A sample of liquid from a drainage ditch is analyzed, and the percent distribution of its contents, by mass, is determined, as shown in the graph above. If the sample contains 15 grams of water, how many grams of acid are in the sample?
There are 3 grams of acid in the sample.
The percent distribution of the contents indicates that the sample has a specific ratio of acid to water. Given that there are 15 grams of water, we can use the percentage to calculate the mass of acid present in the sample.
This choice suggests that there are 15 grams of acid in the sample, which would imply a one-to-one ratio with water. However, if the sample contains 15 grams of water, it cannot contain more acid than water unless the total mass of the sample is less than 30 grams, which contradicts the given percent distribution.
A total of 9 grams of acid would indicate a specific concentration that does not align with the percent distribution of contents. If 9 grams of acid were present, the total mass of the sample would be 24 grams (15 grams of water + 9 grams of acid), which does not align with the common ratios typically found in such samples.
Choosing 5 grams of acid would suggest a very low concentration relative to the 15 grams of water. This calculation would yield a total sample mass of 20 grams, which does not accurately reflect the expected distribution of contents based on typical measurements for such scenarios.
This choice correctly identifies the mass of acid in the sample. Given the percent distribution, if there are 15 grams of water, the acid mass is calculated to be 3 grams, maintaining a consistent ratio that aligns with the overall mass of the sample.
This option indicates only 2 grams of acid, which is too low compared to the mass of water present. This would create an unrealistic concentration and total mass for the sample, conflicting with the expected distribution percentages.
To find the mass of acid in the sample, we must analyze the percent distribution relative to the mass of water present. Given that the sample contains 15 grams of water and using the established ratios, it is determined that there are 3 grams of acid in the sample. Thus, the correct calculation aligns with choice D.
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