A vessel with an internal volume of 15.3 L contains 2.80 g of nitrogen gas, 0.403 g of hydrogen gas, and 79.9 g of argon gas. At 25^oC, what is the pressure (in atm) inside the vessel? A) 860 atm B) 0.308 atm C) 3.68 atm D) 0.272 atm E) 133 atm

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To find the total pressure inside the vessel, we use the ideal gas law, $PV = nRT$, where $P$ is the pressure, $V$ is the volume, $n$ is the number of moles of gas, $R$ is the ideal gas constant, and $T$ is the temperature in Kelvin. First, we convert the temperature from Celsius to Kelvin: $25^\circ C = 298 K$. Then, we calculate the moles of each gas: Nitrogen ($N_2$): $2.80 \, \text{g} / 28.02 \, \text{g/mol} = 0.1 \, \text{mol}$ Hydrogen ($H_2$): $0.403 \, \text{g} / 2.02 \, \text{g/mol} = 0.2 \, \text{mol}$ Argon ($Ar$): $79.9 \, \text{g} / 39.95 \, \text{g/mol} = 2 \, \text{mol}$ Total moles of gas = $0.1 + 0.2 + 2 = 2.3 \, \text{mol}$ Using $R = 0.0821 \, \text{L atm/mol K}$, and $V = 15.3 \, \text{L}$, $P = \frac{nRT}{V} = \frac{2.3 \times 0.0821 \times 298}{15.3} \approx 3.68 \, \text{atm}$.

A Vessel with an Internal Volume of 15