Question

How can I determine the molecular formula for a compound that contains only $C$ and $H$ and has a molecular ion with $\dfrac{m}{z}$ value of $72$ ?

Answer 1

Hint: We have to know that $\dfrac{m}{z}$ value means ratio of mass to charge. We are given the information that the compound contains carbon and hydrogen. So, we can predict the compound should be alkane. We have to know that alkanes are hydrocarbons which have only carbon and hydrogen present in the structure. We can say that the general formula of alkane is ${C_n}{H_{2n + 2}}$.

Complete answer:
We can say that $\dfrac{m}{z}$ ratio means mass to charge ratio. We can use the $\dfrac{m}{z}$ ratio to determine the path of the electron present in the vacuum. We can say that the ratio of mass/charge is the region of cathode ray tube, electron microscopy, and cosmology. We have to know in $\dfrac{m}{z}$ ratio, we can say m indicates the molecular mass (or) atomic mass number whereas the charge number of ions is indicated by z. We have to know the $\dfrac{m}{z}$ ratio is dimensionless quantity. We have to know we can use the $\dfrac{m}{z}$ ratio to indicate the empirical observation in mass spectrometry.
Let us now determine the molecular formula of the compound.
Firstly, we have to divide $72$ to $32$ to get the number of atoms of carbons. So, when we divide the number $72$ by $13$, we will get the numerator as five and the denominator as seven. We have to know that the numerator indicates the number of carbon atoms whereas we can determine the number of hydrogen atoms by adding the number of carbon atoms and denominator.
So, we have found that the number of carbon atoms is five. Let us now determine the number of hydrogen atoms, when we add five and seven, we will get the answer as twelve. So, the number of hydrogen atoms is fourteen.
So, the number of carbon atoms is five and the number of hydrogen atoms is $12$ . So, we can get the molecular formula as ${C_5}{H_{12}}$.
We have found the molecular formula of the compound that has $\dfrac{m}{z}$ $72$ is ${C_5}{H_{12}}$.

Note:
We have to know that there is a difference between $\dfrac{m}{z}$ and $\dfrac{z}{m}$. $\dfrac{m}{z}$ indicates mass to charge ratio and $\dfrac{z}{m}$ indicates charge to mass ratio. We have to know that the charge to mass ratio is nothing but the division of charge of an object to the mass of the same object. We can use charge to mass ratio for objects that could be taken as particles.