To determine the pressure exerted by the mixture of hydrogen and nitrogen, we need to use the ideal gas law equation:
PV = nRT
Where: P is the pressure of the gas (in pascals) V is the volume of the gas (in liters) n is the number of moles of gas R is the ideal gas constant (8.314 J/(mol·K)) T is the temperature of the gas (in Kelvin)
First, we need to calculate the number of moles of each gas. We can use the formula:
n = m/M
Where: n is the number of moles m is the mass of the gas (in grams) M is the molar mass of the gas (in grams/mole)
For hydrogen (H₂): m(H₂) = 2.0 g M(H₂) = 2.016 g/mol
n(H₂) = 2.0 g / 2.016 g/mol = 0.9921 mol
For nitrogen (N₂): m(N₂) = 8.0 g M(N₂) = 28.014 g/mol
n(N₂) = 8.0 g / 28.014 g/mol = 0.2856 mol
Now, let's calculate the total number of moles for the mixture: n(total) = n(H₂) + n(N₂) = 0.9921 mol + 0.2856 mol = 1.2777 mol
Next, we'll convert the temperature to Kelvin: T = 273 K
Now we can substitute the values into the ideal gas law equation to solve for the pressure (P): P * V = n * R * T
P = (n * R * T) / V
P = (1.2777 mol * 8.314 J/(mol·K) * 273 K) / 10 L
P = 286.99 J / 10 L
To convert from Joules per liter (J/L) to Pascals (Pa), we use the conversion factor:
1 J/L = 1 Pa
Therefore, the pressure exerted by the mixture of hydrogen and nitrogen in the 10 L vessel at 273 K is approximately 286.99 Pa.