Cumene is a compound containing only C and H that is used in the production of Phenol and acetone in industry. combustion of 47.6 mg cumene produce some CO2 and 42.80 mg water. the molar mass of cumene is between 115-125 g/mol. Determine the empirical and molecular formula of cumene?
42.80 mg H2O. Convert to mg H (not H2).
47.6 mg cumene - mg H = mg C
moles H = mg H/atomic mass H.
moles C = mg C/atomic mass C.
Now fine the ratio. The easy way to do that is divide the smaller moles by itself thereby assuring you of getting 1.00 for the smallest value. Then divide the other number by the same small number. I did this and obtained 1:1.33 and those aren't whole numbers. So you multiply by 2, 3, 4, 5, etc until you come up with values that can be rounded to whole numbers. (Hint: Thae multiplier is 3). That will give you the empirical formula.
To fine the molecular formula,
115/empirical formula mass = n. Round to a whole number and the molecular formula will be
(empirical formula)n
According to google the molecular formula is C9H12.
THANKS
To determine the empirical and molecular formula of cumene, we need to calculate the empirical formula first.
First, we need to calculate the moles of CO2 produced during combustion. We know that the molar mass of CO2 is 44.01 g/mol.
Moles of CO2 = mass of CO2 / molar mass of CO2
Moles of CO2 = 42.80 mg / 44.01 g/mol
Next, we need to calculate the moles of H2O produced during combustion. We know that the molar mass of H2O is 18.02 g/mol.
Moles of H2O = mass of H2O / molar mass of H2O
Moles of H2O = 42.80 mg / 18.02 g/mol
Next, let's determine the moles of carbon in cumene. We know that the molar mass of carbon is 12.01 g/mol and we can use the following equation:
Moles of Carbon = Moles of CO2 - Moles of H2O
Next, we'll determine the moles of hydrogen in cumene. We'll use the following equation:
Moles of Hydrogen = (2 * Moles of H2O) - Moles of Carbon
Now, we'll calculate the mole ratio of carbon to hydrogen. We'll divide the moles of carbon and hydrogen by the smallest value to get a simple ratio:
Mole Ratio = Moles of Carbon / Smallest value
Mole Ratio = Moles of Hydrogen / Smallest value
Finally, we'll determine the empirical formula using the mole ratio. We'll round the values to whole numbers if necessary.
Empirical formula = CxHy
Now, we can check if the molecular formula falls within the given range of molar masses (115-125 g/mol). We'll calculate the molar mass of the empirical formula:
Molar Mass of empirical formula = (12.01 g/mol * x) + (1.008 g/mol * y)
If the molar mass falls within the given range, the empirical formula is also the molecular formula. Otherwise, we'll calculate the molecular formula using the following equation:
Molecular formula = (Empirical formula)n
Where n is equal to the molar mass given divided by the molar mass of the empirical formula.
By following these steps, we can determine the empirical and molecular formulas of cumene.
To determine the empirical formula of cumene, we need to find the ratio of carbon to hydrogen in the compound and simplify it to the smallest whole numbers.
Step 1: Find the number of moles of carbon and hydrogen.
- The molar mass range of cumene is given between 115-125 g/mol, so let's assume its molar mass is 120 g/mol for simplicity.
Number of moles of carbon:
1 mole of carbon = 12 grams
So, the number of moles of carbon = mass of carbon / molar mass of carbon
= 47.6 mg / 12 g/mol * 1000 mg/g
= 3.967 mol
Number of moles of hydrogen:
1 mole of hydrogen = 1 gram
So, the number of moles of hydrogen = mass of hydrogen / molar mass of hydrogen
= 42.80 mg / 1 g/mol * 1000 mg/g
= 0.0428 mol
Step 2: Divide the number of moles of each element by the smallest number of moles.
In this case, the smallest number of moles is 0.0428 mol (hydrogen).
Ratio of carbon to hydrogen = 3.967 mol / 0.0428 mol ≈ 92.6
Step 3: Round the ratio to the nearest whole number.
The simplified ratio becomes approximately 93:1.
Step 4: Determine the empirical formula.
The empirical formula shows the simplest whole number ratio of atoms in a compound. Thus, the empirical formula of cumene is C93H.
To determine the molecular formula of cumene, we need to find the molar mass of the empirical formula and compare it to the given molar mass range (115-125 g/mol).
Step 5: Calculate the molar mass of the empirical formula.
Molar mass of 1 carbon atom = 12 g/mol
Molar mass of 1 hydrogen atom = 1 g/mol
Molar mass of empirical formula = (molar mass of carbon * number of carbon atoms) + (molar mass of hydrogen * number of hydrogen atoms)
= (12 g/mol * 93) + (1 g/mol * 1)
= 1128 g/mol + 1 g/mol
= 1129 g/mol
Step 6: Compare the calculated molar mass to the given range.
The calculated molar mass of the empirical formula (1129 g/mol) is outside the given range (115-125 g/mol).
Step 7: Determine the multiple of the empirical formula that gives a molar mass within the given range.
To find the multiple, divide the given range upper limit by the calculated molar mass:
Multiple = Upper limit of given range / calculated molar mass
= 125 g/mol / 1129 g/mol
≈ 0.111
Step 8: Multiply the empirical formula by the multiple to find the molecular formula.
Molecular formula = Empirical formula * multiple
= C93H * 0.111
≈ C10H10
Therefore, the empirical formula of cumene is C93H, and the molecular formula is C10H10.