Question

The reaction between potassium chlorate and red phosphorus takes place when you strike a match on a matchbox. If you were to react \(52.9 \mathrm{g}\) of potassium chlorate \(\left(\mathrm{KClO}_{3}\right)\) with excess red phosphorus, what mass of tetraphosphorus decaoxide \(\left(\mathbf{P}_{4} \mathbf{O}_{10}\right)\) could be produced? $$\mathrm{KClO}_{3}(s)+\mathrm{P}_{4}(s) \longrightarrow \mathrm{P}_{4} \mathrm{O}_{10}(s)+\mathrm{KCl}(s) \quad \text { (unbalanced) }$$

Short answer

40.87 grams of tetraphosphorus decaoxide (P4O10) could be produced in this reaction.

Step-by-step solution

Balance the chemical equation

Balance the given chemical equation: 3KClO3 (s) + 2P4 (s) ⟶ P4O10 (s) + 3KCl (s) We now have a balanced equation.

Convert mass of potassium chlorate to moles

To convert the mass of potassium chlorate to moles, use its molar mass: Molar mass of KClO3 = 39.10 (K) + 35.45 (Cl) + 3 × 16.00 (O) = 122.55 g/mol 52.9 g KClO3 × (1 mol KClO3 / 122.55 g/mol) = 0.4318 mol KClO3

Determine the stoichiometry between KClO3 and P4O10

According to our balanced equation, 3 moles of KClO3 react with 2 moles of P4 to produce 1 mole of P4O10: 3 mol KClO3 ⟶ 1 mol P4O10 Now we can find the moles of P4O10 produced by converting the moles of KClO3, based on the stoichiometry: 0.4318 mol KClO3 × (1 mol P4O10 / 3 mol KClO3) = 0.1439 mol P4O10

Convert moles of P4O10 to mass

To convert the moles of P4O10 to mass, use its molar mass: Molar mass of P4O10 = 4 × 30.97 (P) + 10 × 16.00 (O) = 283.88 g/mol 0.1439 mol P4O10 × (283.88 g/mol) = 40.87 g P4O10 Therefore, 40.87 grams of tetraphosphorus decaoxide (P4O10) could be produced in this reaction.

Key concepts

Chemical Equation Balancing

To comprehend the essence of chemical reactions, one must first become proficient in balancing chemical equations. This crucial step ensures that the law of conservation of mass is upheld, meaning the quantity of each element remains constant through the reaction.

Imagine each element as an actor in a play, and each equation as the script outlining their roles. To balance a reaction, like the one with potassium chlorate and phosphorus, we start by tallying each element on both sides of the equation. Adjust coefficients—essentially, how many 'copies' of each compound participate—to ensure an equal number of each type of 'actor' appears on both the stage's halves.

Why is this pertinent? Without a balanced equation, predictions about the products, like tetraphosphorus decaoxide in our exercise, are rendered meaningless. It's like trying to ensure every actor has a role to return to after intermission without a proper script; the play would be chaos. Balancing equations is the first step to predicting the outcomes of a chemical reaction.

Mole Concept

The mole concept is the bridge connecting the microscopic world of atoms to the tangible quantities we can measure. A mole is defined as a collection of exactly 6.022 x 10^23 particles, be they atoms, molecules, or ions—the Avogadro's number.

This is akin to a dozen eggs representing a count of 12; a mole represents a far larger 'dozen' for particles. In our reaction, we measured potassium chlorate not in individual molecules, but in moles. By converting the 52.9 grams into moles, we linked the mass of a substance to an amount we can use in chemical equations.

Understanding the mole concept allows us to transition from the mass of a substance to the number of particles involved, and, crucially, to relate this to the stoichiometry of the reaction, predicting the quantity of products formed from given reactants.

Molar Mass

Molar mass is the weight of one mole of a substance, acting as a gateway between the mass of a sample and the number of moles present. It is measured in grams per mole (g/mol).

Consider molar mass a special 'conversion factor' that lets us switch from the macroscopic world of grams to the microscopic vista of moles. Every substance has a characteristic molar mass, which is the sum of the atomic masses of all the atoms in its molecular formula. For the problem at hand, we calculated the molar mass of both potassium chlorate and tetraphosphorus decaoxide to find out how many moles of each substance we were dealing with.

By using the concept of molar mass, we navigated from the mass given for a reactant to the mass of the product. It's the intricacy in understanding that allows us to not only make predictions about the outcomes of reactions but also to understand how much of each substance will be involved.