Answer:
Explanation:
To find the temperature of the cylinder, we can use the Ideal Gas Law equation:
\[ PV = nRT \]
Where:
- \( P \) is the pressure of the gas (in atm)
- \( V \) is the volume of the gas (in liters)
- \( n \) is the number of moles of the gas
- \( R \) is the ideal gas constant (\( 0.0821 \, \text{atm} \cdot \text{L/mol} \cdot \text{K} \))
- \( T \) is the temperature of the gas (in Kelvin)
We are given:
- Pressure \( P = 52.0 \, \text{atm} \)
- Volume \( V = 11.0 \, \text{L} \)
- Moles \( n = 23.8 \, \text{moles} \)
- Ideal gas constant \( R = 0.0821 \, \text{atm} \cdot \text{L/mol} \cdot \text{K} \)
We need to solve for \( T \).
\[ T = \frac{PV}{nR} \]
\[ T = \frac{(52.0 \, \text{atm})(11.0 \, \text{L})}{(23.8 \, \text{mol})(0.0821 \, \text{atm} \cdot \text{L/mol} \cdot \text{K})} \]
\[ T = \frac{572.0}{1.9438} \]
\[ T ≈ 294.3 \, \text{K} \]
Therefore, the temperature of the cylinder is approximately \( 294.3 \, \text{K} \).
