To find the molar mass of element X, we need to use the given information to determine the number of moles of oxygen in the sample, and then use that to calculate the number of moles of element X in the sample. Then we can divide the mass of the sample by the number of moles of element X to get the molar mass.
First, we need to calculate the number of moles of oxygen in the sample. We can use the molar mass of oxygen (16.00 g/mol) to convert the mass of oxygen atoms to moles:
moles of oxygen = mass of oxygen / molar mass of oxygen
moles of oxygen = 14.4 g / 16.00 g/mol
moles of oxygen = 0.900 mol
Next, we need to use the formula of X2O3 to determine the number of moles of element X in the sample. The formula indicates that there are 2 moles of element X for every 3 moles of oxygen in the compound. Therefore:
moles of X = 2/3 × moles of oxygen
moles of X = 2/3 × 0.900 mol
moles of X = 0.600 mol
Now we can use the mass of the sample and the number of moles of element X to calculate the molar mass of X:
molar mass of X = mass of sample / moles of X
molar mass of X = 30.6 g / 0.600 mol
molar mass of X = 51.0 g/mol
Therefore, the molar mass of element X is 51.0 g/mol.