7.25 g of iron were reacted with sulfur until the product reached a constant mass of 13.50 g. If the experimental molecular mass of the product was measured as 572 u, what is the molecular formula of the product? What is the actual molecular mass of the product?
To determine the molecular formula and actual molecular mass of the product, we need to calculate the empirical formula and use the experimental molecular mass.
Step 1: Calculate the number of moles of iron used.
To find the number of moles of iron, we can use the formula:
moles = mass / molar mass
Given:
Mass of iron (Fe) = 7.25 g
Molar mass of iron (Fe) = 55.85 g/mol
moles of iron = 7.25 g / 55.85 g/mol
moles of iron ≈ 0.13 mol
Step 2: Determine the empirical formula.
The empirical formula represents the simplest whole-number ratio of atoms in a compound.
Since we reacted iron with sulfur, and the compound reached a constant mass, we know that the ratio of iron to sulfur is 1:1. So the empirical formula is FeS.
Step 3: Calculate the empirical formula mass.
The empirical formula mass can be calculated by summing up the atomic masses of each element in the empirical formula.
Atomic mass of iron (Fe) = 55.85 g/mol
Atomic mass of sulfur (S) = 32.07 g/mol
Empirical formula mass = atomic mass of Fe + atomic mass of S
Empirical formula mass = 55.85 g/mol + 32.07 g/mol
Empirical formula mass ≈ 87.92 g/mol
Step 4: Calculate the molecular formula.
To find the molecular formula, we need to compare the empirical formula mass to the experimental molecular mass.
Experimental molecular mass = 572 u
Molecular formula = (Experimental molecular mass) / (Empirical formula mass)
Molecular formula = 572 u / 87.92 g/mol
Molecular formula ≈ 6.50
Since the molecular formula should be a whole number, we can multiply by a whole number to get a molecular formula. In this case, we can multiply the empirical formula by 8 to get the molecular formula.
Molecular formula = 8 * empirical formula
Molecular formula = 8 * FeS
Molecular formula = Fe8S8
Step 5: Calculate the actual molecular mass.
To determine the actual molecular mass, we multiply the empirical formula mass by the number of empirical formula units in the molecular formula.
Actual molecular mass = 8 * empirical formula mass
Actual molecular mass ≈ 8 * 87.92 g/mol
Actual molecular mass ≈ 703.36 g/mol
Therefore, the molecular formula of the product is Fe8S8, and the actual molecular mass is approximately 703.36 g/mol.
To determine the molecular formula of the product, we need to first find the empirical formula and then calculate the molecular formula.
Step 1: Determine the empirical formula
1. Calculate the moles of iron (Fe) reacted:
- Moles of Fe = mass of Fe / molar mass of Fe
- Moles of Fe = 7.25 g / 55.845 g/mol (molar mass of Fe)
- Moles of Fe = 0.13 mol (approx.)
2. Calculate the moles of sulfur (S):
- Since iron reacts with sulfur in a 1:1 ratio, the moles of sulfur will be the same as the moles of iron. Therefore, the moles of sulfur are also 0.13 mol.
3. Write the empirical formula using the moles of each element:
- Empirical formula = FeS
- This means there is one iron atom and one sulfur atom in each formula unit of the compound.
Step 2: Calculate the molecular formula
1. Calculate the molar mass of the empirical formula:
- Molar mass of FeS = (molar mass of Fe) + (molar mass of S)
- Molar mass of FeS = (55.845 g/mol) + (32.06 g/mol) (molar mass of S)
- Molar mass of FeS = 87.905 g/mol
2. Calculate the ratio between the experimental molar mass and the molar mass of the empirical formula:
- Ratio = (experimental molar mass) / (molar mass of empirical formula)
- Ratio = 572 u / 87.905 g/mol (molar mass of FeS)
- Ratio ≈ 6.5
3. Multiply the subscripts in the empirical formula by the ratio obtained in step 2:
- Molecular formula = (empirical formula) × ratio
- Molecular formula = FeS6.5
However, in this case, we can't have a fractional subscript in a molecular formula, so we need to round it to the nearest whole number:
- Molecular formula = FeS6.5 ≈ FeS7
So, the molecular formula of the product is FeS7.
To find the actual molecular mass of the product, we multiply the molar mass of the empirical formula (FeS) by the whole number subscript:
- Actual molecular mass = (molar mass of empirical formula) × (subscript)
- Actual molecular mass = 87.905 g/mol × 7
- Actual molecular mass = 615.335 g/mol (approx.)
Therefore, the actual molecular mass of the product is approximately 615.335 g/mol.