Respuesta :
Answer: The theoretical yield of the product is 0.320 grams and its percent yield is 67.81 %
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)
- For trans-cinnamic acid:
Given mass of trans-cinnamic acid = 155 mg = 0.155 g (Conversion factor: 1 g = 1000 mg)
Molar mass of trans-cinnamic acid = 148.2 g/mol
Putting values in equation 1, we get:
[tex]\text{Moles of trans-cinnamic acid}=\frac{0.155g}{148.2g/mol}=0.00104mol[/tex]
- For pyridinium tribromide:
Given mass of pyridinium tribromide = 458 mg = 0.458 g
Molar mass of pyridinium tribromide = 319.82 g/mol
Putting values in equation 1, we get:
[tex]\text{Moles of pyridinium tribromide}=\frac{0.458g}{319.82g/mol}=0.00143mol[/tex]
- The chemical equation for the reaction of trans-cinnamic acid and pyridinium tribromide follows:
[tex]\text{trans-cinnamic acid}+\text{pyridinium tribromide}\xrightarrow[]{CH_3COOH}\text{2,3-dibromo-3-phenyl propanoic acid}[/tex]
Here, glacial acetic acid is considered as a buffer reagent so as to maintain the pH of the reaction.
By Stoichiometry of the reaction:
1 mole of trans-cinnamic acid reacts with 1 mole of pyridinium tribromide
So, 0.00104 moles of trans-cinnamic acid will react with = [tex]\frac{1}{1}\times 0.00104=0.00104mol[/tex] of pyridinium tribromide
As, given amount of pyridinium tribromide is more than the required amount. So, it is considered as an excess reagent.
Thus, trans-cinnamic acid is considered as a limiting reagent because it limits the formation of product.
By Stoichiometry of the reaction:
1 mole of trans-cinnamic acid produces 1 mole of 2,3-dibromo-3-phenyl propanoic acid
So, 0.00104 moles of trans-cinnamic acid will produce = [tex]\frac{1}{1}\times 0.00104=0.00104moles[/tex] of 2,3-dibromo-3-phenyl propanoic acid
Now, calculating the mass of 2,3-dibromo-3-phenyl propanoic acid from equation 1, we get:
Molar mass of 2,3-dibromo-3-phenyl propanoic acid = 308 g/mol
Moles of 2,3-dibromo-3-phenyl propanoic acid = 0.00104 moles
Putting values in equation 1, we get:
[tex]0.00104mol=\frac{\text{Mass of 2,3-dibromo-3-phenyl propanoic acid}}{308g/mol}\\\\\text{Mass of 2,3-dibromo-3-phenyl propanoic acid}=0.320g[/tex]
- To calculate the percentage yield of 2,3-dibromo-3-phenyl propanoic acid, we use the equation:
[tex]\%\text{ yield}=\frac{\text{Experimental yield}}{\text{Theoretical yield}}\times 100[/tex]
Experimental yield of 2,3-dibromo-3-phenyl propanoic acid = 0.217 g
Theoretical yield of 2,3-dibromo-3-phenyl propanoic acid = 0.320 g
Putting values in above equation, we get:
[tex]\%\text{ yield of 2,3-dibromo-3-phenyl propanoic acid}=\frac{0.217g}{0.320g}\times 100\\\\\% \text{yield of 2,3-dibromo-3-phenyl propanoic acid}=67.81\%[/tex]
Hence, the theoretical yield of the product is 0.320 grams and its percent yield is 67.81 %
