Use the Ar values below to calculate

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Use the Ar values below to calculate: (Ar values: Fe = 55.80, B = 10.80, O = 16.00) 1-the relative molecular mass of iron(III) borate, Fe(BO2 )3 . 2- the number of moles in 92.1g of iron(III) borate

The Correct Answer and Explanation is:

Let’s solve each part step by step using the given Ar values:

  • Fe = 55.80
  • B = 10.80
  • O = 16.00

1. Relative Molecular Mass of Iron(III) Borate, Fe(BO₂)₃

Iron(III) borate has the chemical formula Fe(BO₂)₃.

We break this compound down:

  • 1 Fe atom
  • 3 BO₂ groups
    • Each BO₂ group has 1 B and 2 O atoms

So, in total:

  • 1 Fe
  • 3 × 1 = 3 B
  • 3 × 2 = 6 O

Now multiply the Ar (atomic relative mass) by the number of atoms:

  • Fe: 1 × 55.80 = 55.80
  • B: 3 × 10.80 = 32.40
  • O: 6 × 16.00 = 96.00

Add them all together:
Relative molecular mass = 55.80 + 32.40 + 96.00 = 184.20 g/mol

2. Number of Moles in 92.1 g of Iron(III) Borate

Use the formula: Moles=MassRelative Molecular Mass\text{Moles} = \frac{\text{Mass}}{\text{Relative Molecular Mass}}

Given:

  • Mass = 92.1 g
  • Relative Molecular Mass = 184.20 g/mol

Moles=92.1184.20≈0.500 mol\text{Moles} = \frac{92.1}{184.20} ≈ 0.500 \text{ mol}

Explanation

To find the relative molecular mass of a compound, we sum up the relative atomic masses (Ar) of each element, considering how many atoms of each are present. For iron(III) borate, the chemical formula is Fe(BO₂)₃. This means the compound consists of one iron (Fe) atom and three borate units (BO₂). Each BO₂ group contains one boron (B) and two oxygen (O) atoms.

By multiplying the Ar values with the number of respective atoms—Fe (55.80), B (10.80), and O (16.00)—we find the total relative molecular mass is 184.20 g/mol.

In part two, we apply a basic concept from chemistry: the mole. A mole is a standard unit for amount of substance, and one mole of a compound has a mass equal to its molecular mass in grams. To calculate how many moles are in a given mass (here, 92.1 g), we divide the mass by the relative molecular mass. Moles=Given MassMolar Mass=92.1184.20≈0.500 mol\text{Moles} = \frac{\text{Given Mass}}{\text{Molar Mass}} = \frac{92.1}{184.20} ≈ 0.500 \text{ mol}

This tells us that 92.1 g of Fe(BO₂)₃ contains 0.500 moles of the compound. These calculations are foundational in chemistry, especially when converting between mass and amount in reactions, determining reagent quantities, or calculating yield.

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