Respuesta :
Answer: The theoretical yield and percent yield of chromium (III) oxide is 434.72 grams and 92.6 % respectively.
Explanation:
To calculate the number of moles, we use the equation:
[tex]\text{Number of moles}=\frac{\text{Given mass}}{\text{Molar mass}}[/tex] .....(1)
Given mass of [tex]CrO_2[/tex] = 480.1 g
Molar mass of [tex]CrO_2[/tex] = 84 g/mol
Putting values in equation 1, we get:
[tex]\text{Moles of }CrO_2=\frac{480.1g}{84g/mol}=5.72mol[/tex]
For the given chemical equation:
[tex]4CrO_2\rightarrow 2Cr_2O_3+O_2[/tex]
By Stoichiometry of the reaction:
4 moles of [tex]CrO_2[/tex] produces 2 moles of chromium (III) oxide
So, 5.72 moles of [tex]CrO_2[/tex] will produce = [tex]\frac{2}{4}\times 5.72=2.86mol[/tex] of chromium (III) oxide
Now, calculating the mass of chromium (III) oxide from equation 1, we get:
Molar mass of chromium (III) oxide = 152 g/mol
Moles of chromium (III) oxide = 2.86 moles
Putting values in equation 1, we get:
[tex]2.86mol=\frac{\text{Mass of chromium (III) oxide}}{152g/mol}\\\\\text{Mass of chromium (III) oxide}=(2.86mol\times 152g/mol)=434.72g[/tex]
To calculate the percentage yield of chromium (III) oxide, we use the equation:
[tex]\%\text{ yield}=\frac{\text{Experimental yield}}{\text{Theoretical yield}}\times 100[/tex]
Experimental yield of chromium (III) oxide = 402.4 g
Theoretical yield of chromium (III) oxide = 434.72 g
Putting values in above equation, we get:
[tex]\%\text{ yield of chromium (III) oxide}=\frac{402.4g}{434.72g}\times 100\\\\\% \text{yield of chromium (III) oxide}=\%[/tex]
Hence, the theoretical yield and percent yield of chromium (III) oxide is 434.72 grams and 92.6 % respectively.
