Viridicatumtoxin B, C30H31NO10, is a natural antibiotic compound. It requires a synthesis of 12 steps in the laboratory. Assuming all steps have equivalent yields of 85%, which is the final percent yield of the total synthesis?

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Identify that the problem involves calculating the overall percent yield of a multi-step synthesis, where each step has an equivalent yield of 85%.

Recall that the overall yield of a multi-step process is the product of the yields of each individual step.

Express the yield of each step as a decimal: 85% becomes 0.85.

Since there are 12 steps, raise the yield of one step to the power of 12: \((0.85)^{12}\).

Convert the result back to a percentage by multiplying by 100 to find the final percent yield of the total synthesis.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Percent Yield

Percent yield is a measure of the efficiency of a chemical reaction, calculated as the ratio of the actual yield to the theoretical yield, multiplied by 100. It indicates how much product is obtained from a reaction compared to the maximum possible amount, helping chemists assess the effectiveness of their synthetic processes.

Sequential Reactions

In synthetic chemistry, sequential reactions refer to a series of chemical transformations where the product of one reaction serves as the reactant for the next. Each step can affect the overall yield, as the final product yield is influenced by the yields of all preceding steps, necessitating careful calculation of cumulative effects.

Multiplicative Yield Calculation

When dealing with multiple steps in a synthesis, the overall yield is calculated by multiplying the yields of each individual step. For example, if each step has a yield of 85%, the final yield is determined by raising the yield to the power of the number of steps, reflecting the compounding effect of losses at each stage.

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When a mixture of 10.0 g of acetylene (C₂H₂) and 10.0 g of oxygen (O₂) is ignited, the resulting combustion reaction produces CO₂ and H₂O. (c) How many grams of C₂H₂are present after the reaction is complete?

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