<u>Answer:</u> The theoretical yield of the product is 0.320 grams and its percent yield is 67.81 %
<u>Explanation:</u>
To calculate the number of moles, we use the equation:
.....(1)
- <u>For trans-cinnamic acid:</u>
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:
![\text{Moles of trans-cinnamic acid}=\frac{0.155g}{148.2g/mol}=0.00104mol](https://tex.z-dn.net/?f=%5Ctext%7BMoles%20of%20trans-cinnamic%20acid%7D%3D%5Cfrac%7B0.155g%7D%7B148.2g%2Fmol%7D%3D0.00104mol)
- <u>For pyridinium tribromide:</u>
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:
![\text{Moles of pyridinium tribromide}=\frac{0.458g}{319.82g/mol}=0.00143mol](https://tex.z-dn.net/?f=%5Ctext%7BMoles%20of%20pyridinium%20tribromide%7D%3D%5Cfrac%7B0.458g%7D%7B319.82g%2Fmol%7D%3D0.00143mol)
- The chemical equation for the reaction of trans-cinnamic acid and pyridinium tribromide follows:
![\text{trans-cinnamic acid}+\text{pyridinium tribromide}\xrightarrow[]{CH_3COOH}\text{2,3-dibromo-3-phenyl propanoic acid}](https://tex.z-dn.net/?f=%5Ctext%7Btrans-cinnamic%20acid%7D%2B%5Ctext%7Bpyridinium%20tribromide%7D%5Cxrightarrow%5B%5D%7BCH_3COOH%7D%5Ctext%7B2%2C3-dibromo-3-phenyl%20propanoic%20acid%7D)
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 =
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 =
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:
![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](https://tex.z-dn.net/?f=0.00104mol%3D%5Cfrac%7B%5Ctext%7BMass%20of%202%2C3-dibromo-3-phenyl%20propanoic%20acid%7D%7D%7B308g%2Fmol%7D%5C%5C%5C%5C%5Ctext%7BMass%20of%202%2C3-dibromo-3-phenyl%20propanoic%20acid%7D%3D0.320g)
- To calculate the percentage yield of 2,3-dibromo-3-phenyl propanoic acid, we use the equation:
![\%\text{ yield}=\frac{\text{Experimental yield}}{\text{Theoretical yield}}\times 100](https://tex.z-dn.net/?f=%5C%25%5Ctext%7B%20yield%7D%3D%5Cfrac%7B%5Ctext%7BExperimental%20yield%7D%7D%7B%5Ctext%7BTheoretical%20yield%7D%7D%5Ctimes%20100)
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:
![\%\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\%](https://tex.z-dn.net/?f=%5C%25%5Ctext%7B%20yield%20of%202%2C3-dibromo-3-phenyl%20propanoic%20acid%7D%3D%5Cfrac%7B0.217g%7D%7B0.320g%7D%5Ctimes%20100%5C%5C%5C%5C%5C%25%20%5Ctext%7Byield%20of%202%2C3-dibromo-3-phenyl%20propanoic%20acid%7D%3D67.81%5C%25)
Hence, the theoretical yield of the product is 0.320 grams and its percent yield is 67.81 %