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.

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