A sample of a compound of nitrogen and oxygen contains 1,52 g of N and 3,47 of O. The molar mass of the compound is between 90 g and 95 g. Determine the molecular formula and molar mass of the compound.
To determine the molecular formula and molar mass of the compound, we need to find the ratio of nitrogen (N) to oxygen (O) atoms in the compound.
1. Determine the number of moles of N and O in the sample:
Moles of N = mass of N / molar mass of N = 1.52 g / 14.01 g/mol = 0.108 moles
Moles of O = mass of O / molar mass of O = 3.47 g / 16.00 g/mol = 0.217 moles
2. Find the simplified ratio of moles of N to O by dividing both moles by the smaller value:
Ratio of N to O = 0.108 moles of N / 0.108 moles of N = 1
= 0.217 moles of O / 0.108 moles of N ≈ 2
3. Determine the empirical formula by using the ratio obtained in step 2:
Empirical formula = N1O2 = NO2
4. Calculate the empirical molar mass of the empirical formula:
Empirical molar mass = molar mass of N + (2 * molar mass of O)
= 14.01 g/mol + (2 * 16.00 g/mol)
= 46.01 g/mol
5. Given that the molar mass of the compound is between 90 g and 95 g, we need to determine how many empirical formula units are present in the compound:
Number of empirical formula units = molar mass of the compound / empirical molar mass
= 95 g / 46.01 g/mol
≈ 2.06
Since the number of empirical formula units is greater than 1, the molecular formula of the compound should be a multiple of the empirical formula.
6. Determine the molecular formula by multiplying the empirical formula by whole numbers to obtain a molar mass within the given range:
Potential molecular formula options:
- Multiply the empirical formula by 2: (NO2)2 = N2O4 (Molar mass ≈ 92.02 g/mol)
- Multiply the empirical formula by 3: (NO2)3 = N3O6 (Molar mass ≈ 138.03 g/mol)
Since the molecular mass of the compound is between 90 g and 95 g, the correct molecular formula is likely N2O4 with a molar mass of approximately 92.02 g/mol.
To determine the molecular formula and molar mass, we need to follow these steps:
Step 1: Find the moles of nitrogen (N) and oxygen (O).
To find the moles of an element, we divide the mass of that element by its molar mass.
Molar mass of N = 14.01 g/mol
Molar mass of O = 16.00 g/mol
Number of moles of N = 1.52 g / 14.01 g/mol ≈ 0.1085 mol
Number of moles of O = 3.47 g / 16.00 g/mol ≈ 0.2169 mol
Step 2: Determine the ratio of nitrogen to oxygen.
To find the ratio of elements, we divide the number of moles of each element by the smallest number of moles.
Ratio of N to O = (Number of moles of N) / (Number of moles of O)
≈ 0.1085 mol / 0.1085 mol ≈ 1.000
Step 3: Find the empirical formula.
The empirical formula represents the simplest whole-number ratio of elements in a compound. Since the ratio of N to O is approximately 1:1, the empirical formula is N1O1, which simplifies to NO.
Step 4: Determine the molar mass of the empirical formula.
The molar mass of the empirical formula is the sum of the molar masses of its constituent elements.
Molar mass of NO = (Molar mass of N) + (Molar mass of O)
≈ 14.01 g/mol + 16.00 g/mol ≈ 30.01 g/mol
Step 5: Determine the molecular formula.
The molecular formula represents the actual number of atoms of each element in a compound. To find the molecular formula, we need to know the molar mass of the compound.
Based on the given information, the molar mass of the compound is between 90 g and 95 g.
Dividing the molar mass of the compound by the molar mass of the empirical formula will give us the ratio of the molecular formula to the empirical formula.
Molecular formula ratio = (Molar mass of the compound) / (Molar mass of the empirical formula)
= (between 90 g and 95 g) / 30.01 g/mol
≈ 3
Thus, the molecular formula is 3 times the empirical formula:
Molecular formula = (N1O1)3 ≈ N3O3, which simplifies to N2O3.
Therefore, the molecular formula of the compound is N2O3 and the molar mass of the compound is 3 × (Molar mass of NO) ≈ 3 × 30.01 g/mol ≈ 90.03 g/mol.