Answer :
Sure! Let's solve each part of the problem step by step to find the grams of the specified elements in their respective compounds:
### a. Sulfur in [tex]\(3.54 \, \text{g} \, \text{H}_2\text{S}\)[/tex]
1. Determine the molar mass of [tex]\(\text{H}_2\text{S}\)[/tex]:
[tex]\[ \text{H}_2\text{S} = 2 \times 1.01 \, \text{g/mol (for H)} + 32.07 \, \text{g/mol (for S)} = 34.08 \, \text{g/mol} \][/tex]
2. Calculate the moles of [tex]\(\text{H}_2\text{S}\)[/tex]:
[tex]\[ \text{Moles of } \text{H}_2\text{S} = \frac{3.54 \, \text{g}}{34.08 \, \text{g/mol}} \][/tex]
3. Determine the grams of sulfur:
[tex]\[\text{Grams of sulfur} = \text{moles of } \text{H}_2\text{S} \times 32.07 \, \text{g/mol (for S)}\][/tex]
### b. Nitrogen in [tex]\(25.0 \, \text{g} \, \left( \text{NH}_4\right)_2 \text{C}_2 \text{O}_4\)[/tex]
1. Determine the molar mass of [tex]\(\left( \text{NH}_4\right)_2 \text{C}_2 \text{O}_4\)[/tex]:
[tex]\[ \left( \text{NH}_4\right)_2 \text{C}_2 \text{O}_4 = 2 \times (14.01 + 4 \times 1.01) + 2 \times 12.01 + 4 \times 16.00 = 114.1 \, \text{g/mol} \][/tex]
2. Calculate the moles of [tex]\(\left( \text{NH}_4\right)_2 \text{C}_2 \text{O}_4\)[/tex]:
[tex]\[ \text{Moles of } \left( \text{NH}_4\right)_2 \text{C}_2 \text{O}_4 = \frac{25.0 \, \text{g}}{114.1 \, \text{g/mol}} \][/tex]
3. Determine the grams of nitrogen:
[tex]\[\text{Grams of nitrogen} = \text{moles of } \left( \text{NH}_4\right)_2 \text{C}_2 \text{O}_4 \times 2 \times 14.01 \, \text{g/mol (for N)}\][/tex]
### c. Magnesium in [tex]\(97.4 \, \text{g} \, \text{Mg}(\text{OH})_2\)[/tex]
1. Determine the molar mass of [tex]\(\text{Mg}(\text{OH})_2\)[/tex]:
[tex]\[ \text{Mg}(\text{OH})_2 = 24.31 + 2 \times (16.00 + 1.01) = 58.32 \, \text{g/mol} \][/tex]
2. Calculate the moles of [tex]\(\text{Mg}(\text{OH})_2\)[/tex]:
[tex]\[ \text{Moles of } \text{Mg}(\text{OH})_2 = \frac{97.4 \, \text{g}}{58.32 \, \text{g/mol}} \][/tex]
3. Determine the grams of magnesium:
[tex]\[\text{Grams of magnesium} = \text{moles of } \text{Mg}(\text{OH})_2 \times 24.31 \, \text{g/mol (for Mg)}\][/tex]
### d. Phosphorus in [tex]\(804 \, \text{g} \, \text{Na}_3 \text{PO}_4\)[/tex]
1. Determine the molar mass of [tex]\(\text{Na}_3 \text{PO}_4\)[/tex]:
[tex]\[ \text{Na}_3 \text{PO}_4 = 3 \times 22.99 + 30.97 + 4 \times 16.00 = 163.94 \, \text{g/mol} \][/tex]
2. Calculate the moles of [tex]\(\text{Na}_3 \text{PO}_4\)[/tex]:
[tex]\[ \text{Moles of } \text{Na}_3 \text{PO}_4 = \frac{804 \, \text{g}}{163.94 \, \text{g/mol}} \][/tex]
3. Determine the grams of phosphorus:
[tex]\[\text{Grams of phosphorus} = \text{moles of } \text{Na}_3 \text{PO}_4 \times 30.97 \, \text{g/mol (for P)}\][/tex]
These calculations result in:
- Grams of sulfur: approximately [tex]\(3.33 \, \text{g}\)[/tex]
- Grams of nitrogen: approximately [tex]\(6.14 \, \text{g}\)[/tex]
- Grams of magnesium: approximately [tex]\(40.60 \, \text{g}\)[/tex]
- Grams of phosphorus: approximately [tex]\(151.88 \, \text{g}\)[/tex]
Let me know if you have any further questions!
