A 0.167-g sample of an unknown compound contains 0.00278 mol of the compound. Elemental analysis of the acid gives the following percentages by mass: 40.00% C; 6.71% H; 53.29% O.
1.)Determine the molecular formula of this acid.
2.)Determine the molar mass of the unknown acid.
1.) Well, if we know the percentages of carbon, hydrogen, and oxygen in the compound, we can start by assuming we have 100 grams of the compound. So, we have 40.00 grams of carbon, 6.71 grams of hydrogen, and 53.29 grams of oxygen.
Now, we can convert these grams into moles by dividing by the molar masses of carbon (12.01 g/mol), hydrogen (1.01 g/mol), and oxygen (16.00 g/mol).
40.00 g of C / 12.01 g/mol = 3.33 mol of C
6.71 g of H / 1.01 g/mol = 6.64 mol of H
53.29 g of O / 16.00 g/mol = 3.33 mol of O
Now, we need to find the simplest, whole number ratio between these elements. Dividing all the moles by the smallest number of moles (3.33), we get:
C: 3.33 mol / 3.33 mol = 1
H: 6.64 mol / 3.33 mol = 1.99 ≈ 2
O: 3.33 mol / 3.33 mol = 1
So, the simplest, whole number ratio for the elements is C1H2O1. Therefore, the molecular formula of this acid is CH2O.
2.) To find the molar mass of the unknown acid, we sum up the individual atomic masses of its elements.
C: 1 atom x 12.01 g/mol = 12.01 g/mol
H: 2 atoms x 1.01 g/mol = 2.02 g/mol
O: 1 atom x 16.00 g/mol = 16.00 g/mol
Adding them up, we get:
12.01 g/mol + 2.02 g/mol + 16.00 g/mol = 30.03 g/mol
So, the molar mass of the unknown acid is 30.03 g/mol.
To determine the molecular formula of the acid, we need to calculate the empirical formula first. The empirical formula gives the simplest whole-number ratio of atoms present in a compound.
1.) Determine the empirical formula:
Step 1: Convert the given percentages to grams.
- 40.00% C: (0.4000 g C) = 0.4000 g C
- 6.71% H: (0.0671 g H) = 0.0671 g H
- 53.29% O: (0.5329 g O) = 0.5329 g O
Step 2: Convert the grams to moles.
- Moles of C = (0.4000 g C) / (12.01 g/mol) = 0.0333 mol C
- Moles of H = (0.0671 g H) / (1.008 g/mol) = 0.0667 mol H
- Moles of O = (0.5329 g O) / (16.00 g/mol) = 0.0333 mol O
Step 3: Divide the moles by the smallest number of moles to obtain the simplest ratio.
- Simplified ratio: C:H:O = 1:2:1
Therefore, the empirical formula of the acid is CH2O.
2.) Determine the molar mass of the unknown acid:
The molar mass of the empirical formula (CH2O) is calculated as follows:
- One carbon atom (C) has a molar mass of 12.01 g/mol.
- Two hydrogen atoms (H) have a combined molar mass of (2 × 1.008 g/mol) = 2.016 g/mol.
- One oxygen atom (O) has a molar mass of 16.00 g/mol.
Molar mass of CH2O = (1 × 12.01 g/mol) + (2 × 1.008 g/mol) + (1 × 16.00 g/mol) = 30.03 g/mol.
Therefore, the molar mass of the unknown acid is 30.03 g/mol.
To determine the molecular formula of the acid, we need to find the empirical formula first. The empirical formula represents the ratio of atoms in the simplest whole number ratio.
1.) Determine the empirical formula:
To find the empirical formula, we need to find the mole ratio of each element in the compound.
a) Determine the number of moles of each element:
- Carbon (C): The compound contains 40.00% C by mass. To find the number of moles, we can use the percentage and the molar mass of carbon (12.01 g/mol):
Number of moles of C = (percentage of C / 100) * (mass of the sample / molar mass of C)
= (40.00 / 100) * (0.167 g / 12.01 g/mol)
= 0.027 826 mol
- Hydrogen (H): The compound contains 6.71% H by mass. Using a similar calculation:
Number of moles of H = (percentage of H / 100) * (mass of the sample / molar mass of H)
= (6.71 / 100) * (0.167 g / 1.01 g/mol)
= 0.011 180 mol
- Oxygen (O): The compound contains 53.29% O. Using a similar calculation:
Number of moles of O = (percentage of O / 100) * (mass of the sample / molar mass of O)
= (53.29 / 100) * (0.167 g / 16.00 g/mol)
= 0.045 986 mol
b) Determine the mole ratio:
Divide each of the moles by the smallest mole value to find the simplest whole number ratio.
Mole ratio of C:H:O = 0.027 826 mol / 0.011 180 mol / 0.045 986 mol ≈ 2 : 4 : 2
c) Determine the empirical formula:
Based on the mole ratio, the empirical formula is C2H4O2.
2.) Determine the molar mass of the unknown acid:
To find the molar mass of the acid, we need to know the empirical formula. The molar mass of the acid is the sum of the molar masses of its constituent elements.
a) Molar mass of C = 12.01 g/mol × 2 = 24.02 g/mol
b) Molar mass of H = 1.01 g/mol × 4 = 4.04 g/mol
c) Molar mass of O = 16.00 g/mol × 2 = 32.00 g/mol
Molar mass of the acid = 24.02 g/mol + 4.04 g/mol + 32.00 g/mol = 60.06 g/mol
Therefore, the molecular formula of the acid is C2H4O2, and its molar mass is 60.06 g/mol.
Take 100 g sample which gives
40 g C
6.71 g H
53.29 g O
Convert to mols by mols = grams/atomic mass
40/12 = approx 3.3
6.71/1 = 6.71
53.29/16 = approx 3.3
To determine the empirical formula, find the ratio of these elements to each other with the smallest number being 1.00. The easy way to do that is to divide the smallest number by itself (thereby assuring 1.00 for that one) and divide all of the other numbers by the same small number. So
3.3/3.3 = 1.00 C
6.71/3.3 = 2 H
3.3/3/3 = 1 O
emprical formula is CH2O
From the 0.167 g sample contg 0.00278 mols we an use mol = g/molar mass or
molar mass = g/mol = 0.167/0.00278 = 60.07 for the molar mass.
Then empirical formula mass is 12+2+16 = 30
empirical mass x whole number = molar mass
30 x whole number = 60
whole number = 60/30 = 2
So the molecular formula is (CH2O)2 or C2H4O2 and the molar mass is
2*12.01 + 2*1 + 1*16 = ?