Q3.66P - Chemistry: Molecular Nature Of Matter And Change

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?

Step-by-Step Solution

Answer

Answer

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

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

Step 1: 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.

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

Step 2: Calculate the number of moles of C r 2 S 3

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:

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

Step 3: Relation between the number of moles of C r 2 S 3 and C r 2 O 3

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,

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

Step 4: Calculate the number of moles of C r 2 O 3

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.

Step 4: Calculate the mass of C r 2 O 3

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.