Question

For the following reaction the mass of water produced from 445 g of \[{{\text{C}}_{57}}{{\text{H}}_{110}}{{\text{O}}_6}\] is:
\[{\text{2}}{{\text{C}}_{57}}{{\text{H}}_{110}}{{\text{O}}_6}({\text{s}}) + 163{{\text{O}}_2} \to 114{\text{C}}{{\text{O}}_2}({\text{g}}) + 110{{\text{H}}_2}{\text{O}}({\text{l}})\]
A.495 g
B.490 g
C.890 g
D.445 g

Answer 1

Hint: First of all we will calculate number of moles of \[{{\text{C}}_{57}}{{\text{H}}_{110}}{{\text{O}}_6}\] using the formula. From the balanced chemical reaction given we will get to know number of moles of water produced from the calculated number of moles of \[{{\text{C}}_{57}}{{\text{H}}_{110}}{{\text{O}}_6}\] . From the number of moles of water and molar mass, we can calculate the mass of water produced.
Formula used:
\[{\text{no}}{\text{. of moles}} = \dfrac{{{\text{mass}}}}{{{\text{molar mass}}}}\]

Complete step by step answer:
Let us first calculate the molar mass of \[{{\text{C}}_{57}}{{\text{H}}_{110}}{{\text{O}}_6}\]. Molar mass of carbon is 12 amu, molar mass of hydrogen is 1 and molar mass of oxygen is 16 amu. Molar mass can be calculated by multiplying molar mass of respective elements multiplied their number of atoms.
Hence the molar mass will be:
\[57 \times 12 + 1 \times 110 + 6 \times 16 = 890{\text{ g mo}}{{\text{l}}^{ - 1}}\]
Given mass of \[{{\text{C}}_{57}}{{\text{H}}_{110}}{{\text{O}}_6}\] is 445 g.
\[{\text{no}}{\text{. of moles of }}{{\text{C}}_{57}}{{\text{H}}_{110}}{{\text{O}}_6} = \dfrac{{{\text{445}}}}{{{\text{890}}}} = 0.5\]
The given equation is:
\[{\text{2}}{{\text{C}}_{57}}{{\text{H}}_{110}}{{\text{O}}_6}({\text{s}}) + 163{{\text{O}}_2} \to 114{\text{C}}{{\text{O}}_2}({\text{g}}) + 110{{\text{H}}_2}{\text{O}}({\text{l}})\].
From the equation it is clear that 2 mole of \[{{\text{C}}_{57}}{{\text{H}}_{110}}{{\text{O}}_6}\] produces 110 moles of water. So 1 mole of \[{{\text{C}}_{57}}{{\text{H}}_{110}}{{\text{O}}_6}\] will give us 55 moles of water and hence,
\[0.5\] mole of \[{{\text{C}}_{57}}{{\text{H}}_{110}}{{\text{O}}_6}\] will give \[\dfrac{{55}}{2} = 27.5\] mole of water.
So the number of moles of water are \[27.5\]. The molar mass of water is \[1 \times 2 + 16 = 18{\text{ g mo}}{{\text{l}}^{ - 1}}\]
Using the formula we will get mass of water as:
\[{\text{mass}} = 27.5 \times 18{\text{ g}} = 495{\text{ g}}\]

Hence the correct option is A.

Note:
The above reaction is a combustion reaction. The complete combustion of hydrocarbons in the presence of oxygen produces carbon dioxide gas and water. The partial oxidation results in production of carbon monoxide and unburnt hydrocarbons. The name of \[{{\text{C}}_{57}}{{\text{H}}_{110}}{{\text{O}}_6}\] is stearin. It is used in candles and soaps as a hardening agent. When mixed with sodium hydroxide it gives sodium stearate which is a main ingredient of soap.