Question

A mass spectrum of an organic compound shows the relative abundances of M to be 40.58% and M 1 to be 7.022%. Assuming the peaks are caused by 12C and 13C isotopes, determine the number of carbon atoms in the compound. Natural abundances: 12C is 98.93% and 13C is 1.07%

Answer 1

Answer:

The number of carbon atoms in the organic compound is 16.

Explanation:

The relative intensity of M + 1 peak (relative to M = 100) in organic compounds can be predicted by the following formula:

[M + 1] = (number of C x 1.07) ---------------------------------------------------- (1)

This formula can also be used to determine the number of carbon from the given intensity. But first, the intensity of [M + 1] relative to [M] = 100 needs to be determined, for which, consider the following calculations,

$[M+1]=(\frac{M+1}{M}) (100)$

$[M+1]=(\frac{7.022}{40.58}) (100)$

$[M+1]=17.30$

Using equation 1 we get,

$number of C=\frac{[M+1]}{1.07}$

$number of C=\frac{17.3}{1.07}\\number of C = 16.168$

or number of C = 16

The remaining value, 0.168, can be due to the isotopes of hydrogen and oxygen in the organic compound.

Answer 2

The number of carbon atoms in the compound is; 16 carbon atoms.

We are given the natural abundances of 12C and 13C as;

12C = 98.93%

13C = 1.07%

Ratio of 13C to 12C abundances is;

13C/12C; 1.07%/98.93%

⇒ 1.08%

Now, to find the number of atoms in the compound with relative abundances of M to be 40.58% and M1 to be 7.022% we will use the formula;

number of carbon atoms = (M1 Relative abundance/M2 relative abundance) *100 ÷ Ratio of 13C to 12C abundance

Plugging in the relevant values;

Number of carbon atoms = (7.022/40.58) ÷ 1.08%

Number of carbon atoms ≈ 16 carbon atoms

Read more about relative abundance of a mass spectrum of an organic compound at; https://brainly.com/question/8615318