Density of the mixture:
The given density of the mixture of O2 and N2 at NTP (Normal Temperature and Pressure) is 1.3 g litre⁻¹.

Partial pressure of N2:
We need to find the partial pressure of N2 in the mixture.

Explanation:
To determine the partial pressure of N2, we need to consider the ideal gas law. The ideal gas law equation is as follows:

PV = nRT

Where:
P = pressure
V = volume
n = number of moles
R = ideal gas constant
T = temperature

Step 1: Calculate the number of moles:
The number of moles of a substance can be calculated using the equation:

n = mass / molar mass

Given the density of the mixture is 1.3 g litre⁻¹, we can convert it to kg m⁻³ by dividing by 1000 and multiplying by 1000 (since 1 L = 1000 cm³).

Density = mass / volume
1.3 g litre⁻¹ = mass / (1 L)
mass = 1.3 g

To convert grams to kilograms, we divide by 1000:
mass = 1.3 g / 1000 = 0.0013 kg

Now, we need to calculate the number of moles using the molar mass of the mixture. The molar mass of the mixture can be obtained by considering the molar mass of O2 and N2 and their respective mole fractions.

Assuming the mole fraction of N2 is x, the mole fraction of O2 would be (1 - x).

Molar mass of N2 = 28 g/mol
Molar mass of O2 = 32 g/mol

Molar mass of the mixture = (x * 28) + ((1 - x) * 32)

Now, using the given density of the mixture, we can calculate the number of moles:

density = mass / volume
density = (mass of mixture) / (volume of mixture)
1.3 g litre⁻¹ = (0.0013 kg) / (volume of mixture)

Step 2: Calculate the volume:
To calculate the volume of the mixture, we can use the ideal gas law equation.

PV = nRT

Rearranging the equation, we have:

V = (nRT) / P

Now we can substitute the values into the equation. The temperature at NTP is 273 K, and the ideal gas constant R is 0.0821 L atm K⁻¹ mol⁻¹.

V = [(mass of mixture) / (molar mass of mixture)] * (R * T) / P

Step 3: Calculate the partial pressure of N2:
To find the partial pressure of N2, we need to consider the mole fraction of N2 (x) in the mixture.

The mole fraction of N2 is given by:

x = (number of moles of N2) / (total number of moles)

The total number of moles can be calculated by dividing the mass of the mixture by the molar mass of the mixture.

Now we can substitute the values into the equation:

partial pressure of N2 = x * total pressure

Answer: