Answer: The theoretical yield of triphenylmethanol is 0.173 grams
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 benzophenone = 121 mg = 0.121 g (Conversion factor: 1 g = 1000 mg)
Molar mass of benzophenone = 182.21 g/mol
Putting values in equation 1, we get:
[tex]\text{Moles of benzophenone}=\frac{0.121g}{182.21g/mol}=6.64\times 10^{-4}mol[/tex]
The chemical equation for the formation of triphenylmethanol from benzophenone follows:
[tex]\text{Benzophenone}+Mg+\text{Bromobenzene}\rightarrow \text{Triphenylmethanol}+MgBr[/tex]
As, bromobenzene is the limiting reagent. So, it will limit the formation of products
By Stoichiometry of the reaction:
1 mole of bromobenzene produces 1 mole of triphenylmethanol
So, [tex]6.64\times 10^{-4}mol[/tex] of bromobenzene will produce = [tex]\frac{1}{1}\times 6.64\times 10^{-4}=6.64\times 10^{-4}[/tex] moles of triphenylmethanol
Now, calculating the mass of triphenylmethanol from equation 1, we get:
Molar mass of triphenylmethanol = 260.33 g/mol
Moles of triphenylmethanol = [tex]6.64\times 10^{-4}[/tex] moles
Putting values in equation 1, we get:
[tex]6.64\times 10^{-4}mol=\frac{\text{Mass of triphenylmethanol}}{260.33g/mol}\\\\\text{Mass of triphenylmethanol}=(6.64\times 10^{-4}mol\times 260.33g/mol)=0.173g[/tex]
Hence, the theoretical yield of triphenylmethanol is 0.173 grams