Question

Chromium(III) oxide reacts with hydrogen sulfide $\left(H_{2}S\right)$gas to form chromium(III) sulfide and water: $\mathit{C}{\mathit{r}}_{\mathbf{2}}{\mathit{O}}_{\mathbf{3}}\mathbf{\left(}\mathbf{s}\mathbf{\right)}\mathbf{+}\mathbf{3}{\mathit{H}}_{\mathbf{2}}\mathit{S}\mathbf{\left(}\mathbf{g}\mathbf{\right)}\mathbf{\to }\mathit{C}{\mathit{r}}_{\mathbf{2}}{\mathit{S}}_{\mathbf{3}}\mathbf{\left(}\mathbf{s}\mathbf{\right)}\mathbf{+}\mathbf{3}{\mathit{H}}_{\mathbf{2}}\mathit{O}\mathbf{\left(}\mathbf{I}\mathbf{\right)}$

To produce 421 g of $\mathit{C}{\mathit{r}}_{\mathbf{2}}{\mathit{S}}_{\mathbf{3}}\mathbf{,}$

(a) How many moles of $\mathit{C}{\mathit{r}}_{\mathbf{2}}{\mathit{O}}_{\mathbf{3}}$are required?

(b) How many grams of $\mathit{X}{\mathit{r}}_{\mathbf{2}}{\mathit{O}}_{\mathbf{3}}$are required?

Short answer

Answer

1. Thenumber of moles of $\mathit{C}{\mathit{r}}_{\mathbf{2}}{\mathit{O}}_{\mathbf{3}}$is 2.103 mol.

2. Themass of $\mathit{C}{\mathit{r}}_{\mathbf{2}}{\mathit{O}}_{\mathbf{3}}$is 319.63 g.

Step-by-step solution

Relation between mass and number of moles

The number of moles is calculated by the mass and Molar mass. The relationship between the number of moles, mass, and molar mass is given below.

$\mathit{N}\mathit{u}\mathit{m}\mathit{b}\mathit{e}\mathit{r}\mathbf{}\mathit{o}\mathit{f}\mathbf{}\mathit{m}\mathit{o}\mathit{l}\mathit{e}\mathit{s}\mathbf{=}\frac{\mathbf{m}\mathbf{a}\mathbf{s}\mathbf{s}}{\mathbf{M}\mathbf{o}\mathbf{l}\mathbf{a}\mathbf{r}\mathbf{}\mathbf{m}\mathbf{a}\mathbf{s}\mathbf{s}}$

Calculate the number of moles of Cr2S3

The mass of $\mathit{C}{\mathit{r}}_{\mathbf{2}}{\mathit{S}}_{\mathbf{3}}$= 421 g.

The molar mass of $\mathit{C}{\mathit{r}}_{\mathbf{2}}{\mathit{S}}_{\mathbf{3}}$=200.19 g/mol

Thus, the number of moles of$\mathit{C}{\mathit{r}}_{\mathbf{2}}{\mathit{S}}_{\mathbf{3}}$is:

$$\begin{gathered} \mathit{N}\mathit{u}\mathit{m}\mathit{b}\mathit{e}\mathit{r}\mathbf{}\mathit{o}\mathit{f}\mathbf{}\mathit{M}\mathit{o}\mathit{l}\mathit{e}\mathit{s}\mathbf{}\mathit{o}\mathit{f}\mathbf{}\mathit{C}{\mathit{r}}_{\mathbf{2}}{\mathit{S}}_{\mathbf{3}}\mathbf{=}\frac{\mathbf{mass}\mathbf{}\mathbf{of}\mathbf{}{\mathbf{Cr}}_{\mathbf{2}}{\mathbf{S}}_{\mathbf{3}}}{\mathbf{Molar}\mathbf{}\mathbf{mass}\mathbf{}\mathbf{of}\mathbf{}{\mathbf{Cr}}_{\mathbf{2}}{\mathbf{S}}_{\mathbf{3}}} \\ \mathbf{=}\frac{\mathbf{421}\mathbf{g}}{\mathbf{2000}\mathbf{.}\mathbf{19}\mathbf{}\mathbf{g}\mathbf{/}\mathbf{mol}} \\ \mathbf{=}\mathbf{2}\mathbf{.}\mathbf{103}\mathbf{}\mathit{m}\mathit{o}\mathit{l} \end{gathered}$$

