Final answer:
The empirical formula for ascorbic acid is C3H4O3, and the molecular formula is C6H8O6, which is option (a).
Step-by-step explanation:
The student is asking for the empirical formula of ascorbic acid based on its percentage composition by mass. First, we need to find the number of moles of each element present in 100 grams of ascorbic acid. For carbon (C), with an atomic mass of 12.011 g/mol, we have 40.92 g divided by 12.011 g/mol, giving us approximately 3.406 moles of carbon. For hydrogen (H), with an atomic mass of 1.008 g/mol, we have 4.58 g divided by 1.008 g/mol, yielding about 4.543 moles of hydrogen. For oxygen (O), with an atomic mass of 15.999 g/mol, we have 54.50 g divided by 15.999 g/mol, which results in approximately 3.407 moles of oxygen.
To find the simplest whole-number ratio, we divide by the smallest number of moles, which in this case is approximately 3.4 moles. This gives us a ratio close to 1:1:1 for C:H:O. However, we must consider the molecular mass of ascorbic acid, which is 176 amu. The molecular mass of the empirical formula (C1H1O1) is about 30 amu, which is much smaller than 176 amu. We find that the molecular mass of the empirical formula C3H4O3 is 88.062 amu, which is exactly half of the molecular mass of ascorbic acid (176 amu). Therefore, we multiply the subscripts in the empirical formula by 2 to get the molecular formula.
The empirical formula is C3H4O3, and the molecular formula, which is twice the empirical formula, is C6H8O6. The answer to the student's question is (a) C6H8O6.