Stoichiometry 27: What mass of X₂O₃ is formed when 0.83 moles of metal X reacts with oxygen?

Introduction

Stoichiometry is all about connecting the dots between reactants and products. Consequently, if you know how many moles of a metal react, you can find out exactly how much product will be created. In this example, your goal is to find the mass of X₂O₃ formed when 0.83 moles of metal X completely reacts with oxygen.

Without further ado, let’s turn this mole value into grams by following a step-by-step process.

Step 1: Understand the chemical formula

The formula for the product is X₂O₃.

This means every two atoms of metal X react with three atoms of oxygen to form one formula unit of X₂O₃.

The mole ratio from the formula is 2 moles of X produce 1 mole of X₂O₃.

This is your key to solving the problem.

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Step 2: Find moles of X₂O₃ produced

You are given 0.83 moles of metal X.

Set up the ratio:

Number of moles of X₂O₃ = 0.83 moles X × (1 mole X₂O₃ / 2 moles X)

Calculate the value:

0.83 ÷ 2 = 0.415 moles of X₂O₃

This means you will form 0.415 moles of X₂O₃.

Step 3: Determine the molar mass of X₂O₃

To get the mass, you need the molar mass of X₂O₃.

Alternatively, if you do not know the atomic mass of metal X, use a variable and let the atomic mass of X be M.

So:

Molar mass of X₂O₃ = (2 × M) + (3 × 16)

Sixteen is the atomic mass of oxygen.

The total mass becomes (2M + 48) grams per mole.

Step 4: Calculate the mass of X₂O₃ formed

Now multiply the moles by the molar mass:

Mass of X₂O₃ = 0.415 × (2M + 48) grams

This gives the answer in terms of the atomic mass M.

Otherwise, if you know M, substitute its value to get a specific number.

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Step 5: Why the ratios matter

You always solve stoichiometry problems like this using the mole ratio from the balanced chemical formula.

However, if you forget to use the correct ratio, you will get the wrong answer or find yourself stuck.

Using the right ratio helps you follow the chemical equation and ensures your answer makes sense.

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Step 6: Mistakes to avoid

A common mistake is to multiply the number of moles of metal X by the total molar mass of X₂O₃, skipping the ratio step.

You form only 0.415 moles of X₂O₃, not 0.83.

Similarly, another mistake is to use the atomic mass of O₂ (32 g/mol) instead of using individual oxygen atoms (16 g/mol).

Careful attention to these details makes a difference.

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Step 7: Real-world perspective

Metal oxides like X₂O₃ have many uses.

Manufacturers use them in ceramics, pigments, catalysts, and electronic materials.

Predicting product mass helps chemists and engineers design better processes, estimate costs, and ensure safety.

Every calculation counts, from research labs to industrial factories.

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Final Wrap-Up

To wrap it up, when 0.83 moles of metal X react fully with oxygen to form X₂O₃, you use the formula’s ratio to find the answer.

First, you convert moles of X to moles of X₂O₃.

You get 0.415 moles of X₂O₃.

Next, you multiply by the molar mass: mass = 0.415 × (2M + 48) grams.

This simple chain of steps helps you connect the number of atoms to the real mass you’d measure in the lab.

Every accurate answer builds your confidence and skills in stoichiometry.

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