Using the Ideal Gas Law, calculate the pressure in atm of a 25.0 L metal tank containing 12.0 moles of hydrogen gas and 4.0 moles of nitrogen gas at a temperature of 298 K.

• A. 22.4 atm
• B. 15.8 atm
• C. 10.5 atm
• D. 19.1 atm

Answer: (D)

Verified step by step guidance

1. Identify the Ideal Gas Law equation: \( PV = nRT \), where \( P \) is pressure, \( V \) is volume, \( n \) is the number of moles, \( R \) is the ideal gas constant, and \( T \) is temperature in Kelvin.
2. Determine the total number of moles of gas in the tank by adding the moles of hydrogen and nitrogen: \( n_{\text{total}} = n_{\text{H}_2} + n_{\text{N}_2} = 12.0 + 4.0 \).
3. Use the ideal gas constant \( R = 0.0821 \text{ L atm K}^{-1} \text{ mol}^{-1} \) for calculations involving pressure in atm, volume in liters, and temperature in Kelvin.
4. Substitute the known values into the Ideal Gas Law equation: \( P = \frac{nRT}{V} \), where \( n = 16.0 \text{ moles} \), \( R = 0.0821 \text{ L atm K}^{-1} \text{ mol}^{-1} \), \( T = 298 \text{ K} \), and \( V = 25.0 \text{ L} \).
5. Solve for \( P \) to find the pressure in atm: \( P = \frac{(16.0)(0.0821)(298)}{25.0} \).