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Stoichiometry 30: What is the mass of metal X required to produce 0.42 moles of X₂O₃?
Introduction
Stoichiometry gives you the power to connect what you want to make with the raw materials you need to start.
In this particular problem, you know the number of moles of X₂O₃ you want to produce.
From there, your job is to work backward and figure out how much of the metal X is required to make it happen.
Ultimately, this is a core skill for laboratory science, chemical manufacturing, and even exam success.
Let’s walk through every step so you can solve similar problems with total confidence.
Step 1: Start with what you’re given
You are told you want to produce 0.42 moles of X₂O₃.
There is no information about the atomic mass of X yet, so you will use a variable, M, for now.
Your goal is to find the mass of metal X needed for this reaction.
Step 2: Use the mole ratio from the chemical formula
The chemical formula X₂O₃ tells you a lot.
It means that for every 1 mole of X₂O₃ formed, you need 2 moles of metal X.
This 2:1 ratio is vital.
This further tells you that for every unit of product, you need twice as many units of the metal.
Never skip this step, or you’ll end up with the wrong answer.
Step 3: Calculate moles of X required
Since you are making 0.42 moles of X₂O₃, and you need 2 moles of X for every 1 mole of X₂O₃, just multiply.
Moles of X needed = 0.42 × 2 = 0.84 moles of metal X.
This is the exact amount of metal atoms that must react to yield your target product.
Step 4: Find the mass of X required
Now you have the number of moles of X.
To find the mass, use the atomic mass variable M.
Mass = moles × atomic mass
Mass = 0.84 × M
This gives your answer in terms of M.
If you know the value of M, substitute it to get the numerical mass in grams.
Step 5: Why are we using the atomic mass of X, not X₂O₃?
This is a key point.
Many students mistakenly try to use the molar mass of X₂O₃ or the mass of oxygen.
But you are being asked for the starting metal.
So you use only the moles of X and its atomic mass.
This keeps your answer logical and chemically correct.
Step 6: Watch out for common mistakes
Sometimes, people mix up the 2:1 ratio and accidentally divide instead of multiplying.
If you divided instead, you’d get a number that makes no chemical sense.
Be sure to keep your ratios aligned with the chemical formula.
Another common error is forgetting to multiply by the atomic mass at the end, leaving the answer in moles instead of grams.
Details matter.
Step 7: How does this apply to real chemistry?
Knowing how much raw material you need is essential in every chemistry lab.
Industrial chemists use these calculations to order the right amount of metal, keep costs down, and avoid waste.
If a company is making tons of a metal oxide, being off by even a few grams per batch can cost thousands of dollars over time.
In research, getting the stoichiometry right can be the difference between a breakthrough and a failed experiment.
Step 8: Using a real metal for X
Suppose X is aluminum.
The atomic mass of aluminum is 27 grams per mole.
Plug it in.
Mass of Al needed = 0.84 × 27 = 22.68 grams
So you would need 22.68 grams of aluminum to produce 0.42 moles of Al₂O₃.
Additionally, the process is the same for iron, magnesium, or any other metal.
Just use the right atomic mass.
Step 9: Connect each step for confidence
First, you start with the moles of product you want.
Then you use the ratio in the formula to get moles of metal needed.
Finally, you multiply by the atomic mass to convert moles to grams.
These three moves will help you solve almost any stoichiometry problem involving mass and moles.
Step 10: Practice the logic to get faster
Chemistry exams and real-life projects are all about accuracy and speed.
Therefore, the more you break down these problems, the quicker and more automatic the process becomes.
If you make a mistake, trace it back through the steps and correct your ratio or your units.
Moreover, every correct answer adds to your confidence and skill.
Final Wrap-Up
When you are asked how much metal X is required to make 0.42 moles of X₂O₃, you always start with the product.
You use the 2:1 ratio from the formula.
Multiply 0.42 by 2 to get 0.84 moles of metal X.
To get the mass, multiply by the atomic mass M.
Your answer is 0.84 × M grams.
If X is aluminum, your mass is 22.68 grams.
Every part of this calculation relies on careful attention to the chemical formula and the precise use of ratios and units.
In fact, this is what stoichiometry is all about — connecting your target to your starting materials, one logical step at a time.
So, are you ready to become a stoichiometry expert?
To get there, practice more questions and review guided solutions on our page or visit our YouTube channel.
With every problem you solve, your chemistry skills grow and your confidence builds — both for exams and real-world success.
