Understanding the Problem
We have two elements, A and B, with given weights and quantities of their atoms. We will determine the atomic weight of element A based on the information provided.
Given Data
- n atoms of element A weigh 15 g
- 4n atoms of element B (atomic weight = 30 u) weigh 45 g
Calculating Atomic Weight of B
- To find the number of moles of B:
- Moles of B = Mass / Molar mass = 45 g / 30 g/mol = 1.5 moles
- Since 4n atoms correspond to 1.5 moles:
- 4n = 1.5 * Avogadro's number (6.022 x 10^23 atoms/mol)
- n = (1.5 * 6.022 x 10^23) / 4 = 2.26 x 10^23 atoms
Finding Atomic Weight of A
- We know n atoms of A weigh 15 g:
- Weight of 1 atom of A = Total weight / Number of atoms = 15 g / n
- Calculate the number of moles of A:
- Moles of A = n / Avogadro's number
- The molar mass (atomic weight) of A can be calculated:
- Atomic weight of A = Mass / Moles = 15 g / (n / 6.022 x 10^23)
Substituting for n
- We previously calculated n = 2.26 x 10^23 atoms
- Thus, substituting into the equation:
- Atomic weight of A = 15 g / (2.26 x 10^23 / 6.022 x 10^23)
- Atomic weight of A = 15 g * (6.022 x 10^23 / 2.26 x 10^23)
Final Calculation
- The atomic weight of A is approximately 4u.
Through these calculations, we determine that the atomic weight of element A is around 4 u.