Problem 9 - Chemistry Matter and Change

Question

Challenge 106.5 g of HCl(g) react with an unknown amount of \(\mathrm{NH}_{3}(\mathrm{g})\) to produce 157.5 \(\mathrm{g}\) of \(\mathrm{NH}_{4} \mathrm{Cl}(\mathrm{s})\) . How many grams of \(\mathrm{NH}_{3}(\mathrm{g})\) reacted? Is the law of conservation of mass observed in the reaction? Justify your answer.

Step-by-Step Solution

Answer

50.19 grams of \( \mathrm{NH}_3 \) reacted. The law of conservation of mass is observed with slight deviations due to rounding.

Step 1: Write the Balanced Chemical Equation

The reaction between hydrogen chloride gas \( \mathrm{HCl(g)} \) and ammonia gas \( \mathrm{NH}_3(g) \) forms ammonium chloride as a solid \( \mathrm{NH}_4Cl(s) \). The balanced chemical equation is: \[ \mathrm{HCl(g)} + \mathrm{NH}_3(g) \rightarrow \mathrm{NH}_4Cl(s) \] This shows that one mole of \( \mathrm{HCl} \) reacts with one mole of \( \mathrm{NH}_3} \) to form one mole of \( \mathrm{NH}_4Cl} \).

Step 2: Calculate Molar Masses

Calculate the molar masses of the compounds involved: - Molar mass of \( \mathrm{HCl} = 1.01 + 35.45 = 36.46 \, \text{g/mol} \)- Molar mass of \( \mathrm{NH}_3 = 14.01 + 3.03 = 17.04 \, \text{g/mol} \)- Molar mass of \( \mathrm{NH}_4Cl = 14.01 + 4.04 + 35.45 = 53.50 \, \text{g/mol} \)

Step 3: Convert Mass to Moles for NH4Cl

The mass of \( \mathrm{NH}_4Cl \) produced is given as 157.5 grams. Use the molar mass to find the moles of \( \mathrm{NH}_4Cl \): \[ \text{Moles of } \mathrm{NH}_4Cl = \frac{157.5 \, \text{g}}{53.50 \, \text{g/mol}} \approx 2.945 \, \text{moles} \]

Step 4: Determine Moles of Reactants Using Stoichiometry

According to the balanced equation, 1 mole of \( \mathrm{NH}_3 \) and 1 mole of \( \mathrm{HCl} \) produce 1 mole of \( \mathrm{NH}_4Cl \). Thus, 2.945 moles of \( \mathrm{NH}_4Cl \) require 2.945 moles of \( \mathrm{NH}_3 \) to react.

Step 5: Convert Moles of NH3 to Grams

Convert the moles of \( \mathrm{NH}_3 \) to grams: \[ \text{Mass of } \mathrm{NH}_3 = 2.945 \, \text{moles} \times 17.04 \, \text{g/mol} = 50.19 \, \text{grams} \]

Step 6: Verify the Conservation of Mass

Check the total mass before and after the reaction: - Total mass of reactants = 106.5 g of HCl + 50.19 g of NH3 = 156.69 g - Total mass of product = 157.5 g of NH4Cl There is a small difference, which might be due to rounding in calculations, but generally, the mass is conserved within experimental error.

Key Concepts

Stoichiometry

Stoichiometry is a key concept in chemistry that deals with the quantitative relationships between the reactants and products in a chemical reaction. Think of stoichiometry as a recipe guiding you on how much of each ingredient you need to make your dish turn out perfectly. When applying stoichiometry, we use the balanced chemical equation as our guide to determine the precise amounts of reactants and products involved.

In the given exercise, stoichiometry helps us determine the amount of ammonia gas (\(\mathrm{NH}_3\)) needed to react with hydrogen chloride gas (\(\mathrm{HCl}\)) to produce a specific amount of ammonium chloride (\(\mathrm{NH}_4Cl\)). By using stoichiometry, we first convert all given masses into moles. We then use the balanced chemical equation to find out how these moles correlate. This approach ensures that the reaction follows the law of conservation of mass, meaning the total mass of reactants equals the total mass of products, accounting for all rounding errors during calculations.

Balanced Chemical Equation

A balanced chemical equation is fundamental in chemistry, as it provides the necessary proportions of reactants and products in a reaction. This balancing ensures that the number of atoms for each element is consistent on both the reactant and product sides.

The balanced chemical equation for this exercise is:\[\mathrm{HCl(g)} + \mathrm{NH}_3(g) \rightarrow \mathrm{NH}_4Cl(s)\]
This equation tells us that one mole of hydrogen chloride gas reacts with one mole of ammonia gas to produce one mole of solid ammonium chloride. By ensuring the equation is balanced, we can reliably predict how much of a substance is needed or produced, maintaining the principle of conservation of mass.

Molar Mass Calculation

Molar mass is the mass of one mole of a substance (usually in grams). Calculating molar mass is crucial because it allows the conversion of mass to moles, and vice versa, which is essential for stoichiometric calculations.

In this chemical reaction:

• The molar mass of hydrogen chloride (\(\mathrm{HCl}\)) is approximately 36.46 g/mol.
• The molar mass of ammonia (\(\mathrm{NH}_3\)) is approximately 17.04 g/mol.
• The molar mass of ammonium chloride (\(\mathrm{NH}_4Cl\)) is approximately 53.50 g/mol.

These calculations are carried out by adding the atomic masses of the elements within each compound. For example, for \(\mathrm{NH}_3\), the molar mass calculation goes as follows:
\[\text{Molar mass of } \mathrm{NH}_3 = 14.01 + (3 \times 1.01) = 17.04 \, \text{g/mol}\]
Remember, precision in these calculations is key to ensuring that the stoichiometric conversions remain accurate.

Chemical Reaction

A chemical reaction is a process where substances, the reactants, are transformed into different substances, known as products. Chemical reactions involve the breaking of old bonds and the creation of new ones.

In this exercise, hydrogen chloride gas reacts with ammonia gas in a simple yet fascinating chemical reaction that forms ammonium chloride. This process can be directly observed by the formation of a solid product from gaseous reactants.
The chemical equation for this reaction:

• Reacts \(\mathrm{HCl(g)}\) with \(\mathrm{NH}_3(g)}\).
• Forms \(\mathrm{NH}_4Cl(s)\), a solid.

The equation indicates that each molecule of hydrogen chloride pairs with a molecule of ammonia to create ammonium chloride. Observing whether the mass remains the same before and after the reaction is an excellent way to understand the law of conservation of mass, which states that in a closed system, matter is neither created nor destroyed.