Terephthalic acid is an important chemical used in the manufacture of polyesters and plasticizers. It contains only C, H, and O. Combustion of 21.79 mg terephthalic acid produces 46.18 mg CO2 and 7.10 mg H2O. If 0.250 mol of terephthalic acid has a mass of 41.5 g, determine the molecular formula of terephthalic acid. (Type your answer using the format CO2 for CO2.)
Convert CO2 to C, H2O to H.
46.18 mg x (atomic mass C/molar mass CO2) = 46.18 x 12/44 = approx 13
7.10 x (2*atomic mass H/molar mass H2O) = 7.10 x 2/18 = about 0.8
mg O = 46.18-13 - 0.8 = about 8.
Convert to mols.
C = 13/12 = about 1
H = 0.8/1 = 0.8
O = 8/16 = 0.5
Find the ratio of C to H to O which will be about 2 C to 1.5 H to 0.5 O or approx C4H3O2 for the empirical formula. You should check ALL of the calculations above.
Since 1/4 mol has a mass of 41.5 then a mol is 41.6*4 = 166.
empirical mass x whole number = 166 or
83 x whole number = 166 or whole number = 2 so molecular formula is (C4H3O2)2 = C8H6O4
Remember to check all of those numbers above and use more accurate numbers.
Whoa, slow down there with all those numbers and formulas! I'm a clown bot, not a chemistry whiz. But hey, since you asked for my help, I'll do my best to clown around with this question.
So, we've got 21.79 mg of terephthalic acid burning up, and it gives us 46.18 mg of CO2 and 7.10 mg of H2O. Now, if we could capture some of that carbon dioxide and water vapor, we'd have a carbonated acid-watery drink! 😄
Okay, back to the question. Let's convert those masses to moles. The molar mass of CO2 is about 44 g/mol, and the molar mass of H2O is about 18 g/mol.
So, for CO2, we have 46.18 mg (0.04618 g) divided by the molar mass of CO2 (44 g/mol), which gives us approximately 0.00105 moles of CO2. And for H2O, we have 7.10 mg (0.0071 g) divided by the molar mass of H2O (18 g/mol), which gives us approximately 0.00039 moles of H2O.
Now let's calculate the number of moles of terephthalic acid. We know that 0.250 moles of terephthalic acid has a mass of 41.5 g. Therefore, 1 mole of terephthalic acid has a mass of 41.5 g divided by 0.250 moles, which is approximately 166 g/mol.
Finally, let's divide the number of moles of each element in CO2 and H2O by the number of moles of terephthalic acid. In CO2, we have 1 mole of carbon for every 1 mole of CO2, and in H2O, we have 2 moles of hydrogen for every 1 mole of H2O.
So, in the terephthalic acid, we have approximately 0.00105 moles of carbon (that's about 0.00105 times 166 g/mol), and 0.00039 moles of hydrogen (that's about 0.00039 times 166 g/mol).
Now, we know that terephthalic acid only contains carbon, hydrogen, and oxygen. So, if we subtract the moles of carbon and hydrogen from the total number of moles in terephthalic acid (0.250 moles), we get the moles of oxygen.
Once you have the moles of each element, it's time to find the ratio of carbon, hydrogen, and oxygen atoms. Divide the moles of each element by the smallest value to get the simplest whole number ratio.
And there you have it, the molecular formula of terephthalic acid! Just plug in those numbers, do some calculations, and you'll find your answer. Good luck, and don't forget to have fun along the way! 🤡
To determine the molecular formula of terephthalic acid, we will first calculate the empirical formula using the given information.
1. Calculate the moles of carbon (C) in CO2:
- The molar mass of CO2 is 44.01 g/mol (12.01 g/mol for each C and 16.00 g/mol for O).
- The mass of CO2 produced in the combustion is 46.18 mg, which is equivalent to 0.04618 g.
- Convert the mass of CO2 to moles: 0.04618 g / 44.01 g/mol ≈ 0.00105 mol.
2. Calculate the moles of hydrogen (H) in H2O:
- The molar mass of H2O is 18.02 g/mol (2.02 g/mol for each H and 16.00 g/mol for O).
- The mass of H2O produced in the combustion is 7.10 mg, which is equivalent to 0.00710 g.
- Convert the mass of H2O to moles: 0.00710 g / 18.02 g/mol ≈ 0.00039 mol.
3. Calculate the moles of oxygen (O) consumed:
- The moles of O consumed can be determined by subtracting the sum of C and H moles from the total moles of terephthalic acid.
- The moles of terephthalic acid are given as 0.250 mol.
- Moles of O = 0.250 mol - (0.00105 mol + 0.00039 mol) ≈ 0.24856 mol.
4. Determine the empirical formula:
- Divide the moles of each element by the smallest number of moles calculated.
- Carbon: 0.00105 mol / 0.00039 mol ≈ 2.6923 (approximately 3)
- Hydrogen: 0.00039 mol / 0.00039 mol = 1
- Oxygen: 0.24856 mol / 0.00039 mol ≈ 636.2051 (approximately 636).
The empirical formula is C3H1O636. However, these numbers need to be simplified to obtain a whole number ratio.
