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Chapter 2: Problem 39

A sample of chloroform is found to contain 12.0 g of carbon, 106.4 g of chlorine, and 1.01 g of hydrogen. If a second sample of chloroform is found to contain 30.0 g of carbon, what is the total mass of chloroform in the second sample?

Short Answer

Expert verified
The total mass of chloroform in the second sample is approximately 298.53 g.

Step by step solution

01

Find the mass ratio of carbon, chlorine, and hydrogen in chloroform.

We have a sample of chloroform with the following masses of elements: - Carbon: 12.0 g - Chlorine: 106.4 g - Hydrogen: 1.01 g To find the mass ratio, we divide the mass of each element by the total mass of the sample: Total mass of the sample = 12.0 g (C) + 106.4 g (Cl) + 1.01 g (H) = 119.41 g Mass ratio of Carbon = \(\frac{12.0}{119.41}\) Mass ratio of Chlorine = \(\frac{106.4}{119.41}\) Mass ratio of Hydrogen = \(\frac{1.01}{119.41}\)
02

Find the mass of chloroform in the second sample using the mass ratio.

We are given that the second sample of chloroform contains 30.0 g of carbon. We can use the mass ratio of carbon found in step 1 to find the total mass of chloroform in the second sample. Let x be the total mass of the second sample of chloroform. The mass ratio of carbon in the second sample would be the same as that in the first sample, thus; \(\frac{30.0}{x}\) = \(\frac{12.0}{119.41}\) To find the total mass of the second sample (x), we can cross-multiply and solve for x: \(30.0 * 119.41 = 12.0 * x\) \(x = \frac{30.0 * 119.41}{12.0}\)
03

Calculate the total mass of chloroform in the second sample.

Now we can compute the total mass of chloroform in the second sample using the value of x obtained in step 2: Total mass of the second sample (x) = \(\frac{30.0 * 119.41}{12.0}\) = 298.53 g So, the total mass of chloroform in the second sample is approximately 298.53 g.

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