Answer :
Sure! Let's break down the problem by calculating the number of grams of specific elements in each compound.
### a. Sulfur in [tex]\(3.54 \, \text{g of} \, \text{H}_2\text{S}\)[/tex]
1. Molar Mass of [tex]\(\text{H}_2\text{S}\)[/tex]:
- Hydrogen (H): [tex]\(1.01 \, \text{g/mol}\)[/tex], and there are 2 hydrogens: [tex]\(1.01 \times 2 = 2.02 \, \text{g/mol}\)[/tex].
- Sulfur (S): [tex]\(32.07 \, \text{g/mol}\)[/tex].
Total molar mass of [tex]\(\text{H}_2\text{S}\)[/tex] is [tex]\(2.02 + 32.07 = 34.08 \, \text{g/mol}\)[/tex].
2. Calculate grams of sulfur:
- Find the fraction of sulfur in the molar mass: [tex]\(\frac{32.07}{34.08}\)[/tex].
- Multiply this fraction by the given mass: [tex]\(\frac{32.07}{34.08} \times 3.54 \, \text{g} = 3.33 \, \text{g}\)[/tex].
### b. Nitrogen in [tex]\(25.0 \, \text{g of} \, \left(\text{NH}_4\right)_2\text{C}_2\text{O}_4\)[/tex]
1. Molar Mass of [tex]\(\left(\text{NH}_4\right)_2\text{C}_2\text{O}_4\)[/tex]:
- Nitrogen (N): [tex]\(14.01 \, \text{g/mol}\)[/tex], and there are 2 nitrogens: [tex]\(14.01 \times 2 = 28.02 \, \text{g/mol}\)[/tex].
- Hydrogen (H), Carbon (C), and Oxygen (O) are added, total is [tex]\(124.1 \, \text{g/mol}\)[/tex].
2. Calculate grams of nitrogen:
- Calculate nitrogen's fraction: [tex]\(\frac{28.02}{124.1}\)[/tex].
- Multiply by given mass: [tex]\(\frac{28.02}{124.1} \times 25.0 \, \text{g} = 5.64 \, \text{g}\)[/tex].
### c. Magnesium in [tex]\(97.4 \, \text{g of} \, \text{Mg}(\text{OH})_2\)[/tex]
1. Molar Mass of [tex]\(\text{Mg}(\text{OH})_2\)[/tex]:
- Magnesium (Mg): [tex]\(24.31 \, \text{g/mol}\)[/tex].
- Total molar mass is [tex]\(24.31 + 34.02 = 58.32 \, \text{g/mol}\)[/tex].
2. Calculate grams of magnesium:
- Magnesium's fraction: [tex]\(\frac{24.31}{58.32}\)[/tex].
- Multiply by given mass: [tex]\(\frac{24.31}{58.32} \times 97.4 \, \text{g} = 40.60 \, \text{g}\)[/tex].
### d. Phosphorus in [tex]\(804 \, \text{g of} \, \text{Na}_3\text{PO}_4\)[/tex]
1. Molar Mass of [tex]\(\text{Na}_3\text{PO}_4\)[/tex]:
- Phosphorus (P): [tex]\(30.97 \, \text{g/mol}\)[/tex].
- Total molar mass is [tex]\(163.94 \, \text{g/mol}\)[/tex].
2. Calculate grams of phosphorus:
- Phosphorus's fraction: [tex]\(\frac{30.97}{163.94}\)[/tex].
- Multiply by mass: [tex]\(\frac{30.97}{163.94} \times 804 \, \text{g} = 151.88 \, \text{g}\)[/tex].
There you have it! The amounts of each element in grams are Sulfur: [tex]\(3.33 \, \text{g}\)[/tex], Nitrogen: [tex]\(5.64 \, \text{g}\)[/tex], Magnesium: [tex]\(40.60 \, \text{g}\)[/tex], and Phosphorus: [tex]\(151.88 \, \text{g}\)[/tex].
