Given information:
- Total pressure of the mixture = 1200 mm
- Mass of oxygen (O2) = 6.4 g
- Mass of nitrogen (N2) = 5.6 g
- Volume of the vessel = 2 L

Calculating the number of moles:
To find the partial pressure of nitrogen, we first need to calculate the number of moles of oxygen and nitrogen present in the mixture.

The number of moles can be calculated using the formula:
Number of moles (n) = Mass (m) / Molar mass (M)

The molar mass of oxygen (O2) = 32 g/mol
The molar mass of nitrogen (N2) = 28 g/mol

For oxygen:
Number of moles of oxygen (nO2) = 6.4 g / 32 g/mol = 0.2 mol

For nitrogen:
Number of moles of nitrogen (nN2) = 5.6 g / 28 g/mol = 0.2 mol

Calculating the partial pressure:
The partial pressure of a gas is given by Dalton's law of partial pressures, which states that the total pressure of a mixture of gases is equal to the sum of the partial pressures of the individual gases.

Partial pressure (P) = Mole fraction (X) * Total pressure

Mole fraction (X) can be calculated using the formula:
Mole fraction (X) = Moles of the gas (n) / Total moles of all gases

For oxygen:
Mole fraction of oxygen (XO2) = 0.2 mol / (0.2 mol + 0.2 mol) = 0.5

For nitrogen:
Mole fraction of nitrogen (XN2) = 0.2 mol / (0.2 mol + 0.2 mol) = 0.5

Now, we can calculate the partial pressure of nitrogen:
Partial pressure of nitrogen (PN2) = XN2 * Total pressure
= 0.5 * 1200 mm
= 600 mm

Final answer:
The partial pressure of nitrogen in the mixture is 600 mm.