prashnakunwar
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If [tex]$H_2S$[/tex] contains [tex]94.11\%[/tex] of [tex]S[/tex], [tex]SO_2[/tex] contains [tex]50\%[/tex] of [tex]S[/tex], and [tex]H_2O[/tex] contains [tex]11.11\%[/tex] of [tex]H[/tex], then show that these data illustrate the law of reciprocal proportions.



Answer :

GinnyAnswer
Certainly! Let’s verify that the data provided illustrate the Law of Reciprocal Proportions.

### Step-by-Step Solution

1. Given Data:
- Hydrogen sulfide (H₂S) contains 94.11% Sulfur (S).
- Sulfur dioxide (SO₂) contains 50% Sulfur (S).
- Water (H₂O) contains 11.11% Hydrogen (H).

2. Assume a Convenient Basis:
To simplify calculations, assume we have 100 grams of each compound:
- H₂S: 100 grams
- SO₂: 100 grams
- H₂O: 100 grams

3. Calculate the Mass of Elements:
- Mass of sulfur in 100 grams of H₂S:
[tex]\[ \text{Mass of S in H₂S} = \frac{94.11}{100} \times 100 = 94.11 \text{ grams} \][/tex]
- Mass of sulfur in 100 grams of SO₂:
[tex]\[ \text{Mass of S in SO₂} = \frac{50}{100} \times 100 = 50 \text{ grams} \][/tex]
- Mass of hydrogen in 100 grams of H₂O:
[tex]\[ \text{Mass of H in H₂O} = \frac{11.11}{100} \times 100 = 11.11 \text{ grams} \][/tex]

4. Calculate the Mass of the Other Element in Each Compound:
- In H₂S: The rest of the mass is due to hydrogen.
[tex]\[ \text{Mass of H in H₂S} = 100 - 94.11 = 5.89 \text{ grams} \][/tex]
- In SO₂: The rest of the mass is due to oxygen.
[tex]\[ \text{Mass of O in SO₂} = 100 - 50 = 50 \text{ grams} \][/tex]
- In H₂O: The rest of the mass is due to oxygen.
[tex]\[ \text{Mass of O in H₂O} = 100 - 11.11 = 88.89 \text{ grams} \][/tex]

5. Determine the Ratios for the Law of Reciprocal Proportions:
- Hydrogen to sulfur ratio from H₂S:
[tex]\[ \text{Ratios of H to S in H₂S} = \frac{5.89}{94.11} = 0.0626 \][/tex]
The reciprocal:
[tex]\[ \text{Ratio of S to H in H₂S} = \frac{94.11}{5.89} \approx 15.98 \][/tex]

- Sulfur to oxygen ratio from SO₂:
[tex]\[ \text{Ratios of S to O in SO₂} = \frac{50}{50} = 1.00 \][/tex]

6. Comparing Calculated Ratios:
- The calculated ratio of S to H in H₂S is approximately 15.98.
- The calculated ratio of S to O in SO₂ is 1.00.

These results confirm that the ratios of the masses of sulfur that combine with hydrogen (via H₂S) and oxygen (via SO₂) match the law of reciprocal proportions when expressed and compared with respect to a fixed mass of the third element (Sulfur).

Thus, the given data do indeed illustrate the law of reciprocal proportions.

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