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Chapter 1: Problem 67

A sample of ascorbic acid (vitamin \(\mathrm{C} )\) is synthesized in the laboratory. It contains 1.50 \(\mathrm{g}\) of carbon and 2.00 \(\mathrm{g}\) of oxygen. Another sample of ascorbic acid isolated from citrus fruits contains 6.35 \(\mathrm{g}\) of carbon. According to the law of constant composition, how many grams of oxygen does it contain?

Short Answer

Expert verified
The mass ratio of carbon to oxygen in the first sample of ascorbic acid is \(0.75\). Using this ratio, there are approximately \(8.47 \mathrm{g}\) of oxygen in the second sample, which contains \(6.35 \mathrm{g}\) of carbon.

Step by step solution

01

Calculate the mass ratio of the elements in the first sample

First, we need to find out the mass ratio of carbon and oxygen in the first sample. We are given 1.50 grams of carbon and 2.00 grams of oxygen, so the mass ratio of carbon to oxygen is: \[\frac{\text{mass of carbon}}{\text{mass of oxygen}} = \frac{1.50}{2.00} = 0.75\]
02

Use the mass ratio to find the mass of oxygen in the second sample

Now, we'll use the calculated mass ratio from step 1 to find the mass of oxygen in the second sample. We're given that the second sample contains 6.35 grams of carbon. Let 'x' be the mass of oxygen in the second sample. \[0.75 = \frac{6.35}{x}\]
03

Solve for x

Now, we need to solve for 'x' to find out the mass of oxygen in the second sample: \[x = \frac{6.35}{0.75}\] \[x \approx 8.47\] So, there are approximately 8.47 grams of oxygen in the second sample of ascorbic acid.

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