Use Coulomb's law to calculate the ionization energy in kJ/mol of an atom composed of a proton and an electron separated by 176.00 pm .
To calculate the ionization energy of an atom using Coulomb's law, we need to find the attractive force between the proton and the electron when they are separated by a distance of 176.00 pm. The ionization energy is defined as the amount of energy required to remove an electron from an atom in its gaseous state.
Coulomb's law states that the force between two charged particles is directly proportional to the product of their charges and inversely proportional to the square of the distance between them. Mathematically, it can be expressed as:
F = (k * q1 * q2) / r^2
Where:
F is the force between the particles,
k is Coulomb's constant (8.99 × 10^9 N m^2/C^2),
q1 and q2 are the charges of the particles, and
r is the distance between the particles.
In this case, we have a proton (q1 = +1e) with a charge of +1 elementary charge and an electron (q2 = -1e) with a charge of -1 elementary charge. The elementary charge (e) is approximately 1.602 × 10^-19 C. The distance between them (r) is given as 176.00 pm, which is equivalent to 176.00 × 10^-12 m.
Plugging in the values into Coulomb's law formula, we get:
F = (8.99 × 10^9 N m^2/C^2) * (+1e) * (-1e) / (176.00 × 10^-12 m)^2
Calculating this equation, we find the force (F) between the proton and the electron.
Once we have the force, we can calculate the ionization energy (IE) using the equation:
IE = F * r
Since the ionization energy is typically expressed in kJ/mol, we can convert it by dividing by Avogadro's number (6.022 × 10^23 mol^-1).
Using this procedure, you can determine the ionization energy in kJ/mol for the given setup.
To calculate the ionization energy of an atom using Coulomb's law, we need to determine the force of attraction between the proton and electron at the given separation distance, and then convert it into energy.
Coulomb's law states that the force of attraction (F) between two charged particles is given by:
F = (k * q1 * q2) / r^2
where:
- F is the force of attraction
- k is the Coulomb constant (8.99 × 10^9 N m^2/C^2)
- q1 and q2 are the charges of the particles
- r is the separation distance.
In this case, since we have an atom composed of a proton and an electron, the charges are q1 = +1 (proton) and q2 = -1 (electron). The separation distance r is given as 176.00 pm, but we need to convert it to meters for consistency. Since 1 pm = 10^-12 m, the separation distance in meters is:
r = 176.00 pm * (1 m / 10^12 pm) = 176.00 × 10^(-12) m
Now, we can calculate the force of attraction:
F = (8.99 × 10^9 N m^2/C^2) * (+1 C) * (-1 C) / (176.00 × 10^(-12) m)^2
Simplifying the expression:
F = (8.99 × 10^9 N m^2/C^2) / (176.00 × 10^(-12) m)^2
Next, we need to convert the force into energy. The ionization energy (IE) is the energy required to remove an electron from an atom, so it is equal to the negative of the force:
IE = -F
Finally, we can calculate the ionization energy:
IE = -[(8.99 × 10^9 N m^2/C^2) / (176.00 × 10^(-12) m)^2]
Calculating this expression will give us the ionization energy in joules (J). To convert it into kilojoules per mole (kJ/mol), we need to use Avogadro's number (6.022 × 10^23) to scale the energy to a mole:
IE(kJ/mol) = (IE(J) * 6.022 × 10^23) / 1000
Performing the calculations will give us the final answer for the ionization energy in kJ/mol.