# The Ideal Gas Law Explained – How Many Molecules of N2 are in a 400.0 Ml Container at 780 Mm Hg and 135°C?

## How Many Molecules of N2 are in a 400.0 Ml Container at 780 Mm Hg and 135°C?

Curious about the number of N2 molecules in a 400.0 ml container at 780 mm Hg and 135°C? Let’s dive into the calculations and find out! At these specific conditions, we can use the ideal gas law to determine the number of N2 molecules present.

According to Avogadro’s law, one mole of any gas contains approximately 6.022 x 10^23 molecules. To calculate the number of moles in our container, we’ll need to rearrange the ideal gas equation PV = nRT (where P is pressure, V is volume, n is number of moles, R is the ideal gas constant, and T is temperature) to solve for n.

Firstly, let’s convert our given volume from millilitres to litres by dividing it by 1000: 400.0 ml = 0.4 L. Next, let’s convert our temperature from Celsius to Kelvin by adding 273.15: 135°C + 273.15 = 408.15 K.

Plugging in these values along with the given pressure (780 mm Hg) and solving for n using R = 0.0821 L·atm/(mol·K), we can determine the number of moles of N2 in our container. By multiplying this value by Avogadro’s constant (6.022 x 10^23), we’ll obtain an estimate for how many N2 molecules are present.

Stay tuned as I crunch these numbers for you!

## Determining the Number of Molecules in a Container

To calculate the number of molecules in a container, we can apply Avogadro’s law. This fundamental principle states that equal volumes of gases, at the same temperature and pressure, contain an equal number of molecules. By utilising this law, we can determine the number of molecules present in a 400.0 ml container.

### Analysing the Volume and Temperature Conditions

Before we proceed with our calculations, let’s consider the volume and temperature conditions provided: 400.0 ml and 135°C respectively. It is crucial to note that both volume and temperature play significant roles in determining the number of molecules present.

The given volume tells us how much space is occupied by the gas inside the container. In this case, it is 400.0 ml or millilitres. Meanwhile, temperature affects molecular motion – higher temperatures lead to increased molecular activity.

## Converting Units for Accurate Calculation

To accurately calculate the number of molecules in our container, we need to ensure consistency between units. The pressure value provided is given as 780 mmHg (millimetres of mercury), which is not compatible with other units commonly used in Avogadro’s law calculations.

We’ll need to convert millimetres of mercury (mmHg) into a more standardised unit such as atmospheres (atm). One atmosphere (1 atm) is equivalent to approximately 760 mmHg.

Additionally, when working with gas laws like Avogadro’s law, it’s important to use absolute temperature scales such as Kelvin (K). We’ll need to convert Celsius (°C) into Kelvin by adding 273.15 to our given temperature value.

Once we have all our values converted into appropriate units—volume in litres (L), pressure in atmospheres (atm), and temperature in Kelvin (K)—we can proceed with the calculation to determine the number of molecules in the container.

Let’s dive into the calculations and find out just how many molecules of N2 are present in that 400.0 ml container at 780 mmHg and 135°C! How many molecules of N2 are present in a 400.0 ml container at 780 mm Hg and 135°C? Let’s delve into the given information: volume, pressure, and temperature.

Volume: In this case, we have a container with a volume of 400.0 ml. The volume represents the amount of space occupied by the gas molecules inside the container.

Pressure: The pressure is given as 780 mm Hg. Pressure measures the force exerted by gas molecules on the walls of the container. In this context, it quantifies how compressed or expanded the gas is within the given volume.

Temperature: At 135°C, we have information about the temperature of the system. Temperature affects how fast gas molecules move and collide with each other and with the walls of their container.

Now that we understand these parameters, let’s calculate how many molecules of N2 are present using Avogadro’s law and ideal gas law equations:

- Convert temperature to Kelvin: T(K) = T(°C) + 273.15 T(K) = 135°C + 273.15 = 408.15 K
- Convert pressure to atmospheres (atm): P(atm) = P(mm Hg) / 760 P(atm) = 780 mm Hg / 760 = approximately 1.03 atm
- Apply ideal gas law equation: PV = nRT

Where: P represents pressure (in atm) V represents volume (in liters) n represents number of moles R is known as the ideal gas constant (approximately equal to 0.0821 L·atm/mol·K) T represents temperature (in Kelvin)