Question

3.8 Calculate the molar mass of each of the following:

(a) ${}^{\mathbf{Sr}{\left(\mathrm{OH}\right)}_{\mathbf{2}}}$ (b)${}^{{\mathbf{N}}_{\mathbf{2}}{\mathbf{O}}_{\mathbf{3}}}$ (c)${}^{{\mathbf{NaCIO}}_{\mathbf{3}}}$ (d)${}^{{\mathbf{Cr}}_{\mathbf{2}}{\mathbf{O}}_{\mathbf{3}}}$

Short answer

The molar mass of each of the following:

a)$\mathbf{Sr}{\left(\mathrm{OH}\right)}_{\mathbf{2}}\mathbf{=}\mathbf{121}\mathbf{.}\mathbf{64}\mathbf{}\frac{\mathbf{g}}{\mathbf{mol}}$

b)${\mathbf{N}}_{\mathbf{2}}{\mathbf{O}}_{\mathbf{3}}\mathbf{=}\mathbf{76}\mathbf{.}\mathbf{02}\mathbf{}\frac{\mathbf{g}}{\mathbf{mol}}$

c)${\mathbf{NaCIO}}_{\mathbf{3}}\mathbf{=}\mathbf{106}\mathbf{.}\mathbf{44}\mathbf{}\frac{\mathbf{g}}{\mathbf{mol}}$

d)${\mathbf{Cr}}_{\mathbf{2}}{\mathbf{O}}_{\mathbf{3}}\mathbf{=}\mathbf{152}\mathbf{.}\mathbf{00}\mathbf{}\frac{\mathbf{g}}{\mathbf{mol}}$

Step-by-step solution

Relation between mass and number of moles

The molar mass of a material is defined as the mass of the substance contained in one mole of the substance, and it is equal to the total mass of the component atoms. It may be stated mathematically as follows:

$\mathbf{Molar}\mathbf{}\mathbf{mass}\mathbf{=}\frac{\mathbf{Weightingrams}}{\mathbf{Number}\mathbf{}\mathbf{of}\mathbf{}\mathbf{moles}}$

Step 2: Calculate the molar mass of Sr(OH)2

a)

A compound's molar mass is equal to the sum of the molar masses of the atoms in the formula.

Sr, O, and H have molar massesof ${}^{\mathbf{87}\mathbf{.}\mathbf{62}\mathbf{,}\mathbf{16}\mathbf{.}\mathbf{00}\mathbf{}\mathbf{and}\mathbf{1}\mathbf{.}\mathbf{01}\frac{\mathbf{g}}{\mathbf{mol}}}$respectively.

role="math" localid="1657107817515" $$\begin{gathered} \mathbf{MolarmassofSr}{\mathbf{\left(}\mathbf{OH}\mathbf{\right)}}_{\mathbf{2}}\mathbf{=}\mathbf{}\mathbf{MolarmassofSr}\mathbf{+}\mathbf{2}\mathbf{\times }\mathbf{\left(}\mathbf{MolarmassofH}\mathbf{\right)}\mathbf{+}\mathbf{2}\mathbf{\times }\mathbf{\left(}\mathbf{MolarmassofO}\mathbf{\right)} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{87}\mathbf{.}\mathbf{62}\frac{\mathbf{g}}{\mathbf{mol}}\mathbf{+}\mathbf{2}\mathbf{\times }\mathbf{(}\mathbf{1}\mathbf{.}\mathbf{01}\frac{\mathbf{g}}{\mathbf{mol}}\mathbf{)}\mathbf{+}\mathbf{2}\mathbf{\times }\mathbf{(}\mathbf{16}\mathbf{.}\mathbf{00}\frac{\mathbf{g}}{\mathbf{mol}}\mathbf{)} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\boxed{\mathbf{121}\mathbf{.}\mathbf{64}\frac{\mathbf{g}}{\mathbf{mol}}} \end{gathered}$$

Step 3: Calculate the molar mass ofN2O3

b)

