Question 8 of 36intermediate🔧 ApplyNumerical3 marks

Determine the molecular formula of an oxide of iron, in which the mass per cent of iron and oxygen are 69.9 and 30.1, respectively.

Correct Answer

Fe₂O₃

Exercise: EXERCISES | Q: 1.8 | (Page 26)
For More Understanding

Explanation

To determine the formula, we first convert the given mass percentages into grams, assuming a 100 g sample. This gives 69.9 g of iron and 30.1 g of oxygen. Next, we convert these masses into moles by dividing by their respective atomic masses. Finally, we find the simplest whole number ratio of the moles to obtain the empirical formula. Since the molar mass of the compound is not provided to distinguish it further, the empirical formula Fe₂O₃ serves as the molecular formula for this oxide of iron.

Solution Steps

  1. Step 1: Conversion of mass per cent to grams Assume 100 g of the iron oxide sample. Mass of iron (Fe) = 69.9 g Mass of oxygen (O) = 30.1 g

  2. Step 2: Convert into number of moles of each element Moles of iron = 69.9 g55.85 g mol−1=1.25 mol\frac{69.9 \text{ g}}{55.85 \text{ g mol}^{-1}} = 1.25 \text{ mol} Moles of oxygen = 30.1 g16.00 g mol−1=1.88 mol\frac{30.1 \text{ g}}{16.00 \text{ g mol}^{-1}} = 1.88 \text{ mol}

  3. Step 3: Convert into simplest whole number ratio Ratio of Fe : O = 1.25:1.881.25 : 1.88 Divide by the smallest number (1.25): Fe = 1.251.25=1\frac{1.25}{1.25} = 1 O = 1.881.25=1.5\frac{1.88}{1.25} = 1.5 Multiply by 2 to get whole numbers: Fe = 1×2=21 \times 2 = 2 O = 1.5×2=31.5 \times 2 = 3

    The simplest whole number ratio is 2:3. Thus, the empirical formula is Fe₂O₃. Since no molar mass is given to determine a multiple of the empirical formula, the molecular formula is also Fe₂O₃.

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