Two elements A and B which form 0.15 moles of A₂B and AB₃ type compounds. If both A₂B and AB₃ weigh equally, then the atomic weight of A is _____________ times of atomic weight of B.

Solution

Chemistry ma’am · 3 steps

Same number of moles and same mass means the two molar masses must be equal. Set them equal.

1. Equal moles, equal mass. Mass = moles × molar mass. Both compounds are 0.15 mol and weigh the same, so their molar masses are equal. The 0.15 cancels out.
2. Write molar masses. Let the atomic weights be a for A and b for B. Then A₂B has molar mass 2a + b and AB₃ has molar mass a + 3b.

   0.15 (2a + b) = 0.15 (a + 3b) ⇒ 2a + b = a + 3b

3. So. Rearranging gives a = 2b. The atomic weight of A is 2 times that of B.

The common slip: 0.5. Solving for b/a instead of a/b gives 0.5. The question asks how many times B the atomic weight of A is, so you need a/b.

The idea to keep. When two samples have the same number of moles, equal mass means equal molar mass. The mole count drops out, so do not let it distract you.

Answer from the NTA final answer key. Solution by PrepWiser.