Question

The ionization energy of sodium is $495\text{ KJmo}{{\text{l}}^{-1}}$ . How much energy is needed to convert atoms present in $2.3 mg$ of sodium into sodium ions?
a.) $4.95 J$
b.) $49.5 J$
c.) $495 J$
d.) $0.495 J$

Answer 1

Ionization of the sodium per mole is given, so try to find out the number of moles of the sodium present in the given mass of the sodium and then multiply the given energy per mole and total number of moles to obtain the total energy required for the given mass.

Complete Solution :
- Ionization energy can be defined as the minimum amount of energy required to remove an electron from the outer most orbit of the atom in the ground state of an isolated gaseous atom. This energy is called the Ionization potential.

Given the mass of sodium is $2.3mg$
Convert this into grams
That is the weight of the sodium is $2.3\times {{10}^{-3}}g$
We know that the number of moles in an element is equal to the ratio of the given weight to the molecular weight of the element.
- Therefore the number of moles present in $2.3mg$ of sodium is $\dfrac{2.3\times {{10}^{-3}}}{23} = 0.1\times {{10}^{-3}}$
- The ionization energy required to convert $2.3mg$ of sodium into sodium ions is = (number of moles present in sodium) $\times$ (ionization energy per mole of sodium)
Given ionization energy per mole of sodium is = $495\text{ KJmo}{{\text{l}}^{-1}}$
Therefore the required ionization energy is = $495\text{ KJmo}{{\text{l}}^{-1}}\times 0.1\times {{10}^{-3}}=49.5J$
So, the correct answer is “Option B”.

Note: The number of moles is the ratio of the weight in grams of the atom to the gram molecular weight of the atom, so when the weight is given in any other units other than grams then first we need to convert the weight into grams and should be proceed for the further calculations to avoid the calculation errors.