Question

How many grams of \[O\] are contained in \[8.52{\text{ }}g\] \[{K_2}C{O_3}\] ?

Answer 1

Hint: Here you should recall the concept of molar mass of any chemical compound which refers to the ratio of mass of a sample of that particular compound and the amount of substance in that particular sample (in moles). The molar mass is generally represented as \[gmo{l^{ - 1}}\] .

Complete step by step answer:
 In order to calculate the grams of \[O\] are contained in \[8.52{\text{ }}g\] \[{K_2}C{O_3}\] , first of all we have to calculate the molar mass of \[{K_2}C{O_3}\] . We know that the molar mass of any compound can be found out by adding the relative atomic masses of each element present in that particular compound. The number of atoms in a compound can be determined from their chemical formula.
Now, let us calculate the molar mass of the given compound i.e. potassium carbonate having a chemical formula of \[{K_2}C{O_3}\] . We already know the atomic masses of potassium, carbon and oxygen as stated below:
$
  K = 39.0983amu \\
  C = 12.0107amu \\
  O = 15.999amu \\
$
Molar mass of this compound can be calculated by adding the mass of two potassium atoms, one carbon atom and three oxygen atoms as shown below:
$
  Molar{\text{ }}mass{\text{ }}of{\text{ }}{{\text{K}}_2}C{O_3} = (2 \times K) + (1 \times C) + (3 \times O) \\
   = (2 \times 39.0983) + (1 \times 12.0107) + (3 \times 15.999) = 138.2043gmo{l^{ - 1}} \\
$
Now, in order to calculate the number of moles, we generally use the following formula:
$Number{\text{ }}of{\text{ }}moles = \dfrac{{Mass(g)}}{{Molar{\text{ }}mass(gmo{l^{ - 1}})}}$
Mass of \[{K_2}C{O_3}\] = \[8.52{\text{ }}g\] (Given)
Thus substituting the values, we get:
$Number{\text{ }}of{\text{ }}moles{\text{ }}of{\text{ }}{K_2}C{O_3} = \dfrac{{8.52g}}{{138.2043gmo{l^{ - 1}}}} = 0.0616moles$
Now, we will use the unitary method to get the final answer.
One mole of \[{K_2}C{O_3}\] contains 3 moles of oxygen
 \[0.0616{\text{ }}moles\] \[{K_2}C{O_3}\] will contain $\dfrac{3}{1} \times 0.0616 = 0.1848moles{\text{ }}of{\text{ }}O$
Mass in grams of oxygen can be calculated from number or moles formula as depicted below:
$
  0.1848 = \dfrac{{Mass(g)}}{{15.999}} \\
  Mass(g) = 15.999 \times 0.1848 = 2.9566g \\
$

Hence, \[2.9566\] grams of \[O\] are contained in \[8.52{\text{ }}g\] \[{K_2}C{O_3}\] .

Note: Molar mass plays a significant role in chemistry especially during setting up an experiment. During testing principles which involve specific amounts or quantities of a substance, molar mass is used to figure out the exact quantity to be weighed of that particular substance. Basically molar mass is used to determine the stoichiometry in the chemical reactions as well as equations.