An oxide of a metal (M) contains 40% by mass of oxygen. Metal (M) has atomic mass of 24. The empirical formula of the oxide is-M2OMOM2O3M3O4

To determine the empirical formula of the oxide, we need to calculate the ratio of the metal (M) to oxygen (O) in the compound.

Given that the oxide contains 40% by mass of oxygen, we can assume that the remaining 60% is the metal (M).

To find the empirical formula, we need to convert the percentages to moles. Since the atomic mass of the metal (M) is 24, we can calculate the number of moles of metal (M) as follows:

Number of moles of metal (M) = (60% / 100%) * (mass of oxide / atomic mass of metal (M)) = 0.6 * (mass of oxide / 24)

Similarly, we can calculate the number of moles of oxygen (O) as follows:

Number of moles of oxygen (O) = (40% / 100%) * (mass of oxide / atomic mass of oxygen (O)) = 0.4 * (mass of oxide / 16)

To simplify the ratio, we divide both the number of moles of metal (M) and oxygen (O) by the smaller value obtained. In this case, the smaller value is the number of moles of oxygen (O).

Dividing both values by the number of moles of oxygen (O), we get:

Number of moles of metal (M) = (0.6 * mass of oxide / 24) / (0.4 * mass of oxide / 16) = (0.6 * 16) / (0.4 * 24) = 0.4

Number of moles of oxygen (O) = (0.4 * mass of oxide / 16) / (0.4 * mass of oxide / 16) = 1

Therefore, the empirical formula of the oxide is MO2, indicating that there is one atom of metal (M) and two atoms of oxygen (O) in the compound.