Which of the following sets of empirical formulas

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Which of the following sets of empirical formulas, molar masses, and molecular formulas are correct?

a) HO, 34 g/mol, H2O
b) CH4N, 90 g/mol, C3H12N3
c) CaO, 56 g/mol, Ca2O2
d) C3H8O, 120 g/mol, C3H8O2
e) CH, 78 g/mol, C13H13

The correct answer and explanation is :

a) HO, 34 g/mol, H2O

  • Empirical formula: HO (represents one hydrogen atom and one oxygen atom).
  • Molar mass of HO: The atomic mass of hydrogen is approximately 1 g/mol, and that of oxygen is approximately 16 g/mol. Thus, the molar mass of HO is (1 + 16 = 17 \, \text{g/mol}).
  • Molecular formula: H2O (this is water, so the molecular formula is correct).
  • Issue: The molar mass of HO is 17 g/mol, but it is given as 34 g/mol, which doesn’t match. Therefore, this set is incorrect.

b) CH4N, 90 g/mol, C3H12N3

  • Empirical formula: CH4N (represents 1 carbon, 4 hydrogens, and 1 nitrogen).
  • Molar mass of CH4N: Carbon (12 g/mol), hydrogen (1 g/mol, 4 hydrogens), nitrogen (14 g/mol), so the molar mass is (12 + 4 + 14 = 30 \, \text{g/mol}).
  • Molecular formula: C3H12N3 (this suggests 3 carbons, 12 hydrogens, and 3 nitrogen atoms).
  • Issue: The molar mass of the empirical formula CH4N is 30 g/mol, but it is given as 90 g/mol, which is much higher. This is not consistent with the molecular formula C3H12N3. Therefore, this set is incorrect.

c) CaO, 56 g/mol, Ca2O2

  • Empirical formula: CaO (represents 1 calcium and 1 oxygen).
  • Molar mass of CaO: The atomic mass of calcium is 40 g/mol, and that of oxygen is 16 g/mol. Thus, the molar mass of CaO is (40 + 16 = 56 \, \text{g/mol}).
  • Molecular formula: Ca2O2 (this simplifies to CaO, as 2 calcium atoms and 2 oxygen atoms form the same empirical formula).
  • Issue: The empirical formula and molar mass are correct, and the molecular formula is just a multiple of the empirical formula. Therefore, this set is correct.

d) C3H8O, 120 g/mol, C3H8O2

  • Empirical formula: C3H8O (represents 3 carbons, 8 hydrogens, and 1 oxygen).
  • Molar mass of C3H8O: The atomic mass of carbon is 12 g/mol, hydrogen is 1 g/mol, and oxygen is 16 g/mol. Thus, the molar mass is (3 \times 12 + 8 \times 1 + 16 = 36 + 8 + 16 = 60 \, \text{g/mol}).
  • Molecular formula: C3H8O2 (this suggests 3 carbons, 8 hydrogens, and 2 oxygens).
  • Issue: The molar mass of C3H8O is 60 g/mol, but it is given as 120 g/mol, which is inconsistent with the molecular formula C3H8O2. Therefore, this set is incorrect.

e) CH, 78 g/mol, C13H13

  • Empirical formula: CH (represents 1 carbon and 1 hydrogen).
  • Molar mass of CH: The atomic mass of carbon is 12 g/mol, and hydrogen is 1 g/mol. Thus, the molar mass of CH is (12 + 1 = 13 \, \text{g/mol}).
  • Molecular formula: C13H13 (this suggests 13 carbons and 13 hydrogens).
  • Issue: The molar mass of CH is 13 g/mol, but the molecular formula C13H13 corresponds to a molar mass of (13 \times 12 + 13 \times 1 = 156 + 13 = 169 \, \text{g/mol}). Given that the molar mass is 78 g/mol, this set is incorrect.

Final Answer:

  • Correct: c) CaO, 56 g/mol, Ca2O2
  • Incorrect: a), b), d), e)

Explanation:

  • Empirical formulas represent the simplest whole number ratio of elements in a compound.
  • The molar mass of the empirical formula should match the given molar mass, and the molecular formula is often a multiple of the empirical formula.
  • When the empirical formula, molar mass, and molecular formula are not consistent, the set is incorrect. Only option c) satisfies all conditions.

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