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28 December, 12:26

Calculate the mass of tetraborane (B4 H10) that contains a billion (1.0 x 10 * 9) boron atoms. Be sure your answer has a unit symbol if necessary, and round it to significant digigits.

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  1. 28 December, 15:07
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    a billion boron atoms are contained in a mass m = 2.21*10⁻¹⁴ gr of tetraborane

    Explanation:

    Since there are an Avogadro number (N = 6.023*10²³ molecules/mole) of molecules of tetraborane in a mole of tetraborane, and per each molecule there are 4 atoms of B. Then

    number of moles n = a / (4*N)

    where a = number of atoms

    the corresponding mass of tetraborane m is

    m = n*M

    where M = molecular weight of tetraborane = 53.32 g/mol

    then

    m = n*M = a*M / (4*N)

    replacing values

    m = a*M / (4*N) = 1.0*10⁹ atoms of B * 53.32 gr/mole / (4 atoms of B/molecule * 6.023*10²³ molecules/mole) = 2.21*10⁻¹⁴ gr

    m = 2.21*10⁻¹⁴ gr
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