i need a bit of help finding out how to do this problem. just tell me how and ill take it from there.
Q.A compound containing carbon, hydrogen, and Oxygen is found to be 40% carbon and 6.7% hydrogen by mass. the molar mass of this compound is between 115 g / mol. determine the molecular formula for the compound
To determine the molecular formula for the compound, we need to follow a few steps:
Step 1: Calculate the empirical formula.
- The empirical formula gives the simplest whole-number ratio of atoms in a compound.
- To calculate the empirical formula, we need to find the moles of each element present in the compound.
Given:
- Mass percent of carbon (C) = 40%
- Mass percent of hydrogen (H) = 6.7%
- Let's assume we have 100 grams of the compound, so we have:
- C = 40 grams
- H = 6.7 grams
Step 2: Convert the mass of each element to moles.
- We can calculate the moles of each element using the molar mass of each element. The molar mass of carbon (C) is 12 g/mol, and the molar mass of hydrogen (H) is 1 g/mol.
Moles of carbon (C) = Mass of carbon (g) / Molar mass of carbon (g/mol)
= 40 g / 12 g/mol
= 3.33 moles (approx.)
Moles of hydrogen (H) = Mass of hydrogen (g) / Molar mass of hydrogen (g/mol)
= 6.7 g / 1 g/mol
= 6.7 moles
Step 3: Find the mole ratio between the elements.
- Divide the moles of each element by the smallest number of moles obtained in Step 2 to get the mole ratio.
- The smallest number of moles we obtained was 3.33 moles of carbon.
Mole ratio of carbon (C) = 3.33 moles / 3.33 moles
= 1 mole
Mole ratio of hydrogen (H) = 6.7 moles / 3.33 moles (approx.)
≈ 2 moles
Step 4: Write the empirical formula.
- Based on the mole ratios obtained in Step 3, we can write the empirical formula.
- In this case, the empirical formula is CH2.
Step 5: Determine the molecular formula.
- To determine the molecular formula, we need to know the molar mass of the compound.
- The molar mass of the compound is given to be between 115 g/mol.
Step 6: Compare the empirical formula mass and the molar mass.
- Calculate the empirical formula mass by adding up the atomic masses of the elements in the empirical formula.
- The empirical formula mass for CH2 is 14 g/mol (12 g/mol for carbon + 2 g/mol for hydrogen).
- Compare the empirical formula mass to the molar mass of the compound.
- If the molar mass is a multiple of the empirical formula mass, then the empirical formula is also the molecular formula.
- In this case, 115 g/mol is not a multiple of 14 g/mol.
Step 7: Determine the multiple of the empirical formula.
- Divide the molar mass by the empirical formula mass to get the multiple.
Multiple = Molar mass of the compound / Empirical formula mass
= 115 g/mol / 14 g/mol (approx.)
≈ 8.21
Step 8: Multiply the empirical formula by the multiple obtained in Step 7.
- Multiply each subscript (number) in the empirical formula by the multiple.
Molecular formula = (C1H2) x 8 (approximately)
= C8H16
Therefore, the molecular formula for the compound is C8H16.
To determine the molecular formula for the compound, we need to find the number of carbon, hydrogen, and oxygen atoms present in the molecule.
1. Start by assuming we have 100 grams of the compound.
- 40% carbon means there are 40 grams of carbon in the compound.
- 6.7% hydrogen means there are 6.7 grams of hydrogen in the compound.
- Since we have assumed 100 grams of the compound, the remaining mass is attributed to oxygen.
- So, the mass of oxygen = 100 grams - (40 grams + 6.7 grams) = 53.3 grams.
2. Convert the masses of carbon, hydrogen, and oxygen to moles.
- Determine the molar masses of each element:
Carbon (C) = 12.01 g/mol
Hydrogen (H) = 1.008 g/mol
Oxygen (O) = 16.00 g/mol
- Number of moles of carbon = mass of carbon / molar mass of carbon = 40 g / 12.01 g/mol ≈ 3.33 moles.
- Number of moles of hydrogen = mass of hydrogen / molar mass of hydrogen = 6.7 g / 1.008 g/mol ≈ 6.65 moles.
- Number of moles of oxygen = mass of oxygen / molar mass of oxygen = 53.3 g / 16.00 g/mol ≈ 3.33 moles.
3. Divide the mole numbers obtained by the smallest mole number.
- It is apparent that the smallest mole number is 3.33 moles.
- Divide each mole number by 3.33, we get:
Carbon: 3.33 moles / 3.33 moles = 1 mole
Hydrogen: 6.65 moles / 3.33 moles ≈ 2 moles
Oxygen: 3.33 moles / 3.33 moles = 1 mole
4. Determine the ratio of atoms in the compound.
- Based on the mole ratio, the compound has the empirical formula CH2O.
- The empirical formula represents the simplest whole number ratio of atoms in a compound.
So, it means there is one carbon, two hydrogen, and one oxygen atom.
5. Calculate the empirical formula mass.
- The empirical formula mass (EFM) is the sum of the atomic masses in the empirical formula.
EFM = (carbon atomic mass) + (hydrogen atomic mass * 2) + (oxygen atomic mass)
EFM ≈ (12.01 g/mol) + (1.008 g/mol * 2) + (16.00 g/mol) ≈ 30.03 g/mol
6. Determine the molecular formula.
- Molecular formula mass (MFM) is the actual mass of the compound.
- Given that the molar mass of the compound is between 115 g/mol, let's find the multiple.
- MFM = n * EFM (where n is the multiple)
- From the given range of possible molar masses (115 g/mol), we have:
115 g/mol = n * 30.03 g/mol
n ≈ 3.83
7. Multiply the subscripts of the empirical formula by the multiple (n).
- Multiply each subscript in the empirical formula by 3.83:
Empirical formula * n = (CH2O) * 3.83 = C3.83H7.66O3.83
8. Round the subscripts to the nearest whole number to obtain the molecular formula.
- By rounding, the molecular formula becomes C4H8O4.
Thus, the molecular formula for the compound is C4H8O4.