Problem 116 - Chemistry 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) NH3 gas will remain in the system after the reaction is complete. (b) The final pressure of the system after the reaction will be 0.968 atm.

Step 1: Calculate moles of each gas

We will first calculate the moles of the two gases (NH3 and HCl) present in the flasks, using their molar masses. For ammonia (NH3), the molar mass is 17.03 g/mol, and for hydrogen chloride (HCl), the molar mass is 36.46 g/mol. For NH3: \(moles=\frac{mass}{molar\_mass}\newline moles=\frac{5.00 \,g}{17.03 \,g/mol}\newline moles=0.2937 \,mol\) For HCl: \(moles=\frac{mass}{molar\_mass}\newline moles=\frac{5.00 \,g}{36.46 \,g/mol}\newline moles=0.1371 \,mol\)

Step 2: Identify the limiting reactant

According to the balanced equation, 1 mole of NH3 reacts with 1 mole of HCl. Comparing the moles of NH3 and HCl we can observe that NH3 has more moles than HCl. Hence, the limiting reactant is HCl, as it will be completely consumed during the reaction.

Step 3: Calculate moles of remaining gas

Now, we can calculate the moles of NH3 remaining by subtracting the moles of HCl, since that is the limiting reactant. Moles of remaining NH3: \(0.2937 \,mol - 0.1371 \,mol = 0.1566 \,mol\)

Step 4: Calculate the final pressure of the system

Since we know the moles of NH3 remaining, we can use the ideal gas law (PV=nRT) to find the final pressure. The volume of the flasks is 2.00 L each, so the total volume is 4.00 L. The temperature is given as 25°C, which is equal to 298.15 K. The universal gas constant (R) is 0.0821 L atm / (mol K). PV = nRT \(P=\frac{nRT}{V} \newline P =\frac{0.1566 \,mol\cdot 0.0821 \,\frac{L\cdot atm}{mol\cdot K}\cdot 298.15 \,K}{4.00 \,L} \newline P = 0.968\, atm\)

Step 5: Answers

(a) NH3 gas will remain in the system after the reaction is complete. (b) The final pressure of the system after the reaction will be 0.968 atm.

Key Concepts

Limiting Reactant

Understanding the concept of the limiting reactant is crucial for solving many chemical reaction problems. It is the substance that is totally consumed when a chemical reaction is complete. The remaining reactants are called excess reactants, and they are left over because there is nothing left of the limiting reactant to react with.

In a chemical reaction, the limiting reactant determines the maximum amount of product that can be formed. To identify the limiting reactant, you first need to calculate the moles of each reactant involved, just as was done in the original exercise. Then, using the balanced chemical equation, you can determine the stoichiometric relationship between the reactants and figure out which one will run out first, thus limiting the extent of the reaction.

For example, if a recipe calls for two eggs and three cups of flour to make a cake, and you only have one egg, the egg is the limiting 'reactant', because it restricts how much cake can be made, regardless of how much flour you have.

Mole Concept

The mole concept is a bridge between the micro world of particles and the macro world of grams and liters that we can measure in the lab. One mole is defined as exactly 6.02214076 × 10²³ elementary entities (usually atoms, molecules, ions or electrons).

This is known as Avogadro's number, and it's a central value in chemistry because it allows chemists to count chemicals by weighing them. Just as a dozen refers to 12 items, a mole refers to Avogadro's number of particles. The molar mass, which is the mass of one mole of a substance, is measured in grams per mole (g/mol). It tells us how much one mole of a substance weighs.

In the presented exercise, molar masses were used to convert the mass of ammonia and hydrogen chloride to moles before determining the limiting reactant. This process is pivotal when you're comparing quantities of reactants or products in a chemical reaction.

Ideal Gas Law

The ideal gas law is a fundamental equation that relates the pressure (P), volume (V), number of moles (n), and temperature (T) of a gas. The equation is represented as PV=nRT, where R is the universal gas constant, which has a value of 0.0821 L atm / (mol K) under standard conditions. The ideal gas law assumes that gases consist of many tiny particles moving in constant, random motion and that these particles do not interact except when they collide elastically.

This law allows us to calculate one of the four variables (P, V, n, or T) if the others are known. In the context of the exercise, after determining the limiting reactant and the moles of ammonia left, we applied the ideal gas law to find the final pressure in the system, assuming no change in the volume and temperature. The law is considered 'ideal' because it assumes that gases behave perfectly, with no attraction between particles, and that they have negligible volume – assumptions that are approached closely by real gases under many conditions.