### a. Sulfur in [tex]\(3.54 \, \text{g} \, \text{H}_2\text{S}\)[/tex]
1. Determine the molar mass of [tex]\(\text{H}_2\text{S}\)[/tex]:
[tex]\[ \text{H}_2\text{S} = 2 \times 1.01 \, \text{g/mol (for H)} + 32.07 \, \text{g/mol (for S)} = 34.08 \, \text{g/mol} \][/tex]
2. Calculate the moles of [tex]\(\text{H}_2\text{S}\)[/tex]:
[tex]\[ \text{Moles of } \text{H}_2\text{S} = \frac{3.54 \, \text{g}}{34.08 \, \text{g/mol}} \][/tex]
3. Determine the grams of sulfur:
[tex]\[\text{Grams of sulfur} = \text{moles of } \text{H}_2\text{S} \times 32.07 \, \text{g/mol (for S)}\][/tex]
### b. Nitrogen in [tex]\(25.0 \, \text{g} \, \left( \text{NH}_4\right)_2 \text{C}_2 \text{O}_4\)[/tex]
1. Determine the molar mass of [tex]\(\left( \text{NH}_4\right)_2 \text{C}_2 \text{O}_4\)[/tex]:
[tex]\[ \left( \text{NH}_4\right)_2 \text{C}_2 \text{O}_4 = 2 \times (14.01 + 4 \times 1.01) + 2 \times 12.01 + 4 \times 16.00 = 114.1 \, \text{g/mol} \][/tex]
2. Calculate the moles of [tex]\(\left( \text{NH}_4\right)_2 \text{C}_2 \text{O}_4\)[/tex]:
[tex]\[ \text{Moles of } \left( \text{NH}_4\right)_2 \text{C}_2 \text{O}_4 = \frac{25.0 \, \text{g}}{114.1 \, \text{g/mol}} \][/tex]
3. Determine the grams of nitrogen:
[tex]\[\text{Grams of nitrogen} = \text{moles of } \left( \text{NH}_4\right)_2 \text{C}_2 \text{O}_4 \times 2 \times 14.01 \, \text{g/mol (for N)}\][/tex]
### c. Magnesium in [tex]\(97.4 \, \text{g} \, \text{Mg}(\text{OH})_2\)[/tex]
1. Determine the molar mass of [tex]\(\text{Mg}(\text{OH})_2\)[/tex]:
[tex]\[ \text{Mg}(\text{OH})_2 = 24.31 + 2 \times (16.00 + 1.01) = 58.32 \, \text{g/mol} \][/tex]
2. Calculate the moles of [tex]\(\text{Mg}(\text{OH})_2\)[/tex]:
[tex]\[ \text{Moles of } \text{Mg}(\text{OH})_2 = \frac{97.4 \, \text{g}}{58.32 \, \text{g/mol}} \][/tex]
3. Determine the grams of magnesium:
[tex]\[\text{Grams of magnesium} = \text{moles of } \text{Mg}(\text{OH})_2 \times 24.31 \, \text{g/mol (for Mg)}\][/tex]
### d. Phosphorus in [tex]\(804 \, \text{g} \, \text{Na}_3 \text{PO}_4\)[/tex]
1. Determine the molar mass of [tex]\(\text{Na}_3 \text{PO}_4\)[/tex]:
[tex]\[ \text{Na}_3 \text{PO}_4 = 3 \times 22.99 + 30.97 + 4 \times 16.00 = 163.94 \, \text{g/mol} \][/tex]
2. Calculate the moles of [tex]\(\text{Na}_3 \text{PO}_4\)[/tex]:
[tex]\[ \text{Moles of } \text{Na}_3 \text{PO}_4 = \frac{804 \, \text{g}}{163.94 \, \text{g/mol}} \][/tex]
3. Determine the grams of phosphorus:
[tex]\[\text{Grams of phosphorus} = \text{moles of } \text{Na}_3 \text{PO}_4 \times 30.97 \, \text{g/mol (for P)}\][/tex]
These calculations result in:
- Grams of sulfur: approximately [tex]\(3.33 \, \text{g}\)[/tex]
- Grams of nitrogen: approximately [tex]\(6.14 \, \text{g}\)[/tex]
- Grams of magnesium: approximately [tex]\(40.60 \, \text{g}\)[/tex]
- Grams of phosphorus: approximately [tex]\(151.88 \, \text{g}\)[/tex]
Let me know if you have any further questions!
