Answer to Question #129894 in General Chemistry for Nicole Xie

Question

Carbohydrates are compounds of carbon, hydrogen, and oxygen in which the ratio of hydrogen atoms

to oxygen atoms is 2:1. A certain carbohydrate is known to be 40.0 % carbon. Its molar mass is

approximately 180 g/mol. Determine the carbohydrate’s empirical formula and molecular formula.

Answer 1

The water component per 100.0g of carbohydrate molecule is determined through subtracting the mass of C per 100.0g of carbohydrates from 100.0g of carbohydrate.

$m_{carb}=m_c+m_{H_20}$

Where $m_{carb}$ is the mass of carbohydrate

$m_{H_20}=m_{carb}-m_c$

$=100.0g-40.0g$

$=60.0g$

The mass of each compound is converted to moles using the relative molar mass of the compounds.

$=$ $40gC\over 12.0107gC$ $\times$ $1molC$ $=3.3304 mol C$

$60gH_2O\over 18.0152$ $\times$ $1mol H_20$ $=$ $3.3305mol H_20$

Number of moles of each component relative to other components is determined by dividing all quantities by the smallest amount of moles.

$=($ $3.3304mol\over 3.3304mol$ $)$ $C=1C$

$($ $3.3305mol\over 3.3304mol$ $)H_20=1H_20$

The empirical formula of the compound is $CH_20$

Molar mass of the empirical formula is;

$12.0107g/mol$ $+2(1.0079g/mol)+15.9994g/mol=30.0529g/mol$

Molecular molar mass decided by the empirical molar mass gives us the molecular formula (n)which is a whole number multiple of the empirical formula.

$n=$ $180g/mol\over 30.0259g/mol$ $=$ $6$

The molecular formula is obtained through multiplication of subscripts of the empirical formula by $n$

$6(1)C=6C$

$6(2)H=12H$

$6(1)O=6O$

The molecular formula is therefore;

$C_6H_{12}O_6$