Question

A hydrocarbon contains 10.5g of carbon per gram of hydrogen. If 1L of vapour of hydrocarbon at ${{127}^{\circ }}C$ at 1atm pressure weighs 2.8g, then the molecular formula mass of hydrocarbon is:

Answer 1

Hint: To solve this question you can use the ideal gas equation to find out the molecular mass by replacing the number of moles by weight upon molecular weight. From here you can find the formula of the hydrocarbon and then using it you can find out the formula mass.

Complete step by step solution:
To answer this, firstly let us discuss the meaning of the formula mass of a compound.
We define the formula weight or formula mass of a molecule or a compound as the sum of the atomic weights of the atoms in its empirical formula. We express the formula mass in terms of atomic mass units.
To find the formula mass of the hydrocarbon, we need to find the formula of the hydrocarbon. Let us assume the hydrocarbon is ${{C}_{x}}{{H}_{y}}$.
We know that, $PV =$ $nRT$.
We can replace the number of moles by weight upon molecular weight.
Therefore, $PV=\dfrac{w}{M}RT$
Now from the question, we can deduce that-
Pressure = $1atm$, Volume = $1L$, T = ${{127}^{\circ }}C$ = $127 + 273$ $K$ $= 400K$, $w =$ $2.8g$ and we know,
$R = 0.0821$ $Latm/molK.$
Therefore, putting these values in the equation we will get that-
$\begin{align}
& 1atm\times 1L=\dfrac{2.8g}{M}0.0821\text{ }latm/molK\times 400K \\
& Or,M=91.952g/mol\simeq 92g/mol \\
\end{align}$
We know the atomic weight of carbon is 12 and that of hydrogen is 1.
Therefore, we can write that- $12x + y$ $= 92$.
Now, according to the question, hydrocarbons contain $10.5g$ of carbon per gram of hydrogen.
So, we can write that -$\dfrac{12x}{y}=10.5$
Now, solving these two equations we will get that x = 7 and y = 8.
Therefore, the formula of the hydrocarbon is ${{C}_{7}}{{H}_{8}}$ and its formula mass will be $\left( 12\times 7 \right)+8=92$.

Therefore, the required answer will be, the molecular formula mass of hydrocarbon is 92.

Note: The ideal gas law equation is an equation of state variables of a hypothetical ideal gas. It has many limitations but still used for approximation of the behaviour of a gas under certain conditions. We must not be confused between the formula mass and molar mass. We have already discussed formula mass in the above discussion and we define molar mass as the mass of 1 mole of a substance in grams.