, illustrating how the idea of gases interacting in a closed system predicts pressure changes linked to chemical reactions.

Ammonium Chloride Formation

The formation of ammonium chloride from ammonia and hydrogen chloride is a classic example of a chemical reaction between two gases to form a solid. In the given problem, after mixing, \( \mathrm{NH}_{3} \) and \( \mathrm{HCl} \) gases react to produce a white, solid \( \mathrm{NH}_{4}\mathrm{Cl} \). This reaction is straightforward due to its 1:1 stoichiometry, resulting in complete utilization of hydrogen chloride since it is the limiting reactant.
The process ceases once \( \mathrm{HCl} \) is depleted, leaving some amount of \( \mathrm{NH}_{3} \) since it started in excess. The calculation of the mass of \( \mathrm{NH}_{4}\mathrm{Cl} \) formed uses the previous stoichiometric ratio, resulting in 7.34 g of product. This transformation illustrates the principle of mass conservation in chemical reactions, where the mass of reactants equals the mass of products once the reaction reaches completion.