Chapter 7: Problem 55
Iron(III) oxide reacts with carbon monoxide according to the equation: Fe2O3(s) + 3 CO(g)-2 Fe(s) + 3 CO2(g) A reaction mixture initially contains 22.55 g Fe2O3 and 14.78 g CO. Once the reaction has occurred as completely as possible, what mass (in g) of the excess reactant remains?
Short Answer
Expert verified
After the reaction, 2.915 g of carbon monoxide remains unreacted.
Step by step solution
01
Calculate the molar mass of Fe2O3 and CO
Use the periodic table to find the atomic masses of iron (Fe), oxygen (O), and carbon (C) to calculate the molar masses. For Fe2O3, the molar mass is (2 * 55.85) + (3 * 16.00) = 159.7 g/mol. For CO, the molar mass is (12.01) + (16.00) = 28.01 g/mol.
02
Convert the mass of reactants to moles
Divide the initial masses of Fe2O3 and CO by their respective molar masses to find the number of moles of each reactant. Moles of Fe2O3 = 22.55 g / 159.7 g/mol = 0.1412 mol. Moles of CO = 14.78 g / 28.01 g/mol = 0.5277 mol.
03
Determine the limiting reactant
Use the balanced chemical equation to find the stoichiometric ratios. According to the equation, 1 mole of Fe2O3 reacts with 3 moles of CO. Compare the mole ratio of the reactants to the stoichiometry. For every 0.1412 mol of Fe2O3, you need 0.1412 * 3 = 0.4236 mol of CO. Since there are 0.5277 mol of CO available, CO is in excess, and Fe2O3 is the limiting reactant.
04
Calculate the moles of excess reactant consumed
According to the stoichiometry, 3 moles of CO are needed for every mole of Fe2O3. Thus, 0.1412 mol of Fe2O3 would consume 0.1412 * 3 = 0.4236 mol of CO.
05
Calculate the moles of excess reactant remaining
Subtract the moles of CO consumed from the initial moles to find the amount remaining. Remaining moles of CO = 0.5277 mol - 0.4236 mol = 0.1041 mol.
06
Convert the remaining moles of CO to mass
Multiply the moles of CO remaining by the molar mass of CO to find the mass in grams. Mass of excess CO = 0.1041 mol * 28.01 g/mol = 2.915 g.
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Stoichiometry
Understanding stoichiometry is like having a magical cookbook for chemistry—instead of recipes for cookies, you've got instructions for making new substances from chemical reactions. In chemistry, stoichiometry refers to the relationship between the quantities of reactants and products in a chemical reaction. It's based on the law of conservation of mass, which says that matter is neither created nor destroyed in a reaction. What this means is that the number of atoms of each element must be the same in the reactants and products.
For a stoichiometry calculation, you’ll first need a balanced chemical reaction equation. From this, you can determine the mole ratio of the reactants and products. In the case of our iron(III) oxide and carbon monoxide reaction example, for every 1 mole of Fe2O3, 3 moles of CO are required to produce Iron and Carbon dioxide. With this mole ratio, you can actually figure out how much of each reactant you need to completely use up another reactant and how much of each product will form. It all comes down to the power of ratio and proportions—just like doubling or halving your favorite recipe!
For a stoichiometry calculation, you’ll first need a balanced chemical reaction equation. From this, you can determine the mole ratio of the reactants and products. In the case of our iron(III) oxide and carbon monoxide reaction example, for every 1 mole of Fe2O3, 3 moles of CO are required to produce Iron and Carbon dioxide. With this mole ratio, you can actually figure out how much of each reactant you need to completely use up another reactant and how much of each product will form. It all comes down to the power of ratio and proportions—just like doubling or halving your favorite recipe!
Molar Mass
Have you ever wondered how chemists measure out atoms when they're too tiny to see? They use the concept of molar mass! Molar mass is sort of like the gram weight of one mole of a chemical, and one mole is Avogadro's number (\(6.022 \times 10^{23}\)) worth of something. You can find molar mass by adding up the atomic masses (from the periodic table) of all the atoms in a chemical formula.
For example, in our problem, iron(III) oxide (Fe2O3) has a molar mass calculated by adding twice the atomic mass of iron with three times the atomic mass of oxygen. Knowing the molar mass of the reactants is crucial because it allows us to convert mass in grams (something we can measure) to moles (which is used in stoichiometry calculations). It’s like knowing how many ounces are in a pound when you’re cooking—necessary for getting your quantities right!
For example, in our problem, iron(III) oxide (Fe2O3) has a molar mass calculated by adding twice the atomic mass of iron with three times the atomic mass of oxygen. Knowing the molar mass of the reactants is crucial because it allows us to convert mass in grams (something we can measure) to moles (which is used in stoichiometry calculations). It’s like knowing how many ounces are in a pound when you’re cooking—necessary for getting your quantities right!
Chemical Reaction Equation
A chemical reaction equation is like a detailed script for a molecular-level play. It tells us which molecules are the actors (the reactants), what changes they go through (the reaction), and who leaves the stage transformed (the products). But it's not enough to just list these players; their amounts have to be balanced, just like ensuring there's enough seating for every guest at a dinner party.
The equation for our reaction, iron(III) oxide with carbon monoxide, tells a clear story once balanced: one molecule of Fe2O3 reacts with three molecules of CO to produce iron and three molecules of CO2. It shows that reactions follow specific ratios, which is incredibly important when figuring out how much of each reactant we need and how much of each product we'll get. It’s the blueprint for all stoichiometry calculations and helps predict the outcome of the chemical reaction.
The equation for our reaction, iron(III) oxide with carbon monoxide, tells a clear story once balanced: one molecule of Fe2O3 reacts with three molecules of CO to produce iron and three molecules of CO2. It shows that reactions follow specific ratios, which is incredibly important when figuring out how much of each reactant we need and how much of each product we'll get. It’s the blueprint for all stoichiometry calculations and helps predict the outcome of the chemical reaction.
Excess Reactant
In any good party, it's better to have too much food than not enough—same goes for reactants in a chemical reaction. The reactant that isn’t completely used up is known as the excess reactant. Our chemical reaction can only progress as long as both reactants are present. When one of them runs out, the reaction stops, regardless of how much of the other is left over. That leftover is the excess reactant.
Identifying the limiting reactant (the one that runs out first) and excess reactant tells us a lot about the reaction’s efficiency and allows us to calculate the quantity of leftover reactants. In our scenario, after the limiting reactant (Fe2O3) is used up, there’s still some carbon monoxide left—that's our excess reactant. By knowing this, we can calculate how much CO is left after the reaction is completed, which in practical applications can help manage resources and costs effectively.
Identifying the limiting reactant (the one that runs out first) and excess reactant tells us a lot about the reaction’s efficiency and allows us to calculate the quantity of leftover reactants. In our scenario, after the limiting reactant (Fe2O3) is used up, there’s still some carbon monoxide left—that's our excess reactant. By knowing this, we can calculate how much CO is left after the reaction is completed, which in practical applications can help manage resources and costs effectively.