Here themolar mass ofN is given as ${}^{\mathbf{14}\mathbf{.}\mathbf{01}\frac{\mathbf{g}}{\mathbf{mol}}\mathbf{.}}$

$$\begin{gathered} {\mathbf{MolarmassofN}}_{\mathbf{2}}{\mathbf{O}}_{\mathbf{3}}\mathbf{=}\mathbf{2}\mathbf{\times }\mathbf{}\left(\mathrm{MolarmassofN}\right)\mathbf{+}\mathbf{3}\mathbf{\times }\mathbf{\left(}\mathbf{MolarmassofO}\mathbf{\right)} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{}\mathbf{}\mathbf{2}\mathbf{\times }\mathbf{(}\mathbf{14}\mathbf{.}\mathbf{01}\frac{\mathbf{g}}{\mathbf{mol}}\mathbf{)}\mathbf{+}\mathbf{3}\mathbf{\times }\mathbf{(}\mathbf{16}\mathbf{.}\mathbf{00}\frac{\mathbf{g}}{\mathbf{mol}}\mathbf{)} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\boxed{\mathbf{76}\mathbf{.}\mathbf{02}\frac{\mathbf{g}}{\mathbf{mol}}} \end{gathered}$$

Step 4: Calculate the molar mass of NaCIO3

c)

Na and Cl have molar massesof ${}^{\mathbf{22}\mathbf{.}\mathbf{99}\mathbf{}\mathbf{and}\mathbf{}\mathbf{35}\mathbf{.}\mathbf{45}\frac{\mathbf{g}}{\mathbf{mol}}}$respectively.

$$\begin{gathered} {\mathbf{MolarmassofNaCIO}}_{\mathbf{3}}\mathbf{=}\mathbf{}\mathbf{MolarmassofNa}\mathbf{+}\mathbf{MolarmassofCI}\mathbf{+}\mathbf{3}\mathbf{\times }\mathbf{\left(}\mathbf{MolarmassofO}\mathbf{\right)} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{22}\mathbf{.}\mathbf{99}\frac{\mathbf{g}}{\mathbf{mol}}\mathbf{+}\mathbf{35}\mathbf{.}\mathbf{45}\mathbf{\times }\frac{\mathbf{g}}{\mathbf{mol}}\mathbf{+}\mathbf{3}\mathbf{\times }\mathbf{(}\mathbf{16}\mathbf{.}\mathbf{00}\frac{\mathbf{g}}{\mathbf{mol}}\mathbf{)} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\boxed{\mathbf{106}\mathbf{.}\mathbf{44}\frac{\mathbf{g}}{\mathbf{mol}}} \end{gathered}$$

Step 5: Calculate the molar mass of Cr2o3

d)

Here themolar mass ofCr is given as$52.00\frac{\mathrm{g}}{\mathrm{mol}}$
localid="1657108334371" $$\begin{gathered} \mathbf{Molarmass}\mathbf{}\mathbf{of}\mathbf{}{\mathbf{Cr}}_{\mathbf{2}}{\mathbf{O}}_{\mathbf{3}}\mathbf{=}\mathbf{2}\mathbf{\times }\mathbf{(}\mathbf{Molarmass}\mathbf{}\mathbf{of}\mathbf{}\mathbf{Cr}\mathbf{)}\mathbf{+}\mathbf{3}\mathbf{\times }\mathbf{(}\mathbf{Molarmass}\mathbf{}\mathbf{of}\mathbf{}\mathbf{O}\mathbf{)} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{2}\mathbf{\times }\mathbf{(}\mathbf{52}\mathbf{.}\mathbf{00}\frac{\mathbf{g}}{\mathbf{mol}}\mathbf{)}\mathbf{+}\mathbf{3}\mathbf{\times }\mathbf{(}\mathbf{16}\mathbf{.}\mathbf{00}\frac{\mathbf{g}}{\mathbf{mol}}\mathbf{)} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{}\mathbf{}\boxed{\mathbf{152}\mathbf{.}\mathbf{00}\frac{\mathbf{g}}{\mathbf{mol}}} \end{gathered}$$