In this gravimetric analysis, the goal is to calculate the amount of mercury chloride (HgCl₂) in the sample based on the mercury sulfide (HgS) produced. The reaction for the formation of mercury sulfide (HgS) involves the reaction of mercury (Hg) with hydrogen sulfide (H₂S), which results in:

$\text{Hg}_2\text{Cl}_2 + \text{H}_2\text{S} \to \text{HgS} + \text{Cl}_2$

Given that 0.2551 g of mercury bichloride (HgCl₂) yields 0.1815 g of HgS, we will use stoichiometry to find the mass of HgCl₂.

Step 1: Calculate the moles of HgS produced

The molar mass of HgS is calculated as:

$\text{Molar mass of HgS} = 200.6 \, \text{g/mol (Hg)} + 32.07 \, \text{g/mol (S)} = 232.67 \, \text{g/mol}$

Now, using the given mass of HgS (0.1815 g):

$\text{Moles of HgS} = \frac{\text{Mass of HgS}}{\text{Molar mass of HgS}} = \frac{0.1815 \, \text{g}}{232.67 \, \text{g/mol}} = 0.000780 \, \text{mol}$

Step 2: Calculate the moles of mercury (Hg) in HgS

The mole ratio of Hg to HgS in the reaction is 1:1. Therefore, the moles of Hg in the sample will be the same as the moles of HgS:

$\text{Moles of Hg} = 0.000780 \, \text{mol}$

Step 3: Calculate the mass of mercury (Hg) in HgS

The mass of mercury (Hg) is calculated using its molar mass (200.6 g/mol):

$\text{Mass of Hg} = \text{Moles of Hg} \times \text{Molar mass of Hg} = 0.000780 \, \text{mol} \times 200.6 \, \text{g/mol} = 0.1565 \, \text{g}$

Step 4: Calculate the moles of HgCl₂ in the sample

In HgCl₂, there is 1 mole of Hg for every mole of HgCl₂. Therefore, the moles of HgCl₂ are the same as the moles of mercury:

$\text{Moles of HgCl}_2 = \text{Moles of Hg} = 0.000780 \, \text{mol}$

Step 5: Calculate the mass of HgCl₂ in the sample

The molar mass of HgCl₂ is:

$\text{Molar mass of HgCl}_2 = 200.6 \, \text{g/mol (Hg)} + 2 \times 35.45 \, \text{g/mol (Cl)} = 271.5 \, \text{g/mol}$

Now, calculate the mass of HgCl₂:

$\text{Mass of HgCl}_2 = \text{Moles of HgCl}_2 \times \text{Molar mass of HgCl}_2 = 0.000780 \, \text{mol} \times 271.5 \, \text{g/mol} = 0.2115 \, \text{g}$

Step 6: Calculate the percentage of HgCl₂ in the sample

Finally, to calculate the percentage of HgCl₂ in the sample:

$\text{Percentage of HgCl}_2 = \frac{\text{Mass of HgCl}_2}{\text{Mass of sample}} \times 100 = \frac{0.2115 \, \text{g}}{0.2551 \, \text{g}} \times 100 = 82.9\%$

Final Answer:

The HgCl₂ content of the sample is 82.9%.

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Would you like further explanation or details about any of the steps?

Here are some related questions for further study:

1. What is the importance of using gravimetric analysis in determining the composition of a sample?
2. How would the result change if the sample contained impurities?
3. What are the limitations of gravimetric methods in quantitative analysis?
4. How does the stoichiometric relationship between Hg and HgS play a role in the calculation?
5. What other methods can be used to determine the mercury content in a sample?

Tip: Always ensure that the mole ratios in chemical reactions are considered carefully, as they are crucial for accurate stoichiometric calculations.