# Accurately Determining How Many Molecules of N2 Are in a 500.0 ml Container at 780 mm Hg and 135°C?

## How Many Molecules of N2 Are in a 500.0 ml Container at 780 mm Hg and 135°C?

If you’ve ever wondered how many molecules of N2 are present in a specific volume at a given pressure and temperature, you’ve come to the right place. In this article, I’ll be addressing the question of how many molecules of N2 are in a 500.0 ml container at 780 mm Hg and 135°C.

To determine the number of molecules, we must apply the ideal gas law equation, which relates pressure, volume, temperature, and moles. By rearranging the equation and plugging in the given values for pressure (780 mm Hg), volume (500.0 ml), and temperature (135°C converted to Kelvin), we can calculate the number of moles of N2.

## Understanding the Ideal Gas Law

The Ideal Gas Law is a fundamental concept in thermodynamics that allows us to understand and predict the behavior of gases. It combines several variables, including pressure, volume, temperature, and the number of molecules present, to comprehensively understand gas properties.

Pressure, represented by the symbol “P”, refers to the force exerted by gas molecules on the walls of their container. It is typically measured in atmospheres (atm) or millimeters of mercury (mmHg).

Volume, denoted by “V”, represents the gas molecules’ physical space. This can be measured in units like liters (L) or milliliters (mL). In our case, we have a 500.0 mL container.

Temperature, indicated by “T”, measures the average kinetic energy of gas particles. It is usually expressed in degrees Celsius (°C) or Kelvin (K). In this scenario, we have a temperature of 135°C.

The number of molecules, referred to as “n”, represents how many individual gas particles are in our system. In our case, we want to determine how many molecules of N2 (nitrogen gas) are inside our 500.0 mL container.

## Determining the Number of Moles in a Given Volume

To calculate the number of molecules of N2 in a 500.0 ml container at 780 mm Hg and 135°C, we first need to determine the number of moles present. The equation that relates pressure, volume, temperature, and moles is known as the ideal gas law:

PV = nRT

### Where:

- P represents pressure
- V represents volume
- n represents the number of moles
- R is the ideal gas constant
- T represents temperature in Kelvin

In this case, we are given a pressure of 780 mm Hg and a temperature of 135°C. We’ll need to convert these values to suitable units before proceeding with our calculations.

Let’s start by converting the pressure from mm Hg to atm since it’s a more commonly used unit in gas calculations. One atmosphere (atm) is equal to exactly 760 mm Hg.

780 mm Hg * (1 atm / 760 mm Hg) = 1.02632 atm

Next, let’s convert the temperature from Celsius to Kelvin by adding 273.15:

135°C + 273.15 = 408.15 K

Now that we have all our values converted, we can rearrange the ideal gas law equation to solve for moles (n):

n = PV / RT

### Substituting in our values:

n = (1.02632 atm * 500.0 ml) / (0.0821 L·atm/mol·K * 408.15 K)

#### Simplifying:

n ≈ 12.58 mol

So there are approximately 12.58 moles of N2 present in the given volume.

To calculate the number of molecules, we can use Avogadro’s number, which states that one mole contains 6.022 × 10^23 molecules. Therefore, multiplying the number of moles by Avogadro’s number will give us the total number of molecules:

Number of molecules = (12.58 mol) * (6.022 × 10^23 molecules/mol)

### Calculating:

Number of molecules ≈ 7.57 × 10^24 molecules

Therefore, there are approximately 7.57 × 10^24 N2 molecules in the given 500.0 ml container at a pressure of 780 mm Hg and a temperature of 135°C.

## Final Thoughts

Once we have the number of moles, we can use Avogadro’s constant to convert it into molecules. Avogadro’s constant tells us that approximately 6.022 x 10^23 molecules are in one mole of any substance.