Chapter 5: Problem 195
What is the maximum weight of \(\mathrm{SO}_{3}\) that could be made from \(25.0 \mathrm{~g}\) of \(\mathrm{SO}_{2}\) and \(6.00 \mathrm{~g}\) of \(\mathrm{O}_{2} \mathrm{by}\) the following reaction? \(2 \mathrm{SO}_{2}+\mathrm{O}_{2} \rightarrow 2 \mathrm{SO}_{3}\)
Short Answer
Expert verified
The maximum weight of ³§°¿â‚ƒ that could be produced from the given amounts of ³§°¿â‚‚ and °¿â‚‚ is approximately \(30.1 \mathrm{g}\).
Step by step solution
01
Calculate the molar mass of ³§°¿â‚‚ and °¿â‚‚
To begin, we need to calculate the molar mass of ³§°¿â‚‚ and °¿â‚‚. The molar mass is found by adding the molar masses of each element in the molecule.
The molar mass of Sulfur (S) is 32.07 g/mol, and the molar mass of Oxygen (O) is 16.00 g/mol.
For ³§°¿â‚‚: Molar mass = (1 × 32.07 g/mol) + (2 × 16.00 g/mol) = 64.07 g/mol.
For °¿â‚‚: Molar mass = (2 × 16.00 g/mol) = 32.00 g/mol
02
Convert grams to moles
Next, we convert the initial masses of ³§°¿â‚‚ and °¿â‚‚ into moles using the molar mass of each substance.
For ³§°¿â‚‚: Moles = Mass/Molar mass = 25.0 g / 64.07 g/mol ≈ 0.390 moles
For °¿â‚‚: Moles = Mass/Molar mass = 6.00 g / 32.00 g/mol ≈ 0.188 moles
03
Determine the limiting reactant
To determine the limiting reactant, we need to compare the mole ratios of the reactants available with the mole ratios in the balanced equation.
From the balanced equation, we have a mole ratio of 2 moles of ³§°¿â‚‚ to 1 mole of °¿â‚‚. Let's divide the available moles of each substance by their respective coefficients in the balanced equation.
³§°¿â‚‚: 0.390 moles / 2 = 0.195
°¿â‚‚: 0.188 moles / 1 = 0.188
The reactant with the smallest ratio is the limiting reactant, which in this case is °¿â‚‚.
04
Calculate the maximum moles of ³§°¿â‚ƒ that can be produced
Now that we've identified the limiting reactant (°¿â‚‚), we can determine the maximum moles of ³§°¿â‚ƒ that can be produced.
Using the stoichiometry from the balanced equation, we have a mole ratio of 1 mole of °¿â‚‚ to 2 moles of ³§°¿â‚ƒ. Since we have 0.188 moles of °¿â‚‚, we can produce:
³§°¿â‚ƒ: 2 moles of ³§°¿â‚ƒ / 1 mole of °¿â‚‚ × 0.188 moles of °¿â‚‚ = 0.376 moles of ³§°¿â‚ƒ
05
Convert moles of ³§°¿â‚ƒ to grams
Finally, we will convert the moles of ³§°¿â‚ƒ back into grams using the molar mass of ³§°¿â‚ƒ.
The molar mass of ³§°¿â‚ƒ is (1 × 32.07 g/mol) + (3 × 16.00 g/mol) = 80.07 g/mol.
Maximum weight of ³§°¿â‚ƒ = Moles × Molar mass = 0.376 moles × 80.07 g/mol ≈ 30.1 g
The maximum weight of ³§°¿â‚ƒ that could be produced from the given amounts of ³§°¿â‚‚ and °¿â‚‚ is approximately 30.1 grams.
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Limiting Reactant
When you bake a cake, you need a specific amount of each ingredient. If you run out of eggs, you can't make more cake, even if you have plenty of flour and sugar left. That's how a limiting reactant works in chemistry.
In a chemical reaction, the limiting reactant is the substance that gets used up first and thereby determines how much product can be formed. Identifying this reactant is crucial because it dictates the amount of product that will be produced based on the reactant's quantity that is present in the least amount compared to the required stoichiometric amount.
In our exercise, by calculating and comparing the mole ratios of ³§°¿â‚‚ and °¿â‚‚, it was determined that °¿â‚‚ is the limiting reactant because it has the smallest mole ratio when divided by its coefficient in the balanced chemical equation. Knowing this allows us to predict that all of the oxygen will be used up, while some sulfur dioxide will remain unreacted.
In a chemical reaction, the limiting reactant is the substance that gets used up first and thereby determines how much product can be formed. Identifying this reactant is crucial because it dictates the amount of product that will be produced based on the reactant's quantity that is present in the least amount compared to the required stoichiometric amount.
In our exercise, by calculating and comparing the mole ratios of ³§°¿â‚‚ and °¿â‚‚, it was determined that °¿â‚‚ is the limiting reactant because it has the smallest mole ratio when divided by its coefficient in the balanced chemical equation. Knowing this allows us to predict that all of the oxygen will be used up, while some sulfur dioxide will remain unreacted.
Molar Mass
In cooking, recipes use cups and tablespoons to measure ingredients. In chemistry, we use units called moles, which can be a bit harder to visualize because a mole refers to how many molecules you have. That's where the idea of molar mass comes in—it's like the 'weight' of these molecules.
Every substance has a unique molar mass, which is the mass of one mole of that substance. Its unit is grams per mole (g/mol). To figure out the molar mass, we add together the atomic masses of all the atoms in a molecule, as was done for ³§°¿â‚‚ and °¿â‚‚ in the solution. Molar mass allows us to convert between the weight of a substance (in grams) and the amount of substance (in moles), which is a central step in solving stoichiometry problems.
Every substance has a unique molar mass, which is the mass of one mole of that substance. Its unit is grams per mole (g/mol). To figure out the molar mass, we add together the atomic masses of all the atoms in a molecule, as was done for ³§°¿â‚‚ and °¿â‚‚ in the solution. Molar mass allows us to convert between the weight of a substance (in grams) and the amount of substance (in moles), which is a central step in solving stoichiometry problems.
Mole-to-Mole Ratio
To turn a recipe's ingredients into a delicious dish, you need the right proportions. The same goes for chemical reactions, and that's where the mole-to-mole ratio fits in. This ratio comes from the balanced chemical equation and tells us how much of each reactant is needed to create the products.
For our exercise, the balanced chemical equation gave us a 2:1 mole-to-mole ratio between ³§°¿â‚‚ and °¿â‚‚. After finding the limiting reactant, we used this ratio to figure out that for every 1 mole of °¿â‚‚ consumed, 2 moles of ³§°¿â‚ƒ are produced. Understanding these ratios is crucial because they are the blueprint that dictates the potential quantity of each substance involved in the reaction. They help us predict exactly how much of each reactant is needed and how much of each product will be formed.
For our exercise, the balanced chemical equation gave us a 2:1 mole-to-mole ratio between ³§°¿â‚‚ and °¿â‚‚. After finding the limiting reactant, we used this ratio to figure out that for every 1 mole of °¿â‚‚ consumed, 2 moles of ³§°¿â‚ƒ are produced. Understanding these ratios is crucial because they are the blueprint that dictates the potential quantity of each substance involved in the reaction. They help us predict exactly how much of each reactant is needed and how much of each product will be formed.