To determine the molar masses of Mg and Fe, we can use the ratios given in the problem.
Let the mass of oxygen be x. Then, the mass of magnesium in the simplest compound of magnesium and oxygen is approximately 1.5x. This means that the total mass of the compound is approximately 2.5x (since there is only one oxygen atom in the compound). The molar mass of Mg is then:
Molar mass of Mg = (2.5x) / n
where n is the number of moles of Mg in the compound. Since there is only one Mg atom in the compound, n = 1. Therefore:
Molar mass of Mg = 2.5x
Similarly, let the mass of oxygen be y. Then, the mass of iron in the simplest oxide of iron is approximately 3.5y. This means that the total mass of the oxide is approximately 4.5y (since there is only one oxygen atom in the oxide). The molar mass of Fe is then:
Molar mass of Fe = (4.5y) / m
where m is the number of moles of Fe in the oxide. Since there is only one Fe atom in the oxide, m = 1. Therefore:
Molar mass of Fe = 4.5y
To compare these values with the accepted molar masses of Mg and Fe, we can look up their values in the periodic table. The accepted molar mass of Mg is 24.31 g/mol, and the accepted molar mass of Fe is 55.85 g/mol.
Using the ratios given in the problem, we have:
Molar mass of Mg = 2.5x
Molar mass of Fe = 4.5y
We don't have any information about the values of x and y, so we can't directly compare these expressions with the accepted molar masses of Mg and Fe. However, we can make some observations based on the ratios given in the problem.
The ratio of the molar mass of Mg to the accepted molar mass of Mg is:
(Molar mass of Mg) / (Accepted molar mass of Mg) = (2.5x) / 24.31
The ratio of the molar mass of Fe to the accepted molar mass of Fe is:
(Molar mass of Fe) / (Accepted molar mass of Fe) = (4.5y) / 55.85
We can simplify these expressions by finding the values of x and y in terms of the molar masses of Mg and Fe:
x = (24.31 / 2.5) * (Molar mass of Mg)
y = (55.85 / 4.5) * (Molar mass of Fe)
Substituting these values into the expressions above, we get:
(Molar mass of Mg) / (Accepted molar mass of Mg) = 0.1027 * (Molar mass of Mg)
(Molar mass of Fe) / (Accepted molar mass of Fe) = 0.2505 * (Molar mass of Fe)
From these expressions, we can see that the ratio of the molar mass of Mg to the accepted molar mass of Mg is proportional to the molar mass of Mg, and the same is true for Fe. This means that the values we obtained for the molar masses of Mg and Fe are simply scaled versions of the accepted molar masses, with scaling factors of approximately 0.1027 and 0.2505, respectively.
The reason for these scaling factors is that the ratios given in the problem are only approximate.