A certain amount of energy is completely consumed to convert a sample of gaseous beryllium atoms into Be ²⁺ (g) ions. If the total energy supplied is 13.28 kJ , the mass of the beryllium sample ionized is _______ mg . [Given: First and second ionization enthalpies of Be are 899 kJ mol ⁻¹ and 1757 kJ mol ⁻¹ respectively. Molar mass of Be = 9 g mol ⁻¹ ]

Step-by-step solution

The conversion of Be(g) to Be ²⁺ (g) requires the removal of two electrons. Total ionization energy required per mole = IE₁ + IE₂ = 899 + 1757 = 2656 kJ mol ⁻¹ Total energy supplied = 13.28 kJ Number of moles of Be ionized = 13.28 kJ 2656 kJ mol ⁻¹ = 0.005 mol Mass of Be in grams = 0.005 mol 9 g mol ⁻¹ = 0.045 g Mass in milligrams = 0.045 1000 = 45 mg Answer: 45