A mixture of He, N2, and Ar has a pressure of 13.6 atm at 28.0°C. If the partial pressure of He is 1831 torr, and that of Ar is 997 mm Hg, what is the partial pressure of N2?

Answer: To find the partial pressure of N_2, we'll use 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.

First, it's important to note that torr and mm Hg are equivalent units of pressure. So, 1831 torr is the same as 1831 mm Hg.

The total pressure of the gas mixture is given as 13.6 atm. We need to convert this pressure to mm Hg to be consistent with the other given pressures. To do this, we use the conversion factor: 1 atm = 760 mm Hg.

\( P_{total} (in mm Hg) = 13.6 atm \times 760 mm Hg / atm = 10336 mm Hg \)

Now, we know the following partial pressures: - \( P_{He} = 1831 mm Hg \) - \( P_{Ar} = 997 mm Hg \)

Using Dalton's Law (\( P_{total} = P_{He} + P_{Ar} + P_{N_2} \)), we can find the partial pressure of N_2:

\( P_{N_2} = P_{total} - P_{He} - P_{Ar} \)

\( P_{N_2} = 10336 mm Hg - 1831 mm Hg - 997 mm Hg \)

\( P_{N_2} = 10336 mm Hg - 2828 mm Hg \)

\( P_{N_2} = 7508 mm Hg \)

So, the partial pressure of N_2 is 7508 mm Hg.

Extra: Dalton's Law is a fundamental concept in chemistry and physics, describing the behavior of gas mixtures. It's based on the idea that each gas in a mixture behaves independently of the others. Each gas contributes to the total pressure in proportion to its fraction in the gas mixture.

The partial pressure of a gas is essentially the pressure it would exert if it were alone in the container at the same temperature. The total pressure is the sum of all the partial pressures.

When dealing with gases, it's often necessary to convert between different units of pressure. Common units include atmospheres (atm), millimeters of mercury (mm Hg), torr (which is essentially the same as mm Hg), and Pascals (Pa), which is the SI unit of pressure.

Temperature also plays a significant role in the behavior of gases, described by the Ideal Gas Law (\( PV = nRT \)), which relates the pressure (P), volume (V), number of moles (n), universal gas constant (R), and temperature (T). For a fixed amount of gas at a constant volume, the pressure will increase as the temperature increases. Similarly, at a constant temperature, the pressure will decrease as the volume increases.