Question

Express the molecular mass $\left(\pm \mathit{u}\mathit{n}\mathit{c}\mathit{e}\mathit{r}\mathit{t}\mathit{a}\mathit{i}\mathit{n}\mathit{t}\mathit{y}\right)$of ${\mathbf{C}}_{\mathbf{9}}{\mathbf{H}}_{\mathbf{9}}{\mathbf{O}}_{\mathbf{6}}{\mathbf{N}}_{\mathbf{3}}$ with the correct number of significant figures.

Short answer

The molecular mass $\left(\pm uncertainty\right)$of ${\mathrm{C}}_9{\mathrm{H}}_9{\mathrm{O}}_6{\mathrm{N}}_3$ with the correct number of significant figures = $255.18402\pm 0.0002\mathrm{g}/\mathrm{mol}$

Step-by-step solution

To find

The molecular mass $\left(\pm uncertainty\right)$ of${\mathrm{C}}_9{\mathrm{H}}_9{\mathrm{O}}_6{\mathrm{N}}_3$ with the correct number of significant figures.

Atomic masses of atoms in the given compound

The atomic mass of a given compound ${\mathrm{C}}_9{\mathrm{H}}_9{\mathrm{O}}_6{\mathrm{N}}_3$is written below:

$$\begin{gathered} C=12.0106\pm 0.0002/\sqrt{3}g/mol \\ H=1.00798\pm 0.00002/\sqrt{3}g/mol \\ O=15.9994\pm 0.0002/\sqrt{3}g/mol \\ N=14.0068\pm 0.0002/\sqrt{3}g/mol \end{gathered}$$

Calculate molecular mass of the compound

The standard uncertainty in atomic mass equals to the uncertainty listed in the PSE divided by $\sqrt{3}$.

The molecular mass is calculated by the following:

$$\begin{gathered} M=9C+9H+60+3N \\ =255.18402g/mol \end{gathered}$$

Calculate the standard uncertainty

$$\begin{gathered} e=\sqrt{0.{0002}^2/3+0.{00002}^2/3+0.{0002}^2/3+0.{0002}^2/3} \\ =0.0002 \end{gathered}$$

This is the molar mass with uncertainty of:

$255.18402\pm 0.0002g/\mathrm{mol}$