A metal M forms a metal carbonate M2CO3. If the carbonate contains 48% oxygen by mass, then determine the atomic weight of the metal.
The Correct Answer and Explanation is:
To find the atomic weight of the metal MMM in the metal carbonate M2CO3M_2CO_3M2CO3, we can use the information about the percentage of oxygen in the compound and apply the concept of mass balance.
Step 1: Write the molecular formula
We are given that the metal carbonate is M2CO3M_2CO_3M2CO3, meaning it contains 2 atoms of the metal MMM, 1 atom of carbon, and 3 atoms of oxygen.
Step 2: Calculate the molar mass of M2CO3M_2CO_3M2CO3
To calculate the molar mass of M2CO3M_2CO_3M2CO3, we need to sum the molar masses of each component:
- The molar mass of oxygen (OOO) is 16 g/mol.
- The molar mass of carbon (CCC) is 12 g/mol.
So, the mass of the oxygen atoms in M2CO3M_2CO_3M2CO3 is: Mass of oxygen=3×16=48 g/mol\text{Mass of oxygen} = 3 \times 16 = 48 \, \text{g/mol}Mass of oxygen=3×16=48g/mol
Now, let the atomic mass of the metal MMM be xxx g/mol. The total mass of 2 atoms of MMM is: Mass of metal=2x g/mol\text{Mass of metal} = 2x \, \text{g/mol}Mass of metal=2xg/mol
Thus, the total molar mass of M2CO3M_2CO_3M2CO3 is: Total molar mass=2x+12+48=2x+60 g/mol\text{Total molar mass} = 2x + 12 + 48 = 2x + 60 \, \text{g/mol}Total molar mass=2x+12+48=2x+60g/mol
Step 3: Use the mass percent of oxygen
We are told that oxygen makes up 48% by mass of M2CO3M_2CO_3M2CO3. This means that the mass of oxygen in the compound, which is 48 g/mol, accounts for 48% of the total molar mass of M2CO3M_2CO_3M2CO3.
Thus, we can set up the equation: Mass of oxygenTotal molar mass=482x+60=0.48\frac{\text{Mass of oxygen}}{\text{Total molar mass}} = \frac{48}{2x + 60} = 0.48Total molar massMass of oxygen=2x+6048=0.48
Step 4: Solve for xxx
Now, solve for xxx: 48=0.48×(2x+60)48 = 0.48 \times (2x + 60)48=0.48×(2x+60) 48=0.48×2x+0.48×6048 = 0.48 \times 2x + 0.48 \times 6048=0.48×2x+0.48×60 48=0.96x+28.848 = 0.96x + 28.848=0.96x+28.8 48−28.8=0.96×48 – 28.8 = 0.96×48−28.8=0.96x 19.2=0.96×19.2 = 0.96×19.2=0.96x x=19.20.96=20x = \frac{19.2}{0.96} = 20x=0.9619.2=20
Step 5: Conclusion
The atomic weight of the metal MMM is 20 g/mol20 \, \text{g/mol}20g/mol.
So, the metal MMM is calcium (Ca), as its atomic weight is 20 g/mol.
