Question

What mass (in Kg) of\[{{K}_{2}}O\] contains the same number of moles of K atoms as in 1.0 kg KCl?
A. 0.158 kg
B. 0.315 kg
C. 1.262 kg
D. 0.631 kg

Answer 1

Hint: Number of moles of any atom is the value of Avogadro number of atoms which are $6.022\times {{10}^{23}}$ atoms. The molar mass of any molecule is represented in grams per mole, which is the mass per mole that is $6.022\times {{10}^{23}}$ atoms of that molecule. Gram can be converted to kilogram by the factor 1 kg = 1000 g.

Complete answer:
We have been given to find the mass (in kg) of \[{{K}_{2}}O\], whose number of moles is equal to the number of moles of potassium in KCl with 1.0 kg mass. For this first we have to take out the number of moles in 1.0 kg of KCl, then taking out the moles of \[{{K}_{2}}O\] we will get the mass. We will use the relation between number of moles, given mass and molar mass, which is
Number of moles = $\dfrac{given\,mass}{molar\,mass}$
Now, taking out the number of moles in KCl, we have given mass as 1.0 kg and molar mass of KCl is
Mass of (K + Cl) = 39 + 35.5 = 74.5 g/mol.
Thus we have, Number of moles = $\dfrac{1000\,g}{74.5\,g\,mo{{l}^{-1}}}$(converting kg into g)
Number of moles of KCl = 13.4228 moles
Now, as 1 mole of \[{{K}_{2}}O\] has 2 potassium atoms, so moles of \[{{K}_{2}}O\]=$\dfrac{moles\,of\,KCl}{2}$
So, number of moles of \[{{K}_{2}}O\]=$\dfrac{13.4228}{2}$ = 6.711 moles
Now, calculating the mass for \[{{K}_{2}}O\] in 6.711 moles, and molar mass 94 g/mol we have,
Mass of \[{{K}_{2}}O\]=$moles\,of\,{{K}_{2}}O\times molar\,mass$
Mass of \[{{K}_{2}}O\]= 6.711 moles $\times $94 g/mol
Mass of \[{{K}_{2}}O\]= 630.834 g
Mass of \[{{K}_{2}}O\]= 0.631 kg
Hence, the mass (in Kg) of \[{{K}_{2}}O\] is 0.631 kg.

So option d is correct.

Note:
The molar mass of \[{{K}_{2}}O\] is calculated as 2 (mass of K) + mass of O = 2 (39) + 16 = 94 g/mol. This is the mass in 1 mole of \[{{K}_{2}}O\]. The conversion of kilogram into grams is 1 kg = 1000 g, therefore the conversion of gram into kilogram is 1 g = 0.001 kg or 1 g = $\dfrac{1}{1000}kg$ , so here it is converted as, $\dfrac{630.834}{1000}$ = 0.631 kg.