Chapter 22, Problem 22.12P

Interpretation Introduction

Interpretation:

The theoretical masses of the given sucralose species has to be calculated and the difference in ppm between the observed and calculated m/z has to be found.

Concept and introduction:

Theoretical mass:

The theoretical mass of a species can be calculated by subtracting the individual mass of atoms in the species with the mass value of electron.

Explanation of Solution

The given information in figure 22-9 is recorded as follows,

The molecular formula for the sucralose is ${\text{C}}_{\text{12}}{\text{H}}_{\text{19}}{\text{Cl}}_{\text{3}}{\text{O}}_{\text{8}}$

The species of sucralose at $m/z=395$ is ${\left[{}^{12}{\text{C}}_{\text{12}}{}^1{\text{H}}_{\text{18}}{}^{16}{\text{O}}_{\text{8}}{}^{35}{\text{Cl}}_{\text{3}}\right]}^{-}$

The species of sucralose at $m/z=397$ is ${\left[{}^{12}{\text{C}}_{\text{12}}{}^1{\text{H}}_{\text{18}}{}^{16}{\text{O}}_{\text{8}}{}^{35}{\text{Cl}}_2{}^{37}\text{Cl}\right]}^{-}$

The species of sucralose at $m/z=399$ is ${\left[{}^{12}{\text{C}}_{\text{12}}{}^1{\text{H}}_{\text{18}}{}^{16}{\text{O}}_{\text{8}}{}^{35}{\text{Cl}}^{37}{\text{Cl}}_2\right]}^{-}$

The species of sucralose at $m/z=401$ is ${\left[{}^{12}{\text{C}}_{\text{12}}{}^1{\text{H}}_{\text{18}}{}^{16}{\text{O}}_{\text{8}}{}^{37}{\text{Cl}}_{\text{3}}\right]}^{-}$

We can calculate the theoretical mass of the given sucralose as follows.

$\begin{array}{l}\underset{\_}{Atm/z=395:}\\ {\left[{}^{12}{\text{C}}_{\text{12}}{}^1{\text{H}}_{\text{18}}{}^{16}{\text{O}}_{\text{8}}{}^{35}{\text{Cl}}_{\text{3}}\right]}^{-}\text{=}{}^{12}{\text{C}}_{\text{12}}\text{+}{}^1{\text{H}}_{\text{18}}{\text{+}}^{16}{\text{O}}_{\text{8}}{\text{+ }}^{35}{\text{Cl}}_3{\text{- e}}^{\text{-}}\\ \text{=}12\times 12.0\text{+ 18}\times \text{1}\text{.00782+8}\times \text{15}\text{.99491+3}\times \text{34}\text{.9688 - 0}\text{.00055}\\ \text{=}395.00589\end{array}$

$\begin{array}{l}\underset{\_}{Atm/z=397:}\\ {\left[{}^{12}{\text{C}}_{\text{12}}{}^1{\text{H}}_{\text{18}}{}^{16}{\text{O}}_{\text{8}}{}^{35}{\text{Cl}}_2{}^{37}\text{Cl}\right]}^{-}\text{=}{}^{12}{\text{C}}_{\text{12}}\text{+}{}^1{\text{H}}_{\text{18}}{\text{+}}^{16}{\text{O}}_{\text{8}}{\text{+ }}^{35}{\text{Cl}}_2{\text{+}}^{37}{\text{Cl- e}}^{\text{-}}\\ \text{=}12\times 12.0\text{+ 18}\times \text{1}\text{.00782+8}\times \text{15}\text{.99491+2}\times \text{34}\text{.9688+36}\text{.9659 - 0}\text{.00055}\\ \text{=}397.00299\end{array}$

$\begin{array}{l}\underset{\_}{Atm/z=399:}\\ {\left[{}^{12}{\text{C}}_{\text{12}}{}^1{\text{H}}_{\text{18}}{}^{16}{\text{O}}_{\text{8}}{}^{35}{\text{Cl}}^{37}{\text{Cl}}_2\right]}^{-}\text{=}{}^{12}{\text{C}}_{\text{12}}\text{+}{}^1{\text{H}}_{\text{18}}{\text{+}}^{16}{\text{O}}_{\text{8}}{\text{+ }}^{35}{\text{Cl+}}^{37}{\text{Cl}}_2{\text{- e}}^{\text{-}}\\ \text{=}12\times 12.0\text{+ 18}\times \text{1}\text{.00782+8}\times \text{15}\text{.99491+34}\text{.9688+2}\times \text{36}\text{.9659 - 0}\text{.00055}\\ \text{=}399.00009\end{array}$

$\begin{array}{l}\underset{\_}{Atm/z=401:}\\ {\left[{}^{12}{\text{C}}_{\text{12}}{}^1{\text{H}}_{\text{18}}{}^{16}{\text{O}}_{\text{8}}{}^{37}{\text{Cl}}_{\text{3}}\right]}^{-}\text{=}{}^{12}{\text{C}}_{\text{12}}\text{+}{}^1{\text{H}}_{\text{18}}{\text{+}}^{16}{\text{O}}_{\text{8}}{\text{+ }}^{37}{\text{Cl}}_3{\text{ - e}}^{\text{-}}\\ \text{=}12\times 12.0\text{+ 18}\times \text{1}\text{.00782+8}\times \text{15}\text{.99491+3}\times \text{36}\text{.9659 - 0}\text{.00055}\\ \text{=}400.99719\end{array}$

The difference in ppm $=\text{0}\text{.2, 0 }\text{.6, 1}\text{.2 ppm}\text{.}$

Conclusion

The theoretical masses of the given sucralose species was calculated and the difference in ppm between the observed and calculated m/z was found.