HOW TO SOLVE THIS PROBLEM ACCODING TO THE THEME

The mass of the metal oxide is the sum of the mass of the metal and the mass of the oxygen that reacted.

$$\text{Mass of oxygen} = \text{Mass of } \ce{M2O3} - \text{Mass of M}$$ $$\text{Mass of oxygen} = 1.89\ \text{g} - 1.00\ \text{g} = 0.89\ \text{g}$$

Using the molar mass of oxygen (O) as 16.00 g/mol.

$$\text{Moles of O atoms} = \frac{\text{Mass of oxygen}}{\text{Molar mass of O}}$$ $$\text{Moles of O atoms} = \frac{0.89\ \text{g}}{16.00\ \text{g/mol}} = 0.055625\ \text{mol}$$

From the chemical formula $\ce{M2O3}$, there are 2 moles of metal atoms (M) for every 3 moles of oxygen atoms (O).

$$\text{Moles of M} = \text{Moles of O atoms} \times \frac{2\ \text{mol M}}{3\ \text{mol O}}$$ $$\text{Moles of M} = 0.055625\ \text{mol O} \times \frac{2}{3} = 0.0370833...\ \text{mol M}$$

The molar mass of the metal is its mass divided by the number of moles.

$$\text{Molar mass of M} = \frac{\text{Mass of M}}{\text{Moles of M}}$$ $$\text{Molar mass of M} = \frac{1.00\ \text{g}}{0.0370833...\ \text{mol}} = 26.969...\ \text{g/mol}$$

Rounding to three significant figures, the molar mass of M is 27.0 g/mol.

The molar mass of the metal M is 27.0\ g/mol.