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Question: How much energy in kilojoules must be needed to convert all the atoms of sodium to sodium ions prese...

How much energy in kilojoules must be needed to convert all the atoms of sodium to sodium ions present in 2.3mg2.3mg of sodium vapour? Ionization energy of sodium is 495 KJ/mol495\text{ }KJ/mol (Atomic mass of Sodium is 2323 ).
(A) 295×10−4kJ/mol.295\times {{10}^{-}}^{4}kJ/mol.
(B) 195×10−2kJ/mol.195\times {{10}^{-}}^{2}kJ/mol.
(C) 495×10−4kJ/mol.495\times {{10}^{-}}^{4}kJ/mol.
(D) 412×10−3kJ/mol.412\times {{10}^{-}}^{3}kJ/mol.

Explanation

Solution

We know that the 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 answer:
Ionization energy can be defined as the minimum amount of energy required to remove an electron from the outermost 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.2.3mg. Convert this into grams that is the weight of the sodium is 2.3×10−3g.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. Ionisation energy: The Minimum energy required to remove the most loosely held outermost shell electron in the ground state from an isolated gaseous atom is known as ionization potential.
Thus, Number of moles of sodium =2.3×10−323=0.1×10−3mole=\dfrac{2.3\times {{10}^{-3}}}{23}=0.1\times {{10}^{-3}}mole
So energy needed to convert into ions =495×103(0.1×10−3)=49.5=495\times {{10}^{3}}(0.1\times {{10}^{-3}})=49.5
Thus, it can be rewritten as 49.5=495kJ/moles.49.5=495kJ/moles.
Therefore, the correct answer is option C.

Additional Information:
The energy required to remove an electron from an isolated gaseous atom is known as ionization energy. To remove the first electron the energy required is known as first ionization energy and energy required for the second electron is known as second ionization energy. Ionization energy is additive. If we do not convert the mg amount of magnesium vapour into gram then we will get our answer of moles.

Note:
Remember that 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.