A compound was found to contain 49.98 g carbon and 10.47 g hydrogen. The molar mass of the compound is 58.12 g/mol. What is the molecular formula?
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A compound was found to contain 49.98 g of carbon and 10.47 g of hydrogen. The molar mass of the compound is 58.12 g/mol. Determine the molecular formula?
To determine the molecular formula of a compound, we need to know the empirical formula and the molar mass of the compound.
1. Start by calculating the moles of carbon and hydrogen in the compound using their respective masses and their atomic masses:
Moles of Carbon = mass of carbon / atomic mass of carbon
Moles of Hydrogen = mass of hydrogen / atomic mass of hydrogen
Moles of Carbon = 49.98 g / 12.01 g/mol ≈ 4.163 mol
Moles of Hydrogen = 10.47 g / 1.01 g/mol ≈ 10.366 mol
2. Next, divide the number of moles of each element by the smallest number of moles to find the empirical formula:
Empirical formula = C4.163 H10.366
Since the numbers are relatively close to whole numbers, we can round them off to the nearest whole number:
Empirical formula ≈ C4H10
3. Now, calculate the empirical formula mass by adding up the atomic masses of the individual atoms in the empirical formula:
Empirical formula mass = (atomic mass of C x number of C atoms) + (atomic mass of H x number of H atoms)
Empirical formula mass = (12.01 g/mol x 4) + (1.01 g/mol x 10) = 48.04 g/mol + 10.1 g/mol = 58.14 g/mol
4. Finally, divide the molar mass of the compound given (58.12 g/mol) by the empirical formula mass (58.14 g/mol) to find the whole number ratio between the compound and empirical formula:
Ratio = molar mass of compound / empirical formula mass
Ratio = 58.12 g/mol / 58.14 g/mol ≈ 1
Since the ratio is close to 1, the empirical formula is also the molecular formula of the compound.
Therefore, the molecular formula of the compound is C4H10.
To determine the molecular formula of the compound, we need to calculate the empirical formula first. The empirical formula represents the simplest whole-number ratio of atoms in a compound.
To find the empirical formula, we need to determine the moles of carbon and hydrogen in the compound.
Step 1: Calculate the moles of carbon:
Moles of carbon = Mass of carbon / Molar mass of carbon
= 49.98 g / 12.01 g/mol
≈ 4.16 mol
Step 2: Calculate the moles of hydrogen:
Moles of hydrogen = Mass of hydrogen / Molar mass of hydrogen
= 10.47 g / 1.01 g/mol
≈ 10.36 mol
Step 3: Determine the empirical formula using the mole ratio:
Divide the number of moles of each element by the smallest number of moles to obtain the simplest, whole-number ratio:
Carbon: 4.16 mol / 4.16 ≈ 1 (rounded to the nearest whole number)
Hydrogen: 10.36 mol / 4.16 ≈ 2.5
Since the number of moles for hydrogen is not a whole number, we need to multiply both subscripts by 2 to make it a whole number:
Carbon: 1
Hydrogen: 2 × 2 = 4
Therefore, the empirical formula is CH₄.
To find the molecular formula, we need to know the molar mass of the empirical formula. The molar mass of CH₄ (carbon + hydrogen) is:
Molar mass of CH₄ = (Molar mass of carbon × subscripts) + (Molar mass of hydrogen × subscripts)
= (12.01 g/mol × 1) + (1.01 g/mol × 4)
= 12.01 g/mol + 4.04 g/mol
= 16.05 g/mol
Finally, we can determine the molecular formula by dividing the molar mass of the compound given in the question by the molar mass of the empirical formula:
Molecular formula = Molar mass of compound / Molar mass of empirical formula
= 58.12 g/mol / 16.05 g/mol
≈ 3.62
Since the result is around 3.62, we can round it to the nearest whole number to give us the subscript for the molecular formula:
Molecular formula ≈ 4
Therefore, the molecular formula of the compound is (CH₄)₄, which simplifies to C₄H₁₆.