Problem 13 - General Chemistry: Principles and Modern Applications

Question

Sulfur forms two compounds with oxygen. In the first compound, \(1.000 \mathrm{g}\) sulfur is combined with \(0.998 \mathrm{g}\) oxygen, and in the second, \(1.000 \mathrm{g}\) sulfur is combined with \(1.497 \mathrm{g}\) oxygen. Show that these results are consistent with Dalton's law of multiple proportions

Step-by-Step Solution

Answer

The mass ratios of oxygen to sulfur in the two compounds are approximately 1:1 and 1.5:1. Taylor's law of multiple proportions, which states that these ratios should be small whole numbers, is therefore confirmed by these results, although there is a minor discrepancy, likely due to measurement or rounding errors.

Step 1: Determine the Ratios

First, the mass ratios of oxygen to sulfur in both compounds need to be determined. This can be done by dividing the mass of the oxygen by the mass of the sulfur. In the first compound, the ratio is \(0.998 \, \mathrm{g} / 1.000 \, \mathrm{g} = 0.998\). In the second compound, the ratio is \(1.497 \, \mathrm{g} / 1.000 \, \mathrm{g} = 1.497\).

Step 2: Compare the Ratios

Next, divide the larger ratio by the smaller ratio. This should give a number that is a small whole number or very close to it if the law of multiple proportions is valid. Hence, \(1.497/0.998 = 1.50\).

Step 3: Interpret the Result

The result of the division yields approximately 1.5. Although this is not a whole number, it is very close to the whole number 1.5, which suggests that the given data are generally consistent with the law of multiple proportions. Small deviations from whole numbers can be due to experimental inaccuracies or rounding errors.

Key Concepts

Understanding Chemical Compounds

Chemical compounds are substances formed when two or more elements are chemically bonded together. In this exercise, we're looking at how sulfur forms compounds with oxygen. These substances are S-O compounds, meaning sulfur bonds with oxygen in different ratios to create distinct compounds. This is possible because elements can combine in various ratios to form different compounds, each with unique properties and structures.

• Compounds have a specific set of properties that are different from the individual elements they consist of.
• The composition of a compound is always present in fixed ratios by mass, illustrating Dalton's Law of Definite Proportions.

In our example, sulfur and oxygen form two distinct compounds by combining in different mass ratios. This concept is crucial for understanding the chemical behavior of elements and predicting how they might combine to form various compounds.

Exploring Mass Ratios

Mass ratios play a pivotal role in understanding chemical compounds and their formation. When elements combine, they do so in simple ratios of whole numbers. The mass ratio is the relationship between the masses of the elements involved in a compound.

• In our example, sulfur forms one compound with a mass ratio of oxygen to sulfur as 0.998:1.
• In the second compound, the ratio is 1.497:1.

By comparing these ratios, we can see if they align with Dalton's Law of Multiple Proportions, which states that if two elements form more than one compound, the ratio of the masses of the second element that combine with a fixed mass of the first element are simple whole numbers. The calculated ratio of 1.5 from our exercise suggests that the compounds adhere to this law. Deviations from exact whole numbers can occur, often due to measurement errors or limitations in experimental methods.

The Importance of Experimental Accuracy

Experimental accuracy is crucial in confirming theoretical laws such as Dalton's Law of Multiple Proportions. When scientists conduct experiments to determine mass ratios, precision in measurement is key to obtaining reliable results.

• Accuracy refers to how close a measured value is to the actual (true) value. In our example, accuracy ensures that the measured masses of sulfur and oxygen are correct.
• Experimental errors can arise from improper calibration of instruments, human error, or environmental factors affecting measurements.

In cases where results do not perfectly match theoretical predictions (like a ratio not equalling a whole number), it could be due to minor experimental inaccuracies. These can include slight discrepancies in mass measurements or small loss of materials during the experiments. Recognizing these sources of error allows scientists to make more accurate conclusions and refine their methods for future experiments.