Benzene reacts with hot concentrated nitric acid dissolved in sulfuric acid to give chiefly nitrobenzene, C6H5NO2. A by-product is often obtained, which consists of 42.86% C, 2.40% H, and 16.67% N (by mass). The boiling point of a solution of 5.5 g of the by-product in 45 g of benzene was 1.84°C higher than that of benzene.
I have no idea how to start.
Calculate the molecular formula of the by-product.
empirical formula is C3H2N10.
delta T = Kb*m
molar mass is 178
I thought we did all this yesterday.
You worked the formula on your own and I showed you how to do the molar mass and molecular formula.
To determine the molecular formula of the by-product, we need to calculate the empirical formula and then determine the multiple of the empirical formula that gives us the molecular formula.
Given information: The by-product consists of 42.86% carbon (C), 2.40% hydrogen (H), and 16.67% nitrogen (N) by mass.
Step 1: Calculate the number of moles for each element in the by-product.
To calculate the number of moles, we will assume we have 100 grams of the by-product. This assumption allows us to easily convert the percentages to grams.
- Carbon (C):
42.86% carbon mass = (42.86/100) * 100 g = 42.86 g
Moles of C = mass of C / molar mass of C = 42.86 g / 12.01 g/mol = 3.573 mol
- Hydrogen (H):
2.40% hydrogen mass = (2.40/100) * 100 g = 2.40 g
Moles of H = mass of H / molar mass of H = 2.40 g / 1.01 g/mol = 2.376 mol
- Nitrogen (N):
16.67% nitrogen mass = (16.67/100) * 100 g = 16.67 g
Moles of N = mass of N / molar mass of N = 16.67 g / 14.01 g/mol = 1.189 mol
Step 2: Divide the number of moles by the smallest number of moles.
To find the simplest whole-number ratio, we need to divide all moles by the smallest number of moles, which in this case is 1.189 (moles of nitrogen).
- Carbon (C):
3.573 mol / 1.189 mol = 3
- Hydrogen (H):
2.376 mol / 1.189 mol = 2
- Nitrogen (N):
1.189 mol / 1.189 mol = 1
The empirical formula is C3H2N.
Step 3: Determine the molecular formula.
To determine the molecular formula, we need the molar mass of the by-product. From the given information, the molar mass is 178 g/mol.
- Calculate the empirical formula mass:
Mass of empirical formula = (3 * molar mass of C) + (2 * molar mass of H) + molar mass of N
Mass of empirical formula = (3 * 12.01 g/mol) + (2 * 1.01 g/mol) + (14.01 g/mol)
Mass of empirical formula = 36.03 g/mol + 2.02 g/mol + 14.01 g/mol
Mass of empirical formula = 52.06 g/mol
- Determine the multiple:
Multiple = Molecular mass / Empirical formula mass
Multiple = 178 g/mol / 52.06 g/mol
Multiple = 3.42
- Multiply the empirical formula by the multiple to get the molecular formula:
Molecular formula = (C3H2N) * 3.42
Molecular formula = C10.26H6.84N
Since we need whole-number ratios for the molecular formula, we can round the subscripts:
Molecular formula = C10H7N
Therefore, the molecular formula of the by-product is C10H7N.