Finding Atomic Weights from Two Compounds of Two Elements

Chemistry · Some Basic Concepts Of Chemistry · NEET

If two elements form two different compounds, you can find both atomic weights by making two equations. First turn each "moles + grams" fact into a molar mass (molar mass = grams ÷ moles). Then write each molar mass as a sum of atomic weights and solve the two equations together. Memory hook: "Two unknowns need two compounds" - two equations always crack two atomic weights.
Two Compounds of X and Y - Find Atomic WeightsCompound XY20.1 mol weighs 10 gMolar mass = 10 / 0.1 = 100X + 2Y = 100Compound X3Y20.05 mol weighs 9 gMolar mass = 9 / 0.05 = 1803X + 2Y = 180Subtract: 2X = 80 → X = 40 , Y = 30
Turn each compound's "moles + grams" into a molar mass, write it as a sum of atomic weights, then subtract the two equations to get X = 40 and Y = 30.

Your doubts, answered

How do I even start when I am given moles and grams of two compounds?

First find the molar mass of each compound. Molar mass = grams ÷ moles. Example: 0.1 mole of XY2 weighs 10 g, so its molar mass = 10 ÷ 0.1 = 100 g/mol. Do the same for the second compound. Now you have the total mass of each formula unit, which you will break into atomic weights.

How do I turn a molar mass into an equation with X and Y?

Read the formula. XY2 means 1 atom of X and 2 atoms of Y. So molar mass of XY2 = X + 2Y. If that molar mass is 100, your equation is X + 2Y = 100. For X3Y2, molar mass = 3X + 2Y. This is why you need two compounds: each gives one equation, and two equations let you solve for two unknowns X and Y.

How do I solve the two equations to get X and Y?

Use elimination. Take X + 2Y = 100 and 3X + 2Y = 180. Both have 2Y, so subtract the first from the second: (3X + 2Y) - (X + 2Y) = 180 - 100, giving 2X = 80, so X = 40. Put X = 40 back into X + 2Y = 100: 40 + 2Y = 100, so 2Y = 60 and Y = 30. Answer: X = 40, Y = 30.

Why is molar mass equal to atomic weight sum here?

For a compound, the molar mass (in g/mol) is just the sum of the atomic weights of all atoms in one formula unit. So for X3Y2 you add three X atomic weights and two Y atomic weights. There is no extra rule to memorise; you are only adding the masses of the atoms present.

Do the two compounds have to contain the SAME two elements?

Yes. This method works only when both compounds are made of the exact same two elements X and Y. That is what keeps X and Y as the same two unknowns in both equations. If the elements were different, you could not link the two equations together.

What if the numbers do not subtract nicely?

Line up the equations so one variable cancels. If the Y terms are not equal, multiply one full equation by a number to make them equal, then subtract. In NEET questions the numbers are usually chosen so a clean subtraction works, like both having 2Y.

⚠️ The NEET trap
Reading '0.1 mole weighs 10 g' as the atomic weight of X being 10, instead of the molar mass of the whole compound XY2 being 100.
10 g is the mass of 0.1 mole of the COMPOUND XY2. So molar mass = 10 ÷ 0.1 = 100 g/mol, and this 100 = X + 2Y. Never treat the given grams as one atomic weight.
🧠 Grams belong to the whole compound, not to one atom. Convert to molar mass first, then split into atoms.

Real NEET questions

2016

Suppose the elements X and Y combine to form two compounds XY2 and X3Y2. When 0.1 mole of XY2 weighs 10 g and 0.05 mole of X3Y2 weighs 9 g, the atomic weights of X and Y respectively are:

A · 40, 30
B · 60, 40
C · 20, 30
D · 30, 20
Solution: Step 1: Molar mass of XY2 = 10 g ÷ 0.1 mol = 100 g/mol, so X + 2Y = 100. Step 2: Molar mass of X3Y2 = 9 g ÷ 0.05 mol = 180 g/mol, so 3X + 2Y = 180. Step 3: Subtract the first equation from the second: (3X + 2Y) - (X + 2Y) = 180 - 100, giving 2X = 80, so X = 40. Step 4: Put X = 40 into X + 2Y = 100: 40 + 2Y = 100, so 2Y = 60 and Y = 30. Atomic weights are X = 40, Y = 30. Answer: A.

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Frequently asked

What is the quick formula for this type of question?

Molar mass = mass in grams ÷ number of moles. Do this for both compounds, write each molar mass as a sum of atomic weights (like X + 2Y), then solve the two equations together for the two atomic weights.

Why do I need exactly two compounds?

You have two unknown atomic weights (X and Y). To solve for two unknowns you need two independent equations, and each compound gives you one equation. One compound alone is not enough.

Is atomic weight the same as molar mass in this problem?

Atomic weight is for one element; molar mass is for the whole compound. In this method you first get the compound's molar mass from moles and grams, then break it into the elements' atomic weights.

How is this useful for NEET?

NEET often gives 'moles + grams' data for two compounds of the same two elements and asks for atomic weights. It tests moles, molar mass, and simple two-equation solving together, so it is a fast scoring question if you set it up correctly.