Energy of an electron in the ground state of the hydrogen atom is –2.18×10–18J. Calculate the ionization enthalpy of atomic hydrogen in terms of J mol–

To calculate the ionization enthalpy of atomic hydrogen in terms of J/mol, we start by understanding what ionization enthalpy means. Ionization enthalpy is the energy required to remove an electron from an atom in its gaseous state. For hydrogen, this process involves moving the electron from its ground state to a point where it is no longer bound to the nucleus, which means we need to consider the energy of the electron in its ground state.

Understanding the Ground State Energy

The energy of an electron in the ground state of the hydrogen atom is given as –2.18 × 10^–18 J. This value indicates that the electron is in a bound state, and energy must be supplied to remove it from this state.

Calculating Ionization Energy

To ionize the hydrogen atom, we need to provide enough energy to bring the electron's energy level from –2.18 × 10^–18 J to 0 J (the energy level of a free electron). The energy required for this transition is simply the absolute value of the ground state energy:

• Ionization Energy (E_ion) = 0 J - (–2.18 × 10^–18 J)
• E_ion = 2.18 × 10^–18 J

Converting to J/mol

Now that we have the ionization energy for a single hydrogen atom, we need to convert this value into J/mol. To do this, we use Avogadro's number, which is approximately 6.022 × 10²³ mol^–1. This number tells us how many atoms are in one mole of a substance.

• Ionization Enthalpy (ΔH_ion) = E_ion × Avogadro's number
• ΔH_ion = 2.18 × 10^–18 J × 6.022 × 10²³ mol^–1

Performing the Calculation

Now, let's do the math:

• ΔH_ion = 2.18 × 10^–18 J × 6.022 × 10²³ mol^–1
• ΔH_ion ≈ 1.31 × 10⁶ J/mol

Final Result

The ionization enthalpy of atomic hydrogen is approximately 1.31 × 10⁶ J/mol. This value represents the energy required to completely remove one mole of electrons from one mole of hydrogen atoms in their ground state, highlighting the energy dynamics involved in atomic interactions.