Answer :
To find the pressure in atm of a 5.00 L tank with 2.50 mol of oxygen at 39.3 °C, we can use the Ideal Gas Law equation, which is:
[tex]\[ PV = nRT \][/tex]
Where:
- [tex]\( P \)[/tex] is the pressure in atmospheres (atm),
- [tex]\( V \)[/tex] is the volume in liters (L),
- [tex]\( n \)[/tex] is the number of moles of the gas,
- [tex]\( R \)[/tex] is the ideal gas constant, which is approximately 0.0821 L·atm/(K·mol),
- [tex]\( T \)[/tex] is the temperature in Kelvin (K).
### Step-by-step Solution:
1. Identify and list the given values:
- Volume ([tex]\( V \)[/tex]) = 5.00 L
- Moles of oxygen ([tex]\( n \)[/tex]) = 2.50 mol
- Temperature in Celsius ([tex]\( T_{\text{C}} \)[/tex]) = 39.3 °C
2. Convert the temperature from Celsius to Kelvin:
The conversion formula is:
[tex]\[ T_{\text{K}} = T_{\text{C}} + 273.15 \][/tex]
[tex]\[ T_{\text{K}} = 39.3 + 273.15 = 312.45 \, \text{K} \][/tex]
3. Use the Ideal Gas Law to find the pressure (P):
Rearrange the equation to solve for [tex]\( P \)[/tex]:
[tex]\[ P = \frac{nRT}{V} \][/tex]
Substitute the known values into the equation:
[tex]\[ P = \frac{(2.50 \, \text{mol}) \times (0.0821 \, \text{L·atm/(K·mol)}) \times (312.45 \, \text{K})}{5.00 \, \text{L}} \][/tex]
4. Calculate the pressure:
[tex]\[ P \approx 12.826 \, \text{atm} \][/tex]
Therefore, the pressure in the tank is approximately 12.83 atm.
[tex]\[ PV = nRT \][/tex]
Where:
- [tex]\( P \)[/tex] is the pressure in atmospheres (atm),
- [tex]\( V \)[/tex] is the volume in liters (L),
- [tex]\( n \)[/tex] is the number of moles of the gas,
- [tex]\( R \)[/tex] is the ideal gas constant, which is approximately 0.0821 L·atm/(K·mol),
- [tex]\( T \)[/tex] is the temperature in Kelvin (K).
### Step-by-step Solution:
1. Identify and list the given values:
- Volume ([tex]\( V \)[/tex]) = 5.00 L
- Moles of oxygen ([tex]\( n \)[/tex]) = 2.50 mol
- Temperature in Celsius ([tex]\( T_{\text{C}} \)[/tex]) = 39.3 °C
2. Convert the temperature from Celsius to Kelvin:
The conversion formula is:
[tex]\[ T_{\text{K}} = T_{\text{C}} + 273.15 \][/tex]
[tex]\[ T_{\text{K}} = 39.3 + 273.15 = 312.45 \, \text{K} \][/tex]
3. Use the Ideal Gas Law to find the pressure (P):
Rearrange the equation to solve for [tex]\( P \)[/tex]:
[tex]\[ P = \frac{nRT}{V} \][/tex]
Substitute the known values into the equation:
[tex]\[ P = \frac{(2.50 \, \text{mol}) \times (0.0821 \, \text{L·atm/(K·mol)}) \times (312.45 \, \text{K})}{5.00 \, \text{L}} \][/tex]
4. Calculate the pressure:
[tex]\[ P \approx 12.826 \, \text{atm} \][/tex]
Therefore, the pressure in the tank is approximately 12.83 atm.