How many moles of chlorine gas (Cl_2) are present in a 15.0 L vessel at 110 °C and 28.0 atm? (Use the ideal gas law: PV = nRT, with R = 0.0821 L·atm·mol^{-1}·K^{-1})

• A. 5.6 mol
• B. 19.2 mol
• C. 12.4 mol
• D. 7.0 mol

Answer: (B)

Verified step by step guidance

1. Identify the known variables from the problem: pressure \(P = 28.0\) atm, volume \(V = 15.0\) L, temperature \(T = 110\) °C, and the ideal gas constant \(R = 0.0821\) L\cdot atm\cdot mol^{-1}\cdot K^{-1}$.
2. Convert the temperature from Celsius to Kelvin using the formula \(T(K) = T(°C) + 273.15\). This is necessary because the ideal gas law requires temperature in Kelvin.
3. Write down the ideal gas law equation: \(P V = n R T\), where \(n\) is the number of moles of gas.
4. Rearrange the ideal gas law to solve for \(n\): \(n = \frac{P V}{R T}\).
5. Substitute the known values of \(P\), \(V\), \(R\), and \(T\) (in Kelvin) into the equation and solve for \(n\) to find the number of moles of chlorine gas.