Relation between the number of moles of Cr2S3 and Cr2O3

In the given reaction, 1 mol of $\mathit{C}{\mathit{r}}_{\mathbf{2}}{\mathit{O}}_{\mathbf{3}}$is formed from 1 mol of$\mathit{C}{\mathit{r}}_{\mathbf{2}}{\mathit{S}}_{\mathbf{3}}$

Thus,

$\mathbf{1}\mathbf{}\mathit{m}\mathit{o}\mathit{l}\mathbf{}\mathit{o}\mathit{f}\mathbf{}\mathit{C}{\mathit{r}}_{\mathbf{2}}{\mathit{O}}_{\mathbf{3}}\mathbf{}\mathbf{=}\mathbf{}\mathbf{1}\mathbf{}\mathit{m}\mathit{o}\mathit{l}\mathbf{}\mathit{o}\mathit{f}\mathbf{}\mathit{C}{\mathit{r}}_{\mathbf{2}}{\mathit{S}}_{\mathbf{3}}$

Calculate the number of moles of Cr2O3

The number of $\mathit{C}{\mathit{r}}_{\mathbf{2}}{\mathit{O}}_{\mathbf{3}}$is:

$\overline{)\begin{array}{c}\mathbf{1}\mathbf{}\mathbf{mol}\mathbf{}\mathbf{of}\mathbf{}{\mathbf{Cr}}_{\mathbf{2}}{\mathbf{S}}_{\mathbf{3}}\mathbf{}\mathbf{=}\mathbf{}\mathbf{1}\mathbf{}\mathbf{mol}\mathbf{}\mathbf{of}\mathbf{}{\mathbf{Cr}}_{\mathbf{2}}{\mathbf{O}}_{\mathbf{3}}\\ \mathbf{2}\mathbf{.}\mathbf{103}\mathbf{}\mathbf{mol}\mathbf{}\mathbf{of}\mathbf{}{\mathbf{Cr}}_{\mathbf{2}}{\mathbf{S}}_{\mathbf{3}}\mathbf{}\mathbf{=}\mathbf{}\mathbf{2}\mathbf{.}\mathbf{103}\mathbf{}\mathbf{mol}\mathbf{}\mathbf{of}\mathbf{}{\mathbf{Cr}}_{\mathbf{2}}{\mathbf{O}}_{\mathbf{3}}\end{array}}$

Therefore, the number of moles of $\mathit{C}{\mathit{r}}_{\mathbf{2}}{\mathit{O}}_{\mathbf{3}}$is 2.103 mol.

Calculate the mass of Cr2O3

The molar mass of $\mathit{C}{\mathit{r}}_{\mathbf{2}}{\mathit{O}}_{\mathbf{3}}$= 151.99 g/mol.

The mass of$\mathit{C}{\mathit{r}}_{\mathbf{2}}{\mathit{O}}_{\mathbf{3}}$is:

$$\begin{gathered} \mathit{m}\mathit{a}\mathit{s}\mathit{s}\mathbf{}\mathit{o}\mathit{f}\mathbf{}\mathit{C}{\mathit{r}}_{\mathbf{2}}{\mathit{O}}_{\mathbf{3}}\mathbf{}\mathbf{=}\mathbf{}\mathit{m}\mathit{o}\mathit{l}\mathit{e}\mathit{s}\mathbf{}\mathit{o}\mathit{f}\mathbf{}\mathit{C}{\mathit{r}}_{\mathbf{2}}{\mathit{O}}_{\mathbf{3}}\mathbf{}\mathbf{\times }\mathbf{}\mathit{M}\mathit{o}\mathit{l}\mathit{a}\mathit{r}\mathbf{}\mathit{m}\mathit{a}\mathit{s}\mathit{s}\mathbf{}\mathit{o}\mathit{f}\mathbf{}\mathit{C}{\mathit{r}}_{\mathbf{2}}{\mathit{O}}_{\mathbf{3}} \\ \mathbf{=}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{2}\mathbf{.}\mathbf{103}\mathbf{}\mathit{m}\mathit{o}\mathit{l}\mathbf{}\mathbf{\times }\mathbf{}\mathbf{151}\mathbf{.}\mathbf{99}\mathbf{}\mathit{g}\mathbf{/}\mathit{m}\mathit{o}\mathit{l} \\ \mathbf{=}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{319}\mathbf{.}\mathbf{63497}\mathbf{}\mathit{g} \end{gathered}$$

Therefore, the mass of $\mathit{C}{\mathit{r}}_{\mathbf{2}}{\mathit{O}}_{\mathbf{3}}$is approximately 319.63 g.