Problem 31 - Chemistry and Chemical Reactivity

Question

Iron reacts with hydrochloric acid to produce iron(II) chloride and hydrogen gas: $$ \mathrm{Fe}(\mathrm{s})+2 \mathrm{HCl}(\mathrm{aq}) \longrightarrow \mathrm{Fe} \mathrm{Cl}_{2}(\mathrm{aq})+\mathrm{H}_{2}(\mathrm{g}) $$ The \(\mathrm{H}_{2}\) gas from the reaction of \(2.2 \mathrm{g}\) of iron with excess acid is collected in a \(10.0-\) I. flask at \(25^{\circ} \mathrm{C}\). What is the pressure of the \(\mathrm{H}_{2}\) gas in this flask?

Step-by-Step Solution

Answer

The pressure of the \(\mathrm{H}_{2}\) gas in the flask is approximately 0.0966 atm.

Step 1: Calculate Moles of Iron

First, we need to determine the number of moles of iron (Fe) used. The atomic mass of Fe is approximately 55.85 g/mol. Use the formula: \[ \text{moles of Fe} = \frac{\text{mass of Fe}}{\text{molar mass of Fe}} \]Given mass of Fe is 2.2 g:\[ \text{moles of Fe} = \frac{2.2 \text{ g}}{55.85 \text{ g/mol}} \approx 0.0394 \text{ moles} \]

Step 2: Determine Moles of Hydrogen Gas Produced

According to the balanced chemical equation, 1 mole of iron produces 1 mole of hydrogen gas (\(\mathrm{H}_{2}\)). Therefore, the moles of \(\mathrm{H}_{2}\) produced are the same as the moles of \(\mathrm{Fe}\):\[ \text{moles of } \mathrm{H}_{2} \approx 0.0394 \text{ moles} \]

Step 3: Use Ideal Gas Law to Find Pressure

We will use the Ideal Gas Law equation to find the pressure of \(\mathrm{H}_{2}\) in the flask:\[ PV = nRT \]Where:- \(P\) is the pressure- \(V = 10.0 \text{ L}\)- \(n \approx 0.0394 \text{ moles}\)- \(R = 0.0821 \text{ L atm/mol K}\)- \(T = 25^{\circ} \text{C} = 298 \text{ K}\)Rearrange to solve for \(P\):\[ P = \frac{nRT}{V} \]Substitute the known values:\[ P = \frac{0.0394 \times 0.0821 \times 298}{10.0} \approx 0.0966 \text{ atm} \]

Step 4: Final Answer

The pressure of the hydrogen gas in the flask is approximately 0.0966 atm.

Key Concepts

Chemical Reactions

Chemical reactions are processes where substances, called reactants, transform into different substances, known as products. These transformations occur due to the breaking and forming of chemical bonds. In the reaction between iron and hydrochloric acid, known as a single replacement reaction, iron replaces hydrogen, forming iron(II) chloride and hydrogen gas.
This specific reaction can be represented by the following balanced equation: \[ \mathrm{Fe}(\mathrm{s}) + 2 \mathrm{HCl}(\mathrm{aq}) \longrightarrow \mathrm{FeCl}_2(\mathrm{aq}) + \mathrm{H}_2(\mathrm{g}) \]
Key features of chemical reactions include:

• Substances undergo a chemical transformation.
• Bonds between atoms break and new ones form.
• Reactions can either release energy (exothermic) or absorb energy (endothermic).

Understanding this chemical reaction helps in predicting the products formed and calculating their quantities.

Mole Concept

The mole concept is pivotal in chemistry as it serves as a bridge between the atomic scale and real-world quantities. A mole is defined as the amount of substance that contains as many entities as there are atoms in 12 grams of carbon-12, approximately \(6.022 \times 10^{23}\) entities, also known as Avogadro's number.
In the exercise, to find out how much hydrogen gas is produced, you first calculate the moles of iron used.
Using the formula:

• \(\text{moles of Fe} = \frac{\text{mass of Fe}}{\text{molar mass of Fe}}\)

Given the mass of iron (2.2 g) and its molar mass (55.85 g/mol), the calculation looks like:\[ \text{moles of Fe} = \frac{2.2}{55.85} \approx 0.0394 \text{ moles} \]
Thus, 0.0394 moles of iron are reacting in this exercise.

Stoichiometry

Stoichiometry involves the quantitative relationships between the amounts of reactants and products in a chemical reaction. It's rooted in the law of conservation of mass, meaning that the mass of reactants equates to the mass of products. From the balanced chemical equation, stoichiometry allows us to determine the mole-to-mole ratios and calculate the resulting quantities of substances involved in the reaction.
In this reaction, the balanced equation shows a 1:1 ratio between iron and hydrogen gas:

• 1 mole of iron produces 1 mole of hydrogen gas.

This proportion guides us to determine the moles of hydrogen gas produced using the moles of iron calculated:\[ \text{moles of } \mathrm{H}_2 = \text{moles of Fe} \approx 0.0394 \text{ moles} \]
This method ensures accurate predictions of how much product forms under given conditions, aiding in practical applications such as the use of the ideal gas law to find the pressure of hydrogen gas.