Question

How much sugar will be required if each person on earth is given ${10}^{13}$ molecules of sugar, if the population of earth is taken to be $3\times {10}^{10}$?

• A. $17.0375g$
• B. $170.375g$
• C. $34.086g$
• D. $340.86g$

Answer 1

The correct option is B $170.375g$

Total number of molecules required = $3\times {10}^{10}\times {10}^{13}=3\times {10}^{23}$
Gram atomic mass of a sugar molecule$\left(C_{12}{H}_{22}{O}_{11}\right)$
= {12 $\times$ Atomic mass of carbon} + { 22 $\times$ Atomic mass of hydrogen} + { 11 $\times$ Atomic mass of oxygen}
= {$12\times 12$} + {$22\times 1$} +{$11\times 16$}
$=144+22+176$
$=342$ g
So, $6.022\times {10}^{23}$ molecules weight $342$ g
$3\times {10}^{16}$ molecules weight
= $\frac{342}{6.022\times {10}^{23}}\times 3\times {10}^{23}$
=$170.375g$