Sulphur and oxygen are known to form two compounds. The sulphur content in one of these is 51 % while in the other is 41 %. Show that this data is in agreement with the law of multiple proportions.

Explanation

To show that the data regarding the compounds of sulfur and oxygen is in agreement with the law of multiple proportions, we will follow these steps:

### Step 1: Identify the percentages of sulfur and oxygen in both compounds.
- For the first compound, the percentage of sulfur is 51%. Therefore, the percentage of oxygen is:
\[ \text{Percentage of Oxygen} = 100\% - 51\% = 49\% \]

- For the second compound, the percentage of sulfur is 41%. Therefore, the percentage of oxygen is:
\[ \text{Percentage of Oxygen} = 100\% - 41\% = 59\% \]

### Step 2: Calculate the mass of oxygen per gram of sulfur in each compound.
- For the first compound, if we assume 1 gram of sulfur, the mass of oxygen can be calculated as follows:
\[ \text{Mass of Oxygen in Compound 1} = \frac{49\%}{51\%} = \frac{49}{51} \approx 0.96 \text{ grams} \]

- For the second compound, if we assume 1 gram of sulfur, the mass of oxygen can be calculated as follows:
\[ \text{Mass of Oxygen in Compound 2} = \frac{59\%}{41\%} = \frac{59}{41} \approx 1.43 \text{ grams} \]

### Step 3: Find the ratio of the masses of oxygen in the two compounds.
- The ratio of the mass of oxygen in the first compound to the mass of oxygen in the second compound is:
\[ \text{Ratio} = \frac{1.43 \text{ grams}}{0.96 \text{ grams}} \approx 1.49 \]

### Step 4: Simplify the ratio to whole numbers.
- To express this ratio in whole numbers, we can multiply both sides by a common factor to eliminate the decimal:
\[ \text{Ratio} = \frac{1.43}{0.96} \approx \frac{3}{2} \]

### Step 5: Conclusion.
- The ratio of the masses of oxygen in the two compounds is approximately 3:2. According to the law of multiple proportions, when two elements combine to form more than one compound, the masses of one element that combine with a fixed mass of the other element will be in a simple ratio of whole numbers. Here, we have demonstrated that the ratio of oxygen in the two compounds of sulfur and oxygen is indeed 3:2, which confirms the law of multiple proportions.

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