Final answer:
The total pressure of a sample of air containing 3.55 moles of N₂ and 2.50 moles of O₂ in a 29.51 L container at 300 K is calculated using the Ideal Gas Law. The total pressure is found to be approximately 5.06 atm.
Step-by-step explanation:
The student has asked how to calculate the total pressure of a sample of air containing 3.55 moles of N₂ and 2.50 moles of O₂ at a volume of 29.51 L and temperature of 300 K. To find the total pressure of the gas mixture, we can use the Ideal Gas Law which is PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature in Kelvin.
First, calculate the total number of moles (ntotal) present in the gas mixture:
- ntotal = moles of N₂ + moles of O₂
- ntotal = 3.55 + 2.50
- ntotal = 6.05 moles
Now use the Ideal Gas Law to find the pressure:
- PV = nRT
- P = (nRT) / V
- P = (6.05 moles * 0.0821 L·atm/(mol·K) * 300 K) / 29.51 L
- P ≈ 5.06 atm
Therefore, the total pressure of the gas mixture is approximately 5.06 atm, which corresponds to option (b).