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Consider an element with two isotopes whose natural abundances are aand $\mathit{b}\left(a+b=1\right)$. If there are n atoms of the element in a compound, the probability of finding each combination of isotopes is derived from the expansion of the binomial ${\left(a+b\right)}^{\mathbf{n}}$. For carbon, the abundances are$\mathit{a}\mathbf{=}\mathbf{0}\mathbf{.}\mathbf{9893}$ are${}^{\mathbf{12}}\mathit{C}$ and$\mathit{b}\mathbf{=}\mathbf{0}\mathbf{.}\mathbf{0107}$for ${}^{\mathbf{13}}\mathit{C}$. The probability of finding ${\mathbf{2}}^{\mathbf{12}}\mathit{C}$ atoms in acetylene, HC = CH, is given by the first term of the expansion of ${\left(a+b\right)}^{\mathbf{2}}\mathbf{=}{\mathit{a}}^{\mathbf{2}}\mathbf{+}\mathbf{2}\mathit{a}\mathit{b}\mathbf{+}{\mathit{b}}^{\mathbf{2}}$. The value of${\mathit{a}}^{\mathbf{2}}$is${\left(0.9893\right)}^{\mathbf{2}}\mathbf{=}\mathbf{0}\mathbf{.}\mathbf{9787}$, so the probability of finding $${\mathbf{2}}^{\mathbf{12}}\mathit{C}$ atoms in acetylene is 0.9787. The probability of finding ${}^{\mathbf{12}}\mathit{C}\mathbf{+}{\mathbf{1}}^{\mathbf{13}}\mathit{C}$ is $\mathbf{2}\mathit{a}\mathit{b}\mathbf{=}\mathbf{2}\left(0.9893\right)\left(0.0107\right)\mathbf{=}\mathbf{0}\mathbf{.}\mathbf{0212}$. The probability of finding role="math" localid="1663661299432" ${\mathbf{2}}^{\mathbf{13}}\mathit{C}$ is ${\mathit{b}}^{\mathbf{2}}\mathbf{=}{\left(0.0107\right)}^{\mathbf{2}}\mathbf{=}\mathbf{0}\mathbf{.}\mathbf{000114}$. The molecular ion, by definition, contains ${\mathbf{2}}^{\mathbf{12}}\mathit{C}$atoms. The M + 1 peak contains ${\mathbf{1}}^{\mathbf{12}}\mathit{C}\mathbf{+}{\mathbf{1}}^{\mathbf{13}}\mathit{C}$ . The intensity of M + 1 relative to $M^{+*}$will be $\left(0.01212\right)\mathbf{/}\left(0.9787\right)\mathbf{=}\mathbf{0}\mathbf{.}\mathbf{0217}$. (We are ignoring ${}^{\mathbf{2}}\mathit{H}$ because its natural abundance is small.) in 1 ,2-dichlorobenzene. Draw a stick diagram of the distribution, like Figure 22 - 7.

Step by step solution

01

Concept used.

Relative abundance:

- Relative abundance refers to the fraction of an isotope that occurs naturally.

- The cumulative amount of the isotope percentages must equal 100%.

- The relative atomic mass by average of the isotopic masses may be weighed.

02

Step 2: The resolving power of the spectrometer from the expression m/m1/2 .

It is possible to determine the relative abundance or quantities of the various chemicals.

$$\begin{gathered} {}^{35}clabundance≡a=0.7578 \\ {}^{37}clabundance≡a=0.2422 \end{gathered}$$

Relative abundance of$C_6{H_4}^{35}C{I}_2=a^2=0.57426$

Relative abundance of$C_6{H_4}^{35}C{I}^{37}CI=2ab=0.36708$

Relative abundance of$C_6{H_4}^{35}C{I}_2=b^2=0.058661$

Relative abundance of${}^{35}C{I}_2.{}^{35}C{I}^{37}C{I}^{37}.C{I}_2=1:0.6392:0.1022$.

The distribution's stick diagram is given in the following picture1 .

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