Respuesta :
13%.
When doing problems with linear reactions, convert the percents into decimals, then multiplying the decimals. So the calculation would be 0.98*0.45*0.66*0.87*0.50 = 0.13 = 13%.
Remember to keep significant figures, since we were given only 2 significant figures at most, we keep only 2 in the final answer.
The overall percentage yield of the drug is [tex]\boxed{13{\text{ }}\%}[/tex].
Further explanation:
Percentage yield is defined as the percent ratio of actual yield to theoretical yield. The formula of the percentage yield is actual yield divided by theoretical yield and multiplied by 100.
[tex]{\text{Percent yield }}\left(\%\right)=\left({\frac{{{\text{actual yield}}}}{{{\text{theoretical yield}}}}}\right)\times{\text{100\%}}[/tex] …… (1)
Let the process of synthesis of the drug occurs in five steps such as reactant A gives B in the first step with 98 % yield. Then B produces C in second step with 45 % yield. Then C produces D in third step with 66 % yield. After that, fourth step produces E from D with 87 % yield. The last fifth step produces F from E with 50 % yield.
[tex]{\text{A}}\xrightarrow{{98{\text{\%}}}}{\text{B}}\xrightarrow{{45{\text{\%}}}}{\text{C}}\xrightarrow{{66{\text{\%}}}}{\text{D}}\xrightarrow{{87{\text{\%}}}}{\text{E}}\xrightarrow{{50{\text{\%}}}}{\text{F}}[/tex]
Let the initial amount of A be x.
Since the first step only yields 98 % B and thus the amount of B produced is,
[tex]{\text{Amount of B}}={\text{0}}{\text{.98x}}[/tex]
In the second step, B produces C with 45 % yield. Therefore, the amount of C is 45 % of amount of B.
[tex]\begin{aligned}{\text{Amount of C}}&=\left({0.45}\right)\left({{\text{Amount of B}}}\right)\\&=\left({0.45}\right)\left({{\text{0}}{\text{.98x}}}\right)\\&=0.441{\text{x}}\\\end{aligned}[/tex]
In the third step, C produces D with 66 % yield. Therefore, the amount of D is 66 % of amount of C.
[tex]\begin{aligned}{\text{Amount of D}}&=\left({0.66}\right)\left({{\text{Amount of C}}}\right)\\&=\left({0.66}\right)\left({0.441{\text{x}}}\right)\\&=0.29106{\text{x}}\\\end{aligned}[/tex]
In the fourth step, D produces E with 87 % yield. Therefore, the amount of E is 87 % of amount of D.
[tex]\begin{aligned}{\text{Amount of E}}&=\left({0.87}\right)\left({{\text{Amount of D}}}\right)\\&=\left({0.87}\right)\left({0.29106{\text{x}}}\right)\\&=0.25322{\text{x}}\\\end{aligned}[/tex]
In the fifth step, E produces Fwith 50 % yield. Therefore, the amount of F is 87 % of the amount of E.
[tex]\begin{aligned}{\text{Amount of F}}&=\left({0.50}\right)\left({{\text{Amount of E}}}\right)\\&=\left({0.50}\right)\left({0.25322{\text{x}}}\right)\\&=0.12661{\text{x}}\\\end{aligned}[/tex]
Therefore the final amount of F is 0.12661x.
Substitute 0.12661x for actual yield and x for the theoretical yield in equation (1)
[tex]\begin{aligned}{\text{Percent yield }}\left(\%\right)&=\left({\frac{{{\text{0}}{\text{.12661x}}}}{{\text{x}}}}\right)\times{\text{100}}\\&{\text{= 12}}{\text{.66 \%}}\\&\simeq{\text{13 \%}}\\\end{aligned}[/tex]
Learn more:
1. Determine the Lewis structure of butanal.: https://brainly.com/question/6215269
2. Determine the correct structure of [tex]{{\text{N}}_{\text{2}}}{\text{O}}[/tex]: https://brainly.com/question/9422880
Answer details:
Grade: Senior School
Subject: Chemistry
Chapter: Mole concept
Keywords: synthesis, particular drug, five steps, yield, percentage yield, 98%, 45%, 66%, 87% ,50% and 13%.
