An unidentified compound contains
29.84 g sodium, 67.49 g
chromium, and 72.67 g oxygen. Find the empirical and molecular formula if the molecular mass is 1047.84.
To find the empirical formula, first calculate the moles of each element present in the compound:
1. Convert the grams of each element to moles:
- Sodium (Na): 29.84 g / 22.99 g/mol = 1.3 mol
- Chromium (Cr): 67.49 g / 51.996 g/mol = 1.3 mol
- Oxygen (O): 72.67 g / 16.00 g/mol = 4.5 mol
2. Divide each of the mole values by the smallest mole value to get whole number ratios:
- Na: 1.3 / 1.3 = 1
- Cr: 1.3 / 1.3 = 1
- O: 4.5 / 1.3 = 3.5 (approx.)
The empirical formula is NaCrO3 (rounding the 3.5 to 3).
To find the molecular formula, we need to determine the molecular mass of the empirical formula we found:
NaCrO3: 22.99 g/mol (Na) + 51.996 g/mol (Cr) + 16.00 g/mol (O) * 3 = 137.98 g/mol
Next, calculate the ratio of the molecular mass given to the empirical formula mass:
1047.84 g/mol (molecular mass) / 137.98 g/mol (empirical formula mass) = 7.6 (approx.)
Finally, multiply the subscripts in the empirical formula by the ratio to get the molecular formula:
NaCrO3 * 7.6 ≈ Na7Cr7O22
Therefore, the empirical formula is NaCrO3 and the molecular formula is Na7Cr7O22.