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 \(10.0-\mathrm{L}\). 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 \( \mathrm{H}_{2} \) gas is approximately \( 0.0965 \) atm.

Step 1: Write the balanced chemical equation

The provided equation \( \mathrm{Fe(s)} + 2 \mathrm{HCl(aq)} \rightarrow \mathrm{FeCl}_{2}(\mathrm{aq}) + \mathrm{H}_{2}(\mathrm{g}) \) is already balanced. Each type of atom on the reactant side equals the number of atoms on the product side.

Step 2: Calculate the moles of iron

The molar mass of iron \( (\mathrm{Fe}) \) is approximately 55.85 g/mol. Convert the mass of iron to moles using the formula:\[ \text{moles of Fe} = \frac{\text{mass of Fe}}{\text{molar mass of Fe}} = \frac{2.2 \text{ g}}{55.85 \text{ g/mol}} \approx 0.0394 \text{ mol} \]

Step 3: Mole ratio and moles of hydrogen gas

From the balanced equation, the mole ratio of \( \mathrm{Fe} \) to \( \mathrm{H}_{2} \) is 1:1. So, the moles of \( \mathrm{H}_{2} \) gas produced will be the same as the moles of \( \mathrm{Fe} \) reacted:\[ \text{moles of } \mathrm{H}_2 = 0.0394 \, \text{mol} \]

Step 4: Use the Ideal Gas Law to find pressure

The Ideal Gas Law is \( PV = nRT \). Solve for \( P \), the pressure:- \( n = 0.0394 \text{ mol} \) (moles of \( \mathrm{H}_{2} \) gas)- \( R = 0.0821 \, \text{L atm/mol K} \) (ideal gas constant)- \( T = 25^{\circ} \text{C} = 298 \, \text{K} \)- \( V = 10.0 \text{ L} \)Plug the values into the equation:\[ P = \frac{(0.0394 \text{ mol})(0.0821 \text{ L atm/mol K})(298 \text{ K})}{10.0 \text{ L}} \approx 0.0965 \text{ atm} \]

Key Concepts

Chemical Reactions

Chemical reactions involve the transformation of substances through the breaking and formation of chemical bonds, resulting in the formation of new products. In the given exercise, iron (Fe) reacts with hydrochloric acid (HCl) to yield iron(II) chloride and hydrogen gas.
This specific reaction is a typical example of a single displacement or replacement reaction, where a more reactive metal displaces a less reactive one from a compound. Important features of a chemical reaction include:

• Reactants and products: The starting materials (reactants) change into new substances (products).
• Balanced equations: The number of atoms for each element must be the same on both sides of the reaction equation.
• Conservation of mass: No atoms are lost or gained, and the same total mass exists before and after the reaction.

The balanced chemical equation provided already satisfies the law of conservation of mass. Each element has an equal number of atoms on both sides of the equation, indicating that mass is conserved during the transformation.

Stoichiometry

Stoichiometry is the quantitative relationship that exists between reactants and products in a chemical reaction. It allows chemists to predict the amounts of substances consumed and produced in a given reaction.
In this exercise, stoichiometry was used to determine the moles of hydrogen gas ( \( \text{H}_2 \) ) produced from a known mass of iron. Important aspects of stoichiometry include:

• Mole ratio: Derived from the coefficients of the balanced equation, indicating the proportion of moles for each substance.
• Conversion between mass and moles: Using the formula \( \text{moles} = \frac{\text{mass}}{\text{molar mass}} \), you can convert grams to moles or vice versa.
• Calculations of quantities: Determine the number of moles or grams of products formed from given amounts of reactants using mole ratios.

In our step-by-step solution, a 1:1 mole ratio between iron and hydrogen gas is identified, reflecting that equal moles of both are present after the reaction.

Mole Concept

The mole is a fundamental unit in chemistry representing the amount of substance. One mole contains exactly \(6.022\times 10^{23} \) entities (Avogadro's number), which can be atoms, molecules, or formula units, depending on the context.
Understanding the mole concept is essential for converting between the mass of a substance and the amount of substance in terms of moles. In this exercise, we used the molar mass of iron to find how many moles were involved and consequently, how many moles of hydrogen were produced.
Key points about the mole concept include:

• Molar mass: The mass of one mole of a substance, typically expressed in grams per mole (g/mol), is used for conversions between mass and moles.
• Avogadro's number: Allows conversion between the number of atoms/molecules and moles.
• Practical applications: Enables precise calculation and prediction of product yields in reactions.

The use of the mole concept in chemical calculations simplifies complex reactions and provides a clear understanding of how different quantities of reactants relate to each other.