Problem 31 - Chemistry and Chemical Reactivity

Question

Iron reacts with hydrochloric acid to produce iron(II) chloride and hydrogen gas: $$ \mathrm{Fe}(\mathrm{s})+2 \mathrm{HCl}(\mathrm{aq}) \rightarrow \mathrm{FeCl}_{2}(\mathrm{aq})+\mathrm{H}_{2}(\mathrm{g}) $$ The \(\mathrm{H}_{2}\) gas from the reaction of \(2.2 \mathrm{g}\) of iron with excess acid is collected in a 10.0 -L 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 hydrogen gas is 0.096 atm.

Step 1: Calculate Moles of Iron

First, let's calculate the number of moles of iron (Fe) using its given mass. The molar mass of iron is approximately 55.85 g/mol. \[ \text{moles of Fe} = \frac{2.2 \text{ g}}{55.85 \text{ g/mol}} \approx 0.0394 \text{ mol} \]

Step 2: Determine Moles of Hydrogen Gas

From the balanced chemical equation, we see that 1 mole of iron reacts to produce 1 mole of hydrogen gas. Therefore, the moles of hydrogen gas produced is equal to the moles of iron. \[ \text{moles of } \mathrm{H}_2 = 0.0394 \text{ mol} \]

Step 3: Use Ideal Gas Law to Find Pressure

Next, we use the ideal gas law to find the pressure of the hydrogen gas. The ideal gas law is given by \[ PV = nRT \]where \( P \) is the pressure, \( V \) is the volume (10.0 L), \( n \) is the number of moles (0.0394 mol), \( R \) is the ideal gas constant (0.0821 L·atm/mol·K), and \( T \) is the temperature in Kelvin. Convert the temperature from Celsius to Kelvin by adding 273.15, so \( T = 25 + 273.15 = 298.15 \text{ K} \).Now, solve for \( P \):\[ P = \frac{nRT}{V} = \frac{0.0394 \times 0.0821 \times 298.15}{10.0} \approx 0.096 \text{ atm} \]

Step 4: Conclusion

After performing the calculations, we find that the pressure of the hydrogen gas in the flask is approximately 0.096 atm. This is achieved by using the ideal gas law with the calculated moles of hydrogen.

Key Concepts

Chemical Reaction Stoichiometry

Understanding chemical reaction stoichiometry involves recognizing the proportional relationships in a chemical reaction. In our exercise, we are given that iron reacts with hydrochloric acid, producing iron(II) chloride and hydrogen gas. The balanced equation is:\[ \mathrm{Fe}(\mathrm{s}) + 2 \mathrm{HCl}(\mathrm{aq}) \rightarrow \mathrm{FeCl}_{2}(\mathrm{aq}) + \mathrm{H}_{2}(\mathrm{g}) \]The coefficients in the chemical equation tell us important things. For example, 1 mole of iron reacts with 2 moles of hydrochloric acid to produce 1 mole of iron(II) chloride and 1 mole of hydrogen gas. This mole-to-mole relationship is crucial:

• 1 mole of \( \mathrm{Fe} \) produces 1 mole of \( \mathrm{H}_2 \)
• We used this knowledge to equate the moles of iron to moles of hydrogen gas in the problem.

Thus, understanding stoichiometry ensures you can accurately calculate how much of each product will result from a given amount of reactants, which is a fundamental skill in chemistry.

Pressure Calculation

Once the amount of hydrogen gas is determined, calculating its pressure at a given volume and temperature is done using the ideal gas law:\[ PV = nRT \]The ideal gas law relates pressure \( P \), volume \( V \), and temperature \( T \) of a gas to the number of moles \( n \) and the ideal gas constant \( R \). Here's how it works:

• First, ensure your temperature is in Kelvin by converting \( 25^{\circ} \mathrm{C} \) to \( 298.15 \mathrm{K} \).
• Volume is given as \( 10.0 \mathrm{L} \).
• Use the ideal gas constant \( R = 0.0821 \mathrm{L}\cdot\mathrm{atm}/\mathrm{mol}\cdot\mathrm{K} \).

Substitute these values into the equation and solve for \( P \), the pressure:\[ P = \frac{nRT}{V} = \frac{0.0394 \times 0.0821 \times 298.15}{10.0} \approx 0.096 \text{ atm} \]This formula effectively predicts how gases will behave under various conditions, which is fundamental for many applications in chemistry.

Molar Mass Calculation

Finding the molar mass is essential when converting from grams to moles. Each element has a specific atomic mass, and when combined in a compound, these contribute to the compound’s molar mass. For iron (Fe), we use a molar mass of approximately \( 55.85 \mathrm{g/mol} \).Here’s how to convert mass to moles:

• Identify the given mass of the element. In this case, \( 2.2 \mathrm{g} \) of iron.
• Use the formula: \[ \text{moles of Fe} = \frac{\text{mass of Fe}}{\text{molar mass of Fe}} \]
• Substituting in the values: \[ \text{moles of Fe} = \frac{2.2}{55.85} \approx 0.0394 \text{ moles} \]

Accurate molar mass conversion is vital for stoichiometric calculations in chemical reactions. It bridges the connection between the macroscopic measurements of mass and the microscopic concept of molecules and atoms. This proficiency unlocks the ability to predict and measure the products and reactants in any chemical reaction.