### a. Sulfur in [tex]\(3.54 \, \text{g of} \, \text{H}_2\text{S}\)[/tex]
1. Molar Mass of [tex]\(\text{H}_2\text{S}\)[/tex]:
- Hydrogen (H): [tex]\(1.01 \, \text{g/mol}\)[/tex], and there are 2 hydrogens: [tex]\(1.01 \times 2 = 2.02 \, \text{g/mol}\)[/tex].
- Sulfur (S): [tex]\(32.07 \, \text{g/mol}\)[/tex].
Total molar mass of [tex]\(\text{H}_2\text{S}\)[/tex] is [tex]\(2.02 + 32.07 = 34.08 \, \text{g/mol}\)[/tex].
2. Calculate grams of sulfur:
- Find the fraction of sulfur in the molar mass: [tex]\(\frac{32.07}{34.08}\)[/tex].
- Multiply this fraction by the given mass: [tex]\(\frac{32.07}{34.08} \times 3.54 \, \text{g} = 3.33 \, \text{g}\)[/tex].
### b. Nitrogen in [tex]\(25.0 \, \text{g of} \, \left(\text{NH}_4\right)_2\text{C}_2\text{O}_4\)[/tex]
1. Molar Mass of [tex]\(\left(\text{NH}_4\right)_2\text{C}_2\text{O}_4\)[/tex]:
- Nitrogen (N): [tex]\(14.01 \, \text{g/mol}\)[/tex], and there are 2 nitrogens: [tex]\(14.01 \times 2 = 28.02 \, \text{g/mol}\)[/tex].
- Hydrogen (H), Carbon (C), and Oxygen (O) are added, total is [tex]\(124.1 \, \text{g/mol}\)[/tex].
2. Calculate grams of nitrogen:
- Calculate nitrogen's fraction: [tex]\(\frac{28.02}{124.1}\)[/tex].
- Multiply by given mass: [tex]\(\frac{28.02}{124.1} \times 25.0 \, \text{g} = 5.64 \, \text{g}\)[/tex].
### c. Magnesium in [tex]\(97.4 \, \text{g of} \, \text{Mg}(\text{OH})_2\)[/tex]
1. Molar Mass of [tex]\(\text{Mg}(\text{OH})_2\)[/tex]:
- Magnesium (Mg): [tex]\(24.31 \, \text{g/mol}\)[/tex].
- Total molar mass is [tex]\(24.31 + 34.02 = 58.32 \, \text{g/mol}\)[/tex].
2. Calculate grams of magnesium:
- Magnesium's fraction: [tex]\(\frac{24.31}{58.32}\)[/tex].
- Multiply by given mass: [tex]\(\frac{24.31}{58.32} \times 97.4 \, \text{g} = 40.60 \, \text{g}\)[/tex].
### d. Phosphorus in [tex]\(804 \, \text{g of} \, \text{Na}_3\text{PO}_4\)[/tex]
1. Molar Mass of [tex]\(\text{Na}_3\text{PO}_4\)[/tex]:
- Phosphorus (P): [tex]\(30.97 \, \text{g/mol}\)[/tex].
- Total molar mass is [tex]\(163.94 \, \text{g/mol}\)[/tex].
2. Calculate grams of phosphorus:
- Phosphorus's fraction: [tex]\(\frac{30.97}{163.94}\)[/tex].
- Multiply by mass: [tex]\(\frac{30.97}{163.94} \times 804 \, \text{g} = 151.88 \, \text{g}\)[/tex].
There you have it! The amounts of each element in grams are Sulfur: [tex]\(3.33 \, \text{g}\)[/tex], Nitrogen: [tex]\(5.64 \, \text{g}\)[/tex], Magnesium: [tex]\(40.60 \, \text{g}\)[/tex], and Phosphorus: [tex]\(151.88 \, \text{g}\)[/tex].
