Answer :
Final Answer:
The pressure in atm of a 5.00 L tank containing 6.15 moles of oxygen at 39.3 °C is approximately 23.8 atm.
Explanation:
In order to calculate the pressure inside the tank, we can use the Ideal Gas Law equation:
[tex]\[ PV = nRT \][/tex]
Where:
- [tex]\( P \)[/tex] is the pressure in atm
- [tex]\( V \)[/tex] is the volume in liters
- [tex]\( n \)[/tex] is the number of moles
- [tex]\( R \)[/tex] is the ideal gas constant [tex](\(0.0821 \, \text{L atm / K mol}\))[/tex]
- [tex]\( T \)[/tex] is the temperature in Kelvin
First, let's convert the temperature from Celsius to Kelvin:
[tex]\[ T(K) = 39.3°C + 273.15 = 312.45 \, K \][/tex]
Now, plug in the values into the equation:
[tex]\[ P \cdot 5.00 \, \text{L} = 6.15 \, \text{mol} \cdot 0.0821 \, \text{L atm / K mol} \cdot 312.45 \, \text{K} \][/tex]
Solving for [tex]\( P \):[/tex]
[tex]\[ P = \frac{6.15 \, \text{mol} \cdot 0.0821 \, \text{L atm / K mol} \cdot 312.45 \, \text{K}}{5.00 \, \text{L}} \approx 23.8 \, \text{atm} \][/tex]
The pressure inside the tank is approximately 23.8 atm.
This calculation uses the Ideal Gas Law, which relates the pressure, volume, number of moles, and temperature of an ideal gas. In this case, the given values were the volume (5.00 L), moles of oxygen (6.15 moles), and temperature in Celsius (39.3 °C). After converting the temperature to Kelvin, we plugged the values into the Ideal Gas Law equation and solved for pressure. This calculation helps us understand how gas properties are interconnected and how changing one parameter can affect others.
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