Final answer:
To identify element X in H₂XO₄, the molar mass of the compound is calculated using the given mass and number of moles. After subtracting the molar mass of hydrogen and oxygen from the total, the remaining mass indicates that X is phosphorus (P), with five atoms needed to match the calculated molar mass.
Step-by-step explanation:
To identify the element X in the compound H₂XO₄ with the mass of 0.112 moles being 27.98 g, we first need to calculate the molar mass of the entire compound. We can do this by using the given mass and the number of moles of the compound. The molar mass (MM) is calculated by the formula MM = mass / number of moles.
In this case, MM = 27.98 g / 0.112 moles = 249.8214 g/mol.
Next, we know the atomic masses of hydrogen (H) and oxygen (O) which are 1.008 g/mol and 15.999 g/mol respectively.
Therefore, the molar mass of the known parts of the compound, that is 2 atoms of hydrogen and 4 atoms of oxygen, can be calculated as (2 x 1.008 g/mol) + (4 x 15.999 g/mol) = 95.010 g/mol.
By subtracting this from the total molar mass, we get the molar mass of element X, which can be found by MM(X) = 249.8214 g/mol - 95.010 g/mol = 154.8114 g/mol.
Looking at a periodic table, we find that the atomic mass of sulfur (S) is approximately 32.07 g/mol, which doesn't match our calculation.
However, the element with the atomic mass that closely matches our calculated molar mass is phosphorus (P), with an atomic mass of approximately 30.97 g/mol.
Considering there are 5 atoms of phosphorus to equal around 154.8114 g/mol (5 x 30.97 g/mol ≈ 154.85 g/mol), we can identify X as phosphorus (P).