For Peroxyacyl nitrate (PAN)

A compound of C,H,N,O

Determine the empirical formula from the percent composition by mass:
19.8% C, 2.50% H, 11.6% N

What is its molecular formula given that its molar mass is about 120g?

figured it out :)

To determine the empirical formula of Peroxyacyl nitrate (PAN) based on the percent composition by mass, we need to find the ratio of the elements present.

Step 1: Convert the percent composition to grams.
Given:
- 19.8% C
- 2.50% H
- 11.6% N

Assuming we have 100g of the compound:
- C: 19.8g
- H: 2.50g
- N: 11.6g

Step 2: Calculate the number of moles of each element.
To find the number of moles, divide the mass of each element by its molar mass.

- The molar mass of carbon (C) is approximately 12.01 g/mol, so:
moles of C = 19.8g / 12.01 g/mol ≈ 1.64 mol

- The molar mass of hydrogen (H) is approximately 1.01 g/mol, so:
moles of H = 2.50g / 1.01 g/mol ≈ 2.47 mol

- The molar mass of nitrogen (N) is approximately 14.01 g/mol, so:
moles of N = 11.6g / 14.01 g/mol ≈ 0.829 mol

Step 3: Divide all the moles by the smallest number of moles.
Since the smallest number of moles is approximately 0.829 mol (from nitrogen), we divide the moles of all elements by 0.829.

- Moles of C: 1.64 mol / 0.829 mol ≈ 1.98
- Moles of H: 2.47 mol / 0.829 mol ≈ 2.98
- Moles of N: 0.829 mol / 0.829 mol = 1.00

Step 4: Round the resulting ratio to the simplest whole numbers.
Based on the previous step, we get a ratio of approximately 1.98:2.98:1.00 for C:H:N. By rounding these numbers to the nearest whole numbers, we end up with a ratio of 2:3:1.

Therefore, the empirical formula of Peroxyacyl nitrate (PAN) based on the percent composition by mass is C2H3N.

To determine the molecular formula of PAN, we need to know its molar mass. Given that the molar mass is about 120g, we compare this with the empirical formula mass.

Step 5: Calculate the empirical formula mass.
Empirical formula mass = (molar mass of C) × (# of carbon atoms) + (molar mass of H) × (# of hydrogen atoms) + (molar mass of N) × (# of nitrogen atoms)

The molar masses are:
- Carbon (C): 12.01 g/mol
- Hydrogen (H): 1.01 g/mol
- Nitrogen (N): 14.01 g/mol

Empirical formula mass = (12.01) × 2 + (1.01) × 3 + (14.01) × 1 ≈ 34.05 g/mol

Step 6: Find the factor to multiply the empirical formula by to obtain the molecular formula.
To find the factor, divide the molar mass of the PAN compound (given as about 120g) by the empirical formula mass (approximately 34.05 g/mol).

Factor = molecular mass of PAN / empirical formula mass
Factor = 120 g / 34.05 g/mol ≈ 3.52

Step 7: Multiply the subscripts of the empirical formula by the factor obtained in the previous step.
Empirical formula: C2H3N

Molecular formula = (C2) × 3.52 : (H3) × 3.52 : (N1) × 3.52
Molecular formula ≈ C7H11N3

Therefore, the molecular formula of Peroxyacyl nitrate (PAN) is approximately C7H11N3.