Question

How would you calculate the mass in grams of \[4.52\times {{10}^{-3}}mol\] ${{C}_{20}}{{H}_{42}}$ ? Use the molar masses: $C=12.0gmo{{l}^{-1}}$ ; $H=1.0gmo{{l}^{-1}}$ .

Answer 1

Hint:Mole concept gives the relationship between the number of moles, weight and molar mass of the compound. Molar mass is calculated by adding up the atomic masses of the element combined to form a molecule.

Formula used:$n=\dfrac{w}{m}$
where, $n$ is the number of moles, $w$ is the weight of the compound and $m$ is the molar mass of the compound.
Mole concept gives the relationship between the number of moles, weight and molar mass of the compound. Molar mass is calculated by adding up the atomic masses of the element combined to form a molecule.


Complete step-by-step answer:In this question, it is given that the moles of ${{C}_{20}}{{H}_{42}}$ is $4.52\times {{10}^{-3}}$
The molar mass ${{C}_{20}}{{H}_{42}}$
Molar mass of carbon is $12.0gmo{{l}^{-1}}$
Molar mass of hydrogen is $1.0gmo{{l}^{-1}}$
Molar mass $\left( m \right)=$ $20\times 12+42\times 1$
Molar mass $\left( m \right)=$ $282gmo{{l}^{-1}}$
Now let us see the mole formula,
$n=\dfrac{w}{m}$
where, $n$ is the number of moles, $w$ is the weight of the compound and $m$ is the molar mass of the compound.
Now substitute the value in the above formula we get,
$4.52\times {{10}^{-3}}=\dfrac{w}{282}$
$w=4.52\times {{10}^{-3}}\times 282$
$w=1.27g$
The weight of ${{C}_{20}}{{H}_{42}}$ is $1.27g$.

Additional information:
A mole is defined as a scientific unit which is used to measure large quantities of atoms and molecules. It is defined as the amount of substance present in a sample.
$1mole=6.022\times {{10}^{23}}particles$
This is also called Avogadro's number $\left( {{N}_{A}} \right)$ .
Molar mass is defined as the addition of atomic mass of atoms, combined in a molecule. Here, the molar mass of ${{C}_{20}}{{H}_{42}}$ is $282gmo{{l}^{-1}}$ .
Moles are defined as the weight of the compound per molar mass of the compound.
Formula mass is different from molecular mass. In formula mass, there is an addition of atomic masses of ions present in an ionic compound, whereas molecular mass is the addition of atomic masses of the atoms in a molecule.

Note:In this question, we have concluded that by using molar mass of the compound and moles of the compound, we can easily calculate the weight of the compound by using mole formula. Here, we have substituted the given value in the formula to calculate the weight of the compound.
The molar mass is calculated in $gmo{{l}^{-1}}$ .