Using the ideal gas law, what quantity in moles of chlorine gas (Cl_2) at 120.0 °C and 33.3 atm would occupy a vessel of 12.0 L?

• A. 24.6 mol
• B. 16.4 mol
• C. 8.1 mol
• D. 10.2 mol

Answer: (B)

Verified step by step guidance

1. Identify the known variables from the problem: pressure \(P = 33.3\) atm, volume \(V = 12.0\) L, temperature \(T = 120.0\) °C, and the gas constant \(R = 0.0821\) L·atm/(mol·K).
2. Convert the temperature from Celsius to Kelvin using the formula \(T(K) = T(°C) + 273.15\) to ensure the temperature is in the correct units for the ideal gas law.
3. Write down the ideal gas law equation: \(P \times V = n \times R \times T\), where \(n\) is the number of moles of gas.
4. Rearrange the ideal gas law to solve for \(n\): \(n = \frac{P \times V}{R \times T}\).
5. Substitute the known values of \(P\), \(V\), \(R\), and \(T\) (in Kelvin) into the equation and solve for \(n\) to find the quantity of chlorine gas in moles.