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Calculate the number of atoms in 0.9g of aluminium.

Chemistry

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  1. Calculate the number of moles of aluminium in 0.9 g.

    The molar mass of aluminium (Al) is given as 27 g/mol.

    Moles of Al=Mass of AlMolar mass of Al\text{Moles of Al} = \frac{\text{Mass of Al}}{\text{Molar mass of Al}} Moles of Al=0.9 g27 g/mol\text{Moles of Al} = \frac{0.9 \text{ g}}{27 \text{ g/mol}} Moles of Al=0.0333... mol\text{Moles of Al} = 0.0333... \text{ mol} Moles of Al=130 mol\text{Moles of Al} = \frac{1}{30} \text{ mol}
  2. Calculate the number of atoms in this amount of aluminium.

    We are given that 1 mole of aluminium contains 6×10236 \times 10^{23} atoms.

    Number of atoms=Moles of Al×Avogadro’s number\text{Number of atoms} = \text{Moles of Al} \times \text{Avogadro's number} Number of atoms=130 mol×6×1023 atoms/mol\text{Number of atoms} = \frac{1}{30} \text{ mol} \times 6 \times 10^{23} \text{ atoms/mol} Number of atoms=630×1023 atoms\text{Number of atoms} = \frac{6}{30} \times 10^{23} \text{ atoms} Number of atoms=15×1023 atoms\text{Number of atoms} = \frac{1}{5} \times 10^{23} \text{ atoms} Number of atoms=0.2×1023 atoms\text{Number of atoms} = 0.2 \times 10^{23} \text{ atoms} Number of atoms=2.0×1022 atoms\text{Number of atoms} = 2.0 \times 10^{22} \text{ atoms}

    Comparing this result with the given options:
    A. 1.0×10211.0 \times 10^{21}
    B. 6.6×10216.6 \times 10^{21}
    C. 2.0×10222.0 \times 10^{22}
    D. 6.0×10226.0 \times 10^{22}

    The calculated number of atoms matches option C.

    The number of atoms contained in 0.9g of aluminium is C. 2.0×1022\boxed{\text{C. } 2.0 \times 10^{22}}.

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