Problem 44 - Chemistry Matter and Change

Question

When iron rusts, it undergoes a reaction with oxygen to form iron(III) oxide. $$4 Fe(s)+3 O_{2}(g) \rightarrow 2 Fe_{2} O_{3}(s)$$ Calculate the volume of oxygen gas at STP that is required to completely react with 52.0 g of iron.

Step-by-Step Solution

Answer

The volume of oxygen gas at STP required to completely react with 52.0 g of iron is approximately 15.64 liters.

Step 1: Calculate the moles of iron

First, we need to convert the mass of iron (52.0 g) to moles, using its molar mass. The molar mass of iron (Fe) is 55.85 g/mol. Moles of iron = mass of iron / molar mass of iron Moles of iron = \( \frac{52.0 \; \text{g}}{55.85 \; \text{g/mol}} \)

Step 2: Determine the moles of oxygen needed

Now that we have the moles of iron, we can use the balanced equation to determine the moles of oxygen required. From the balanced equation, 4 moles of Fe react with 3 moles of O2: \( 4 \; \text{Fe} + 3 \; \text{O}_{2} \rightarrow 2 \; \text{Fe}_{2}\text{O}_{3} \) Using stoichiometry, we can write: Moles of O2 = (moles of iron / 4) * 3

Step 3: Calculate the volume of oxygen gas at STP

Finally, we'll find the volume of oxygen gas using the molar volume of a gas at STP (22.4 L/mol): Volume of O2 = moles of O2 * molar volume at STP Volume of O2 = moles of O2 * 22.4 L/mol Note: STP conditions are temperature = 273.15 K (0°C) and pressure = 1 atm.

Step 4: Solve for the volume of oxygen gas

Now, we just need to plug in our calculated values: Moles of iron = \( \frac{52.0 \; \text{g}}{55.85 \; \text{g/mol}} \) Moles of iron = 0.931 mol Moles of O2 = (0.931 mol Fe / 4) * 3 Moles of O2 = 0.698 mol O2 Volume of O2 = 0.698 mol O2 * 22.4 L/mol Volume of O2 = 15.64 L The volume of oxygen gas at STP required to completely react with 52.0 g of iron is approximately 15.64 liters.

Key Concepts

Molar Volume

In chemistry, **molar volume** is a crucial concept when dealing with gases. It refers to the volume occupied by one mole of a gas. Under standard conditions, all gases have the same molar volume. This property simplifies calculations involving gases. The molar volume of any ideal gas at standard temperature and pressure (STP) is 22.4 liters per mole. This means that one mole of any gas occupies 22.4 liters at these conditions.

• Molar volume allows us to convert between moles of a gas and the volume it occupies.
• This conversion is useful when applying stoichiometry to reactions involving gases.

Understanding molar volume helps us predict the behavior of gases in chemical reactions. This is particularly useful when it comes to solving problems like finding the volume of oxygen needed in reactions, such as when iron rusts to form iron(III) oxide.

Iron(III) Oxide

**Iron(III) oxide** is a compound formed when iron reacts with oxygen. It has the chemical formula \( Fe_2O_3 \). It's commonly known as rust and is notable for its reddish-brown color. While it occurs naturally as the mineral hematite, it is usually produced as a result of the corrosion of iron and steel structures.In the balanced chemical equation \( 4 \, Fe(s) + 3 \, O_2(g) \rightarrow 2 \, Fe_2O_3(s) \), iron reacts with oxygen gas to create iron(III) oxide. This equation tells us:

• 4 moles of iron (Fe) react with 3 moles of oxygen (\( O_2 \)).
• This reaction produces 2 moles of iron(III) oxide.

By understanding this equation, we can use stoichiometry to calculate the amounts of reactants and products involved in the reaction. During such reactions under given conditions, combining stoichiometry and molar volumes provides precise measurements, such as determining oxygen gas volume required.

STP Conditions

**STP conditions** are standardized conditions often used in chemistry to compare different sets of data. They standardize temperature and pressure, making calculations easy and consistent. STP stands for Standard Temperature and Pressure and is defined by:

• Temperature: 273.15 Kelvin (or 0°C).
• Pressure: 1 atmosphere (atm).

Under these conditions, gases are assumed to behave ideally, meaning their interactions are consistent with the ideal gas law. This simplifies calculations, particularly when determining the volume of gases produced or consumed in chemical reactions. When performing experiments or solving problems, using STP conditions ensures that results can be directly compared with other data obtained under the same conditions. This is why, in problems like calculating the oxygen volume for a reaction with iron, STP is used. It provides a baseline for comparing experiments and understanding the behavior of gases involved.