Question

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

Short answer

The total mass of chloroform in the second sample can be found by first calculating the mass ratio for each component in the first sample and then using these ratios to find the mass of chlorine and hydrogen in the second sample. The mass ratio for each component in the first sample is: Carbon Ratio = \(12.0\, \text{g} / 119.41\, \text{g}\) Chlorine Ratio = \(106.4\, \text{g} / 119.41\, \text{g}\) Hydrogen Ratio = \(1.01\, \text{g} / 119.41\, \text{g}\) Using these ratios, we can find the mass of chlorine and hydrogen in the second sample: Mass of Chlorine in Sample 2 = Chlorine Ratio * (Mass of Carbon in Sample 2 / Carbon Ratio) Mass of Hydrogen in Sample 2 = Hydrogen Ratio * (Mass of Carbon in Sample 2 / Carbon Ratio) Finally, we can calculate the total mass of the chloroform in the second sample: Total Mass (Sample 2) = Mass of Carbon (Sample 2) + Mass of Chlorine (Sample 2) + Mass of Hydrogen (Sample 2) Plugging the values into the equations, we find the total mass of chloroform in the second sample.

Step-by-step solution

Calculate the mass ratio of the components in the first sample

First, we need to find the mass ratio for carbon, chlorine, and hydrogen in the first sample of chloroform. We can calculate the mass ratio by dividing the mass of each component by the total mass of the sample. The total mass of the first sample is given by: Total Mass = Mass of Carbon + Mass of Chlorine + Mass of Hydrogen Total Mass = \(12.0\mathrm{g} + 106.4\mathrm{g} + 1.01\mathrm{g}\) Total Mass = \(119.41\mathrm{g}\) Now, we can calculate the mass ratio for each component: Carbon Ratio = Mass of Carbon / Total Mass = \(12.0\mathrm{g} / 119.41\mathrm{g}\) Chlorine Ratio = Mass of Chlorine / Total Mass = \(106.4\mathrm{g} / 119.41\mathrm{g}\) Hydrogen Ratio = Mass of Hydrogen / Total Mass = \(1.01\mathrm{g} / 119.41\mathrm{g}\)

Calculate the mass of other components in the second sample

Now that we have the mass ratio for each component in the first sample, we can use that information to find the mass of chlorine and hydrogen in the second sample. Knowing the mass ratio, we can find the mass of Chlorine and Hydrogen in Example 2: Mass of Chlorine in Sample 2 = Chlorine Ratio * (Mass of Carbon in Sample 2 / Carbon Ratio) Mass of Hydrogen in Sample 2 = Hydrogen Ratio * (Mass of Carbon in Sample 2 / Carbon Ratio)

Find the total mass of the second sample

Now that we have the mass of each component in the second sample, we can calculate the total mass of the chloroform in the second sample: Total Mass (Sample 2) = Mass of Carbon (Sample 2) + Mass of Chlorine (Sample 2) + Mass of Hydrogen (Sample 2) After calculating the mass of each component in the second sample in Step 2, plug the values into the equation above to find the total mass of the second sample. After finding the total mass of the chloroform in the second sample, we have our solution.

Key concepts

Mass Ratio in Chemistry

Understanding the mass ratio in chemistry is essential, as it reveals the proportions of different substances involved in a chemical compound or reaction. In the context of stoichiometry—a branch of chemistry that deals with the quantitative relationships between reactants and products in chemical reactions—calculating mass ratios allows us to predict the amounts of substances involved.

For example, in the exercise concerning chloroform, the mass ratios tell us how much carbon, chlorine, and hydrogen are present relative to each other. By knowing the mass of one component, we can calculate the expected masses of the other components in a different sample, assuming that the chemical composition of the substance remains consistent. This aspect of mass ratio is helpful, particularly when dealing with chemical scaling or purifying substances where the proportions must be maintained.

Chemical Composition

Chemical composition refers to the identity and relative number of the elements that make up any particular compound. Each compound has a unique composition that is represented by a chemical formula. This formula not only provides the types of atoms in the compound but also the ratio in which these atoms combine, based on the compound's molecular or empirical formula.

In the chloroform example, the chemical composition is constant, meaning that no matter how large or small a sample you have, the proportion of carbon to chlorine to hydrogen will remain the same. This consistent proportionality allows chemists to predict the outcomes of chemical reactions and to determine the mass of one component in a compound if the masses of the other components are known.

Law of Constant Composition

The law of constant composition, also known as the law of definite proportions, states that in a given chemical substance, the elements are always combined in the same proportions by mass. This law is a foundational principle in chemistry and is critical for understanding that regardless of the amount of the substance we are dealing with, its elemental makeup remains unchanged.

Applying this law to our chloroform problem implies that, no matter how big or small the sample of chloroform is, the mass ratio of carbon to chlorine to hydrogen is fixed. The exercise demonstrates this principle through a practical question — how one can determine the mass of a chloroform sample knowing only the mass of one component. Using the mass ratios derived from the law of constant composition, we can predict the total mass of different samples of a compound, showing the powerful application of this law in chemistry.