Step-by-step explanation:
The given ratio of the mass of magnesium to the mass of oxygen in a 100g sample of MgO is 3:2. This means that out of the 100g of MgO, 3/5 (or 60g) is magnesium and 2/5 (or 40g) is oxygen.
To find the mass ratio of magnesium to oxygen in a 50g sample of MgO, we need to first determine the masses of magnesium and oxygen in this sample. Since the ratio of magnesium to oxygen is constant, we can use the proportion:
Mass of magnesium / Mass of oxygen = 3/2
Let x be the mass of MgO in the 50g sample that is magnesium. Then, the mass of oxygen in the sample is (50-x)g. Using the proportion above, we can write:
x / (50-x) = 3/2
Solving for x, we get:
x = 30g
This means that the mass of magnesium in the 50g sample is 30g, and the mass of oxygen is 20g.
Therefore, the mass ratio of magnesium to oxygen in the 50g sample is:
30g / 20g = 3/2
So, the mass ratio of magnesium to oxygen in a 50g sample of MgO is also 3:2, the same as in the 100g sample.