Problem 34 - Chemistry

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?

Step-by-Step Solution

Answer

The short answer, based on the step-by-step solution, is: To find the total mass of the second chloroform sample, first find the relative masses of carbon, chlorine, and hydrogen in the first sample: \[R_\text{C} = \frac{M_\text{C}}{M_\text{total}}\] \[R_\text{Cl} = \frac{M_\text{Cl}}{M_\text{total}}\] \[R_\text{H} = \frac{M_\text{H}}{M_\text{total}}\] Use the mass of carbon and the relative masses calculated above to find the total mass of the second sample: \[M_\text{total} = \frac{30.0 \mathrm{~g}}{1 - R_\text{Cl} - R_\text{H}}\]

Step 1: 1: Calculate the total mass of the first chloroform sample

To solve this problem, first we need to find the total mass of the first chloroform sample. The mass of each element in the first sample is given as: - Carbon: \(12.0 \mathrm{~g}\) - Chlorine: \(106.4 \mathrm{~g}\) - Hydrogen: \(1.01 \mathrm{~g}\) Total mass of the first chloroform sample can be calculated as: \[M_\text{total} = M_\text{C} + M_\text{Cl} + M_\text{H}\]

Step 2: 2: Calculate relative mass of the elements in the first sample

Now, we need to find the relative mass of each element in the sample, which can be found by dividing the mass of each element by the total mass. Relative mass of carbon: \[R_\text{C} = \frac{M_\text{C}}{M_\text{total}}\] Relative mass of chlorine: \[R_\text{Cl} = \frac{M_\text{Cl}}{M_\text{total}}\] Relative mass of hydrogen: \[R_\text{H} = \frac{M_\text{H}}{M_\text{total}}\]

Step 3: 3: Calculate the total mass of the second chloroform sample

Now, we need to use the relative masses and the mass of carbon in the second chloroform sample to calculate the total mass of the second sample. We are given the mass of carbon in the second sample: - Carbon: \(30.0 \mathrm{~g}\) Applying the relative mass ratio for each element we derived in step 2: - Chlorine: \(R_\text{Cl} \times M_\text{total} = M_\text{Cl}\) - Hydrogen: \(R_\text{H} \times M_\text{total} = M_\text{H}\) Now combine these equations: \[M_\text{total} = M_\text{C} + M_\text{Cl} + M_\text{H}\] \[M_\text{total} = 30.0 \mathrm{~g} + R_\text{Cl} \times M_\text{total} + R_\text{H} \times M_\text{total}\] Solve the equation above for the total mass of the second chloroform sample: \[M_\text{total} = \frac{30.0 \mathrm{~g}}{1 - R_\text{Cl} - R_\text{H}}\]