Question

It takes 554 kJ to remove one mole of electrons from the atoms at the surface of a solid metal. How much energy does it take to remove a single electron from an atom at the surface of this solid metal?

Answer 1

To find the energy needed to remove a single electron from an atom on the metal's surface, divide the total energy for one mole (554 kJ) by Avogadro's number and convert the result to electron-volts, yielding approximately 1.38 eV per electron.

Step-by-step explanation:

To determine the energy required to remove a single electron from an atom at the surface of the solid metal, we start with the information that it takes 554 kJ to remove one mole of electrons. Knowing that one mole contains approximately 6×10²³ atoms, we divide the total energy by the number of atoms to obtain the energy per single electron.

The calculation is as follows:

• 
  
• Energy per mole of electrons = 554,000 J (since 1 kJ = 1000 J)
• 
  
• Number of electrons in one mole = 6×10²³ electrons
• 
  
• Energy per electron = 554,000 J / 6×10²³ electrons

This gives us an energy value in joules. To convert this value to electron-volts (eV), we use the conversion factor where 1 eV = 1.6×10⁻¹⁹ J.

Energy per electron in eVs: (554,000 J / 6×10²³) / 1.6×10⁻¹⁹ J/eV = approximately 1.38 eV per electron

Answer 2

E = 9.2x10^-22 kJ/atom

Step-by-step explanation:

Ok to do this, we only need to do simple conversions, and then, we will get the final answer for this.

Now, we know the energy required to remove one mole of electrons which in this case is 554 kJ. This can be interpreted as 554 kJ/mol, which means that every mol of the solid metal consumes 554 kJ of energy to be removed.

We also know by principle definition that in 1 mole of electron we have 6.02x10^23 atoms.

This works with almost every atom of the periodic table.

So, if 1 mole contains 6.02x10^23 atoms, we can know by rule of three how much energy is required to remove the mole from an atom:

1 mole/6.02x10^23 mol/atom

and if we have the energy of 554 kJ/mole, let's cancel both moles, by doing a division, and we will have the energy required per atom:

E = 554 kJ/mole / 6.02x10^23 mole/atom

E = 9.2x10^-22 kJ/atom

This is the energy required to remove an atom from the metal