Question

the first ionization energy for calcium is 590 kj/mol. which equation represents the second ionization energy for a calcium atom?
$\text{ca}^+ \
ightarrow \text{ca}^{2+} + \text{e}^- + 590\\ \text{kj}$
$\text{ca}^+ \
ightarrow \text{ca}^{2+} + \text{e}^- + 1145\\ \text{kj}$
$590\\ \text{kj} + \text{ca}^+ \
ightarrow \text{ca}^{2+} + \text{e}^-$
$1145\\ \text{kj} + \text{ca}^+ \
ightarrow \text{ca}^{2+} + \text{e}^-$

Explanation:

Step1: Define second ionization energy

Second ionization energy is the energy required to remove a second electron from a +1 cation of an element to form a +2 cation, so energy is a reactant.

Step2: Match Ca's second ionization reaction

Calcium's second ionization starts with $\text{Ca}^+$, requires energy input, produces $\text{Ca}^{2+}$ and $\text{e}^-$. The second ionization energy of Ca is 1145 kJ/mol (higher than first ionization energy).

Answer:

1145 kJ + Ca⁺ → Ca²⁺ + e⁻