Question

How many grams are in 17.83 moles of carbon dioxide?

Answer 1

The mass of the carbon dioxide can be calculated using the formula of number of moles. The number of moles is calculated by dividing the mass by the molecular mass of the compound.

Complete step by step answer:
It is given that the moles present in carbon dioxide is 17.83 moles.
The mass of the substance is defined as the measure of the amount of matter in the substance. The SI unit of mass is kilogram. The smaller units are measured in grams.
The moles is the unit used to measure the large quantity of the small units like atom, molecules. 1 mole of any substance is equal to the value of $6.022 \times {10^{23}}$number be its atom or any molecule.
The relation between the mass and moles is given by the formula where the number of moles is calculated by dividing the mass of the substance with the molecular weight.
The molecular weight is calculated by adding the atomic weight of each atom present in the compound and if the atoms are present in number so the number is multiplied by the atomic weight.
The chemical formula of carbon dioxide is $C{O_2}$. The molecular weight of carbon dioxide is 44.09 g/mol.
The formula is shown below.
$n = \dfrac{m}{M}$
Where,
n is the number of moles
m is the mass
M is the molecular weight
To calculate the mass, substitute the values in the above equation.
$\Rightarrow 17.83 = \dfrac{m}{{44.09g/mol}}$
$\Rightarrow m = 17.83 \times 44.09$
$\Rightarrow m = 786.1247$g
Therefore, 786.1247 grams are in 17.83 moles of carbon dioxide.

Note:
The value $6.022 \times {10^{23}}$is the Avagadro’s number which is defined as the number of atoms present in 12 g of carbon-12. The atomic weight is the average sum of the mass of isotopes of the atoms each multiplied with their natural abundance value.