The percentage yield of a reaction is 24.3%. If an experimental value of 114.86 g of product is obtained, what would be the theoretical value?

Question

BlackTom AI · Accepted Answer

We start by identifying the relationship between actual yield, theoretical yield, and percent yield. Percent yield is defined as (actual yield / theoretical yield) × 100.

Option-by-option analysis:
- 27.87 g: If this were the theoretical yield, then the percent yield would be (114.86 / 27.87) × 100 ≈ 412.5%, which is impossible for a typical reaction. This option is clearly inconsistent with the definition of percent yield.
- 86.99 g: If this were the theoretical yield, the percent yield would be (114.86 / 86.99) × 100 ≈ 132.1%, still impossible since percent yield cannot exceed 100% in ordinary reactions. This option is not viable.
- 424.67 g: If this were the theoretical yield, the percent yield would be (114.86 / 424.67) × 100 ≈ 27.1%. This is a plausible value for percent yield, though it does not match the given 24.3% exactly. It would imply a yield close to 27%, which could occur if there were rounding or measurement issues.
- 357.81 g: If this were the theoretical yield, the percent yield would be (114.86 / 357.81) × 100 ≈ 32.1%, which is again a plausible percentage but not matching the stated 24.3% yield.
- 92.41 g: If this were the theoretical yield, the percent yield would be (114.86 / 92.41) × 100 ≈ 124.5%, which is not physically meaningful for a standard reaction; percent yield cannot exceed 100% under ordinary conditions.

Now, focusing on the key formula: actual = (percent yield) × (theoretical yield) / 100. Rearranging gives theoretical yield = actual × 100 / percent yield. Using actual = 114.86 g and percent yield = 24.3%, we calculate theoretical yield ≈ 114.86 × 100 / 24.3 ≈ 114.86 × 4.115226 = approximately 473 g.

Compare this to the provided options: none of the listed options equals roughly 473 g. The closest option is 424.67 g, which would correspond to a percent yield of about 27.1% if used with the same formula. This suggests a possible inconsistency between the stated percent yield (24.3%) and the answer choices, or a rounding/recording discrepancy in the problem.

In summary, applying the standard definition yields a theoretical value near 473 g, but none of the answer choices matches that result exactly. The option 424.67 g would imply a different percent yield (around 27%), not 24.3%, indicating a mismatch between the provided percent yield and the option set.

The percentage yield of a reaction is 24.3%. If an experimental value of 114.86 g of product is obtained, what would be the theoretical value?

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