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Answer :
To find the volume of the container, we can use the Ideal Gas Law, which is a fundamental equation in chemistry and physics for relating the pressure, volume, temperature, and amount of gas. The equation is given by:
[tex]\[ PV = nRT \][/tex]
Where:
- [tex]\( P \)[/tex] is the pressure of the gas (in atmospheres, atm).
- [tex]\( V \)[/tex] is the volume of the gas (in liters, L).
- [tex]\( n \)[/tex] is the number of moles of the gas.
- [tex]\( R \)[/tex] is the ideal gas constant (0.0821 L·atm/(mol·K)).
- [tex]\( T \)[/tex] is the temperature of the gas in Kelvin (K).
### Given:
- Pressure [tex]\( P = 10.0 \, \text{atm} \)[/tex]
- Moles of gas [tex]\( n = 35.8 \, \text{moles} \)[/tex]
- Temperature [tex]\( T = 70.0 \, \text{°C} \)[/tex]
### Convert Temperature to Kelvin:
To use the equation, we must convert the temperature from Celsius to Kelvin by adding 273.15:
[tex]\[ T = 70.0 + 273.15 = 343.15 \, \text{K} \][/tex]
### Solve for Volume [tex]\( V \)[/tex]:
Rearrange the Ideal Gas Law to solve for [tex]\( V \)[/tex]:
[tex]\[ V = \frac{nRT}{P} \][/tex]
Substitute the known values into the equation:
[tex]\[ V = \frac{(35.8 \, \text{moles}) \times (0.0821 \, \text{L·atm/(mol·K)}) \times (343.15 \, \text{K})}{10.0 \, \text{atm}} \][/tex]
Perform the calculation:
[tex]\[ V \approx 100.86 \, \text{L} \][/tex]
Therefore, the volume of the container is approximately 101 L. Thus, the correct answer is 101 L.
[tex]\[ PV = nRT \][/tex]
Where:
- [tex]\( P \)[/tex] is the pressure of the gas (in atmospheres, atm).
- [tex]\( V \)[/tex] is the volume of the gas (in liters, L).
- [tex]\( n \)[/tex] is the number of moles of the gas.
- [tex]\( R \)[/tex] is the ideal gas constant (0.0821 L·atm/(mol·K)).
- [tex]\( T \)[/tex] is the temperature of the gas in Kelvin (K).
### Given:
- Pressure [tex]\( P = 10.0 \, \text{atm} \)[/tex]
- Moles of gas [tex]\( n = 35.8 \, \text{moles} \)[/tex]
- Temperature [tex]\( T = 70.0 \, \text{°C} \)[/tex]
### Convert Temperature to Kelvin:
To use the equation, we must convert the temperature from Celsius to Kelvin by adding 273.15:
[tex]\[ T = 70.0 + 273.15 = 343.15 \, \text{K} \][/tex]
### Solve for Volume [tex]\( V \)[/tex]:
Rearrange the Ideal Gas Law to solve for [tex]\( V \)[/tex]:
[tex]\[ V = \frac{nRT}{P} \][/tex]
Substitute the known values into the equation:
[tex]\[ V = \frac{(35.8 \, \text{moles}) \times (0.0821 \, \text{L·atm/(mol·K)}) \times (343.15 \, \text{K})}{10.0 \, \text{atm}} \][/tex]
Perform the calculation:
[tex]\[ V \approx 100.86 \, \text{L} \][/tex]
Therefore, the volume of the container is approximately 101 L. Thus, the correct answer is 101 L.
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