5. Simplify the empirical formula:
Divide each subscript by the greatest common divisor (GCD) to obtain a whole number ratio.
- Carbon: 3 / 1 = 3
- Hydrogen: 1 / 1 = 1
- Oxygen: 636 / 1 = 636.
The empirical formula, after simplification, is C3H1O636.
To determine the molecular formula, we need to find the molecular mass of terephthalic acid, compare it to the empirical formula mass, and determine the ratio between them.
6. Calculate the molecular mass of terephthalic acid:
- The mass of 0.250 mol of terephthalic acid is given as 41.5 g.
- Convert the moles to grams: 0.250 mol * (41.5 g / 0.250 mol) = 41.5 g.
7. Calculate the empirical formula mass:
- Carbon: 3 * 12.01 g/mol = 36.03 g/mol
- Hydrogen: 1 * 1.01 g/mol = 1.01 g/mol
- Oxygen: 636 * 16.00 g/mol = 10,176 g/mol
The empirical formula mass is approximately 10,213.04 g/mol (36.03 g/mol + 1.01 g/mol + 10,176 g/mol).
8. Determine the ratio between the molecular formula mass and the empirical formula mass:
- Molecular formula mass / Empirical formula mass = 41.5 g / 10,213.04 g/mol
- The ratio is approximately 0.0041.
9. Multiply the subscripts of the empirical formula by the ratio obtained:
- Carbon: 3 * 0.0041 ≈ 0.0123 (approximately 0.012 or insignificant)
- Hydrogen: 1 * 0.0041 ≈ 0.0041 (approximately 0.004 or insignificant)
- Oxygen: 636 * 0.0041 ≈ 2.6056 (approximately 3).
The molecular formula is C0.012H0.004O3. However, to obtain a whole number ratio, these insignificant approximations can be ignored.
Therefore, the molecular formula of terephthalic acid is CO3.
To determine the molecular formula of terephthalic acid, we need to find the empirical formula first. The empirical formula represents the simplest whole number ratio of atoms present in a compound.
We are given the mass of terephthalic acid, the mass of CO2 produced, and the mass of H2O produced. We need to use this information to calculate the moles of carbon, hydrogen, and oxygen in the compound.
1. Calculate the moles of CO2 produced:
- Mass of CO2 = 46.18 mg = 0.04618 g
- Molar mass of CO2 = 12.01 g/mol (carbon) + 2 * 16.00 g/mol (oxygen) = 44.01 g/mol
- Moles of CO2 = mass of CO2 / molar mass of CO2
2. Calculate the moles of H2O produced:
- Mass of H2O = 7.10 mg = 0.0071 g
- Molar mass of H2O = 2 * 1.01 g/mol (hydrogen) + 16.00 g/mol (oxygen) = 18.02 g/mol
- Moles of H2O = mass of H2O / molar mass of H2O
3. Calculate the moles of carbon (C):
- Moles of C = 2 * Moles of CO2
4. Calculate the moles of hydrogen (H):
- Moles of H = 4 * Moles of H2O
5. Calculate the moles of oxygen (O):
- Moles of O = Total moles of C, H, and O - Moles of C - Moles of H
Next, we calculate the empirical formula:
6. Convert the moles of each element to the lowest whole number ratio by dividing each by the smallest value obtained in steps 3, 4, and 5.
- Divide the moles of each element by the smallest number of moles.
Finally, we convert the empirical formula to the molecular formula by multiplying the subscripts by a whole number, n:
7. Determine the value of n by calculating the molar mass of the empirical formula and dividing it by the molar mass of the compound provided (0.250 mol terephthalic acid has a mass of 41.5 g).
- Molar mass of the empirical formula = sum of atomic masses for each element in the empirical formula
- n = molar mass of the compound provided / molar mass of the empirical formula
With n, we can determine the molecular formula of terephthalic acid by multiplying the subscripts in the empirical formula by n.
I'll perform the calculations for the given data:
1. Moles of CO2 = 0.04618 g / 44.01 g/mol = 0.00105 mol
2. Moles of H2O = 0.0071 g / 18.02 g/mol = 0.000394 mol
3. Moles of C = 2 * 0.00105 mol = 0.0021 mol
4. Moles of H = 4 * 0.000394 mol = 0.001576 mol
5. Moles of O = (0.250 mol - 0.0021 mol - 0.001576 mol) = 0.246324 mol
To convert these values to whole numbers, we divide them by the smallest number of moles:
C: 0.0021 mol / 0.000394 mol ≈ 5.33
H: 0.001576 mol / 0.000394 mol = 4
O: 0.246324 mol / 0.000394 mol ≈ 625.49
Dividing by 5.33, 4, and 625.49, we obtain approximately:
C: 1
H: 3
O: 117
Thus, the empirical formula of terephthalic acid is CH3O117.
Now we can determine the value of n:
Molar mass of empirical formula = (1 * atomic mass of C) + (3 * atomic mass of H) + (117 * atomic mass of O)
The molar mass of the empirical formula would then be divided by the molar mass of the compound provided to obtain n:
n = 41.5 g / molar mass of the empirical formula
By performing these calculations, we can determine the molecular formula of terephthalic acid.