Let's solve the problem step-by-step to determine the volume in liters for 5.90 grams of hydrogen sulfide (H₂S) at standard temperature and pressure (STP).
### Step 1: Determine the molar mass of H₂S
First, we need to find the molar mass of H₂S. Hydrogen sulfide (H₂S) consists of two hydrogen atoms and one sulfur atom.
- The atomic mass of hydrogen (H) is approximately 1.01 g/mol.
- The atomic mass of sulfur (S) is approximately 32.06 g/mol.
The molar mass of H₂S can be calculated as follows:
[tex]\[ \text{Molar mass of } H_2S = 2 \times (\text{atomic mass of H}) + \text{atomic mass of S} \][/tex]
[tex]\[ \text{Molar mass of } H_2S = 2 \times 1.01 \text{ g/mol} + 32.06 \text{ g/mol} \][/tex]
[tex]\[ \text{Molar mass of } H_2S = 2.02 \text{ g/mol} + 32.06 \text{ g/mol} \][/tex]
[tex]\[ \text{Molar mass of } H_2S = 34.08 \text{ g/mol} \][/tex]
### Step 2: Calculate the number of moles of H₂S
Next, using the mass of H₂S given (5.90 grams) and the molar mass of H₂S calculated above, we determine the number of moles of H₂S.
[tex]\[ \text{Number of moles} = \frac{\text{mass of } H_2S}{\text{molar mass of } H_2S} \][/tex]
[tex]\[ \text{Number of moles} = \frac{5.90 \text{ g}}{34.08 \text{ g/mol}} \][/tex]
[tex]\[ \text{Number of moles} = 0.17312206572769956 \][/tex]
### Step 3: Calculate the volume of H₂S gas at STP
At standard temperature and pressure (STP), one mole of an ideal gas occupies 22.414 liters. To find the volume of H₂S gas at STP, we multiply the number of moles of H₂S by the molar volume of a gas at STP.
[tex]\[ \text{Volume} = \text{Number of moles} \times \text{Volume occupied by one mole at STP} \][/tex]
[tex]\[ \text{Volume} = 0.17312206572769956 \times 22.414 \text{ L/mol} \][/tex]
[tex]\[ \text{Volume} = 3.880357981220658 \text{ L} \][/tex]
### Conclusion
The volume of 5.90 grams of hydrogen sulfide (H₂S) at standard temperature and pressure (STP) is approximately 3.88 liters.
