# Find the amount of atoms for a given mass

The atomic mass of two elements A and B is 40 and 80 respectively. If x g of A contains y atoms, how many atoms are present in 2x g of B?

I have tried to solve by assuming that

• x g of A has y atoms
• so x g of B has 2y atoms, because atomic weight of B is 2 times higher than A
• so 2x g of B contains 4 y atoms.

But the answer key says it was wrong, the correct answer is y. What am I doing wrong?

For the elements A and B, the relation between the number of atoms n, the mass m, and the atomic mass M is given by

$$n_A = \frac{m_A}{M_A}\quad,\quad n_B = \frac{m_B}{M_B}$$

Your assignment states: $$m_B = 2\cdot m_A$$ $$M_B = 2\cdot M_A$$

Solve for $n_B$ ;-)

I seriously suggest to practise these calculations a lot. Ask your tutor for more worksheets or find a workbook (with solutions). Solve it alone, or work in groups. No matter how, you have to practise.

If you are in doubt, where to divide and where to multiply, remember: