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# Calculate‌ ‌the‌ ‌ratio‌ ‌of‌ ‌moles‌ ‌of‌ ‌moles‌ ‌of‌ ‌$3.6gm$‌ ‌ ‌water‌ ‌and‌ ‌$4.4gm$of‌ ‌carbon‌ ‌dioxide.‌ ‌

Last updated date: 24th Mar 2023
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Hint: When a given mass of an element having some molecular weight is given, then the number of moles of that element is equal to the given mass divided by the molecular weight. The moles are unitless The moles are unitless because the S.I.unit for both the quantities is grams.

When there is a given mass of a compound and we already know the molecular weight of the compound then the number of moles of that compound is defined as the given mass divided by the molecular weight.
Here in this question, we are given $3.6gm$ of water and $4.4gm$ of carbon dioxide
So first let’s calculate the molecular weight of water, now water has two elements hydrogen and oxygen and hydrogen as two units so the molecular weight of water is
$2 \times H + O \\ = 2 \times 1 + 16 \\ = 18g/mol \\$
Now let’s calculate the molecular weight of carbon dioxide, now in carbon dioxide, it has one atom of carbon and two atoms of oxygen, therefore, the molecular weight is
$C + 2 \times O \\ = 12 + 2 \times 16 \\ = 44g/mol \\$
Now let’s calculate the moles given of water, we have the given mass and the molecular weight of water, so we have to divide the given weight with molecular weight
$moles = \dfrac{{given\,mass}}{{molecular\,weight}} \\ \Rightarrow moles = \dfrac{{3.6}}{{18}} \\ \Rightarrow moles = 0.2 \\$
Now let’s calculate the moles given of carbon dioxide, we have the given mass and the molecular weight of carbon dioxide, so we have to divide the given weight with molecular weight
$moles = \dfrac{{given\,mass}}{{molecular\,weight}} \\ \Rightarrow moles = \dfrac{{4.4}}{{44}} \\ \Rightarrow moles = 0.1 \\$
Now the ratio between the moles of water and carbon dioxide is
$ratio = \dfrac{{mole{s_{{H_2}O}}}}{{mole{s_{C{O_2}}}}} \\ \Rightarrow ratio = \dfrac{{0.2}}{{0.1}} \\ \Rightarrow ratio = 2:1 \\$
The ratio of moles of moles of $3.6gm$of water and $4.4gm$of carbon dioxide is $2:1$.

Note:
The molarity of a compound is defined as the number of moles of a compound in one litre of solution while molality is defined as the number of moles in one kilogram of solvent. Both these quantities are interchangeable and can be calculated from density.