# How many molecules are in 10.8 grams of C_12H_22O_11?

Nov 12, 2015

$1.901 \times {10}^{22}$

#### Explanation:

The question is how many molecules are in a determined amount of an specific compound.

First step to obtain the number of moles, that is the mass/MW

$\text{no. of moles" = "mass"/"molar mass}$

The MW in this case is the sum of the atomic weights of the different atoms in the composition of the compound.

For this specific case it is ${C}_{12} {H}_{22} {O}_{11}$, is possible for a fast calculation to use the integer weights for $C$, $H$ and $O$, $12$, $1$ and $16$ respectively.

Then MW $= 12 \left(12\right) + 22 \left(1\right) + 11 \left(16\right) = \text{342 g/mol}$

moles $= \text{mass"/"MW" = ("10.8 g"/"342 g/mol") = "0.03157 moles}$

The number of molecules per mol is defined by the Avogadro's number $6.0221409 \times {10}^{23}$,

Giving up the numer of molecules as

$0.03157 \times 6.022 \times {10}^{23} = 1.901 \times {10}^{22}$