Using the ideal gas law, what is the pressure (in atm) in a 4.00 L tank containing 6.65 moles of nitrogen gas at 69.6 °C?

• A. 2.45 atm
• B. 3.98 atm
• C. 1.67 atm
• D. 5.12 atm

Answer: (B)

Verified step by step guidance

1. Identify the known variables from the problem: number of moles \(n = 6.65\) mol, volume \(V = 4.00\) L, temperature \(T = 69.6\ ^\circ\mathrm{C}\), and the ideal gas constant \(R = 0.0821\ \mathrm{L\cdot atm/(mol\cdot K)}\).
2. Convert the temperature from Celsius to Kelvin using the formula \(T(K) = T(^\circ C) + 273.15\). 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 \(P\) is the pressure in atm, \(V\) is the volume in liters, \(n\) is the number of moles, \(R\) is the ideal gas constant, and \(T\) is the temperature in Kelvin.
4. Rearrange the ideal gas law to solve for pressure \(P\): \(P = \frac{n R T}{V}\).
5. Substitute the known values of \(n\), \(R\), \(T\) (in Kelvin), and \(V\) into the equation and calculate \(P\) to find the pressure in atm.