Question

The percentage of boron in borax \[{\text{N}}{{\text{a}}_{\text{2}}}{{\text{B}}_{\text{4}}}{{\text{O}}_{\text{7}}}{\text{.10}}{{\text{H}}_{\text{2}}}{\text{O}}\] is:
(H=1, B=11, O=16, Na=23)
A.22.5 %
B.17.4 %
C.11.5 %
D.23 %

Answer 1

Hint: Sodium tetraborate decahydrate also known as borax has the chemical formula, \[{\text{N}}{{\text{a}}_{\text{2}}}{{\text{B}}_{\text{4}}}{{\text{O}}_{\text{7}}}{\text{.10}}{{\text{H}}_{\text{2}}}{\text{O}}\]. The amount of borax can be calculated from the below formula:
\[{\text{Percentage of Boron = }}\dfrac{{{\text{Molecular weight of Boron}}}}{{{\text{Molecular weight of Borax}}}}{\text{x 100}}\]

Complete step by step answer:
The chemical compound Borax is a white powdery mineral that is used as a cleaning product. It is also known as sodium tetraborate decahydrate with chemical formula \[{\text{N}}{{\text{a}}_{\text{2}}}{{\text{B}}_{\text{4}}}{{\text{O}}_{\text{7}}}{\text{.10}}{{\text{H}}_{\text{2}}}{\text{O}}\].
The molecular weight of boron and borax is needed to calculate the percentage of boron in borax.
The compound borax has 4 boron atoms as given in the chemical formula.
Molecular weight of boron = 4 (Atomic weight of Boron)
 \Rightarrow Molecular weight of boron = 44 g/mol
Molecular weight of borax = 2 (Atomic weight of Sodium (Na)) + 4 (Atomic weight of Boron (B)) + 7 (Atomic weight of Oxygen (O)) + 10 (Molecular weight of water (\[{{\text{H}}_{\text{2}}}{\text{O}}\]))
 \Rightarrow Molecular weight of Borax = \[\left( {{\text{2 x 23}}} \right){\text{ + }}\left( {{\text{4 x 11}}} \right){\text{ + }}\left( {{\text{ 7 x 16}}} \right){\text{ + }}\left( {{\text{10 x 18}}} \right)\]
 \Rightarrow Molecular weight of Borax = \[{\text{46 + 44 + 112 + 180 = 382 g/mol}}\]
The amount of borax can be calculated from the below formula:
\[
  {\text{Percentage of Boron = }}\dfrac{{{\text{Molecular weight of Boron}}}}{{{\text{Molecular weight of Borax}}}}{\text{x 100}} \\
   \Rightarrow {\text{Percentage of Boron = }}\dfrac{{{\text{44}}}}{{{\text{382}}}}{\text{x}}100 \\
   \Rightarrow {\text{Percentage of Boron = }}11.5\% \\
\]
The percentage of boron in borax \[{\text{N}}{{\text{a}}_{\text{2}}}{{\text{B}}_{\text{4}}}{{\text{O}}_{\text{7}}}{\text{.10}}{{\text{H}}_{\text{2}}}{\text{O}}\] is 11.5%.

So, the correct option is C.

Additional information:
 Borax is a decahydrate compound. It is a household cleaner and a booster for laundry detergent.
The term borax is used in general for following three chemical compounds:
Anhydrous sodium tetraborate, \[{\text{N}}{{\text{a}}_{\text{2}}}{{\text{B}}_{\text{4}}}{{\text{O}}_{\text{7}}}\]
Sodium tetraborate pentahydrate, \[{\text{N}}{{\text{a}}_{\text{2}}}{{\text{B}}_{\text{4}}}{{\text{O}}_{\text{7}}}{\text{.5}}{{\text{H}}_{\text{2}}}{\text{O}}\]
Sodium tetraborate decahydrate, \[{\text{N}}{{\text{a}}_{\text{2}}}{{\text{B}}_{\text{4}}}{{\text{O}}_{\text{7}}}{\text{.10}}{{\text{H}}_{\text{2}}}{\text{O}}\]or equivalently the octahydrate, \[{\text{N}}{{\text{a}}_{\text{2}}}{{\text{B}}_{\text{4}}}{{\text{O}}_{\text{7}}}{\text{.8}}{{\text{H}}_{\text{2}}}{\text{O}}\]

Note:
Borax is a combination of sodium, oxygen and boron. It is a very useful cleaning agent. But highly toxic when ingested by humans. It also used to disinfect and kill pests.