Subjective Type

How can I find the molecular formula from molar mass?

Solution

We start by determining the empirical formula for the compound.

First, we shall determine the mass in grams of each element in the sample. If we are given the percent composition, we can directly convert the percentage of each element to grams. For example, a molecule has a molecular weight of $$180.18\ g/mol$$. It is said to contain $$40.00\%$$ carbon, $$6.72\%$$ hydrogen, and $$53.28\%$$ oxygen.

We take the entire sample to be of $$100\ g$$, so we convert each percentage directly into gram, which means, the sample contains $$40.00$$ grams of carbon, $$6.72$$ grams of hydrogen, and $$53.28$$ grams of oxygen.

The next step is to determine the number of moles of each element by dividing its mass in grams by its molar mass (atomic weight in $$g/mol$$).

Moles of $$C=\dfrac{40\ g}{12\ g/mol}=3.33$$ moles

Moles of $$H = \dfrac{6.72\ g}{1\ g/mol} =6.65$$ moles

Moles of $$O = \dfrac{53.28\ g}{16\ g/mol}=3.33$$ moles

Now, we shall calculate the molar ratios by dividing the number of moles of each element by the lowest number of moles obtained, to get the lowest whole number ratio.

$$C = \dfrac{3.33}{3.33} = 1.00$$

$$H =\dfrac{ 6.65}{3.33} = 2.00$$

$$O = \dfrac{3.33}{3.33} = 1.00$$

Now, we shall use the whole number ratio of moles to determine the empirical formula of the compound. The whole number ratio for each element becomes its subscript.

Therefore, the empirical formula is $$ C_1H_{2}O_1=CH_2O$$

The next step is to determine the empirical formula weight.

Empirical formula weight $$ = \left ( 1 \times 12\ g/mol \right ) + \left ( 2 \times 1\ g/mol \right ) + \left ( 1 \times 16\ g/mol \right ) = 30\ g /mol $$

Then, we have to divide the molar mass for the molecular formula by the empirical formula mass. The result determines how many times to multiply the subscripts in the empirical formula to get the molecular formula.

The molecular weight of this compound is $$180\ g/mol$$

So, $$\dfrac{180\ g/mol}{30\ g/mol}= 6$$

Multiplying each subscript in the empirical formula, we finally get the molecular formula as $$C_{6}H_{12}O_{6}$$.

Therefore, the molecular formula for every compound can be determined from its molar mass by following the above steps.

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