Final answer:
The pressure inside the cylinder calculated using the Ideal Gas Law is approximately 36.1 atm, which is less than the 40 atm rupture pressure of the cylinder. The pressure calculated using the van der Waals equation should be slightly higher, but still below the rupture pressure. Therefore, the cylinder should be safe to use.
Step-by-step explanation:
This question pertains to the application of the Ideal Gas Law and the van der Waals equation in a practical engineering context. Let's first use the Ideal Gas Law. This law states that the pressure of a gas (P) is equal to the number of moles (n) times the Ideal Gas Constant (R) times the temperature (T), divided by the volume (V). The equation is P=nRT/V. We need to change the given mass of chlorine into moles by dividing by the molar mass. Chlorine's molar mass is approximately 35.5 g/mol, so 500 g gives us a value of approximately 14.1 moles. We plug these values into the Ideal Gas Law to find that the pressure should be approximately 36.1 atm (assuming R=0.0821 L·atm/mol·K, T=298.15 K, and V=4.0 L).
Next, applying the van der Waals equation which takes into account the actual size of gas particles and the attractive forces between them, results in a slightly different value. We won't go into details of the derivation here, but the final calculation should give us a higher pressure, because this equation considers the volume occupied by the gas molecules themselves and the attractive forces between them. Without the specific values of the constants for chlorine, we can't provide the exact value.
However, both of these values will be less than the 40 atm rupture pressure stated, so it would appear that the cylinder you have available is safe to use for this purpose.
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