# How do you calculate the percent composition of lactose, C_12H_22O_11?

Mar 7, 2016

You add up the masses of all the atoms, and then you calculate the percentage of each element.

#### Explanation:

We can calculate the molecular mass of lactose as follows:

12 color(red)(cancel(color(black)("atoms C"))) × "12.01 u"/(1 color(red)(cancel(color(black)("atom C")))) = "144.12 u"
22 color(red)(cancel(color(black)("atoms H"))) × "1.008 u"/(1 color(red)(cancel(color(black)("atom H")))) =color(white)(l) "22.18 u"
11 color(red)(cancel(color(black)("atoms O"))) × "16.00 u"/(1 color(red)(cancel(color(black)("atom O")))) = "176.00 u"
$\text{TOTAL"color(white)(mmmmmmmmll) = "342.30 u}$

The mass percentages of each element are:

"% C" = (144.12 color(red)(cancel(color(black)("u"))))/(342.30 color(red)(cancel(color(black)("u")))) × 100 % = 42.10 %
"% H" = (22.18 color(red)(cancel(color(black)("u"))))/(342.30 color(red)(cancel(color(black)("u")))) × 100 % =color(white)(ll) 6.48 %
"% O" = (176.00 color(red)(cancel(color(black)("u"))))/(342.30 color(red)(cancel(color(black)("u")))) × 100 % =color(white)(l) 51.42 %

The composition of lactose is $\text{42.10 % C, 6.48 % H}$, and $\text{51.42 % O}$.