To calculate the volume of each gas sample at Standard Temperature and Pressure (STP), we use the molar volume concept. The molar volume of a gas at STP is 22.414 liters per mole. Here is the detailed solution for each gas sample:
### (a) [tex]\(73.9 \, \text{g} \, \text{N}_2\)[/tex]
1. Given data:
- Mass of [tex]\( \text{N}_2 \)[/tex]: [tex]\(73.9 \, \text{g}\)[/tex]
- Molar mass of [tex]\( \text{N}_2 \)[/tex]: [tex]\(28.02 \, \text{g/mol}\)[/tex]
2. Calculate the number of moles:
[tex]\[
\text{Moles of } \text{N}_2 = \frac{73.9 \, \text{g}}{28.02 \, \text{g/mol}} \approx 2.638 \, \text{moles}
\][/tex]
3. Calculate the volume at STP:
[tex]\[
\text{Volume of } \text{N}_2 = 2.638 \, \text{moles} \times 22.414 \, \text{L/mol} \approx 59.115 \, \text{L}
\][/tex]
### (b) [tex]\(42.9 \, \text{g} \, \text{O}_2\)[/tex]
1. Given data:
- Mass of [tex]\( \text{O}_2 \)[/tex]: [tex]\(42.9 \, \text{g}\)[/tex]
- Molar mass of [tex]\( \text{O}_2 \)[/tex]: [tex]\(32.00 \, \text{g/mol}\)[/tex]
2. Calculate the number of moles:
[tex]\[
\text{Moles of } \text{O}_2 = \frac{42.9 \, \text{g}}{32.00 \, \text{g/mol}} \approx 1.341 \, \text{moles}
\][/tex]
3. Calculate the volume at STP:
[tex]\[
\text{Volume of } \text{O}_2 = 1.341 \, \text{moles} \times 22.414 \, \text{L/mol} \approx 30.049 \, \text{L}
\][/tex]
### (c) [tex]\(148 \, \text{g} \, \text{NO}_2\)[/tex]
1. Given data:
- Mass of [tex]\( \text{NO}_2 \)[/tex]: [tex]\(148 \, \text{g}\)[/tex]
- Molar mass of [tex]\( \text{NO}_2 \)[/tex]: [tex]\(46.01 \, \text{g/mol}\)[/tex]
2. Calculate the number of moles:
[tex]\[
\text{Moles of } \text{NO}_2 = \frac{148 \, \text{g}}{46.01 \, \text{g/mol}} \approx 3.216 \, \text{moles}
\][/tex]
3. Calculate the volume at STP:
[tex]\[
\text{Volume of } \text{NO}_2 = 3.216 \, \text{moles} \times 22.414 \, \text{L/mol} \approx 72.099 \, \text{L}
\][/tex]
### (d) [tex]\(245 \, \text{mg} \, \text{CO}_2\)[/tex]
1. Given data:
- Mass of [tex]\( \text{CO}_2 \)[/tex]: [tex]\(245 \, \text{mg}\)[/tex]
- Convert mass to grams: [tex]\(245 \, \text{mg} = 0.245 \, \text{g}\)[/tex]
- Molar mass of [tex]\( \text{CO}_2 \)[/tex]: [tex]\(44.01 \, \text{g/mol}\)[/tex]
2. Calculate the number of moles:
[tex]\[
\text{Moles of } \text{CO}_2 = \frac{0.245 \, \text{g}}{44.01 \, \text{g/mol}} \approx 0.00557 \, \text{moles}
\][/tex]
3. Calculate the volume at STP:
[tex]\[
\text{Volume of } \text{CO}_2 = 0.00557 \, \text{moles} \times 22.414 \, \text{L/mol} \approx 0.125 \, \text{L}
\][/tex]
### Summary of Volumes:
- Volume of [tex]\( \text{N}_2 \)[/tex]: [tex]\(59.115 \, \text{L}\)[/tex]
- Volume of [tex]\( \text{O}_2 \)[/tex]: [tex]\(30.049 \, \text{L}\)[/tex]
- Volume of [tex]\( \text{NO}_2 \)[/tex]: [tex]\(72.099 \, \text{L}\)[/tex]
- Volume of [tex]\( \text{CO}_2 \)[/tex]: [tex]\(0.125 \, \text{L}\)[/tex]
These are the volumes of the respective gas samples at STP.
