How Many Atoms of He Gas Are Present in a 450 Ml Container at 35°C and 740 mmHg? A Molecular Calculation
Are you curious how many helium gas atoms are present in a 450 ml container at 35°C and 740 mmHg? Well, I’m here to shed some light on this intriguing question. We can calculate the number of atoms in this scenario by applying the ideal gas law.
Using Avogadro’s constant (6.022 x 10^23) and the molar mass of helium (4 g/mol), we can convert the volume, temperature, and pressure into moles. With these values in hand, we can determine the number of atoms in the container.
How Many Atoms of He Gas Are Present in a 450 Ml Container at 35°C and 740 mmHg?
Let’s dive into determining the number of atoms in a container of helium gas. In this case, we have a 450 ml container at a temperature of 35°C and a pressure of 740 mmHg.
To begin with, we need to understand the concept of ideal gas law. The ideal gas law equation, PV = nRT, relates pressure (P), volume (V), number of moles (n), gas constant (R), and temperature (T). By rearranging this equation, we can solve for the number of moles.
Firstly, let’s convert the given volume from milliliters to liters by dividing it by 1000. So, our volume becomes 0.45 L.
Next, we need to convert the temperature from Celsius to Kelvin by adding 273.15. Therefore, our temperature is now 308.15 K.
The value for R is commonly given as 0.0821 L·atm/(mol·K). Plugging in all these values into our rearranged equation:
PV = nRT (740 mmHg) * (0.45 L) = n * (0.0821 L·atm/(mol·K)) * (308.15 K)
Simplifying this equation gives us:
n ≈ ((740 mmHg) * (0.45 L)) / ((0.0821 L·atm/(mol·K)) * (308.15 K))
Calculating this expression will give us the approximate number of moles in our container.
Now that we know the number of moles, we can use Avogadro’s constant to determine the number of atoms in helium gas.
Avogadro’s constant is approximately equal to 6.022 x 10^23 atoms/mol.
To find the number of atoms, we multiply the number of moles by Avogadro’s constant:
Number of atoms ≈ (number of moles) * (Avogadro’s constant)
By plugging in the calculated value for the number of moles into this equation, we can determine the approximate number of helium atoms in our 450 ml container.
These calculations are based on ideal gas behavior and assumptions. Factors like intermolecular forces and non-ideal conditions may affect the accuracy of our results. However, for practical purposes, this method provides a reasonable estimate.
Volume and Temperature of the Container
When calculating the number of atoms of helium gas present in a 450 ml container at 35°C and 740 mmHg, we need to consider both the volume and temperature of the container. These factors are crucial in determining the amount of gas contained within.
The volume of the container is given as 450 ml. This measurement represents the physical space occupied by the helium gas molecules. To better visualize this, imagine a small flask filled with helium gas.
The temperature inside the container is specified as 35°C. The temperature has a direct impact on the behavior of gas molecules. As we increase the temperature, gas molecules gain more energy and move faster, increasing their kinetic energy.
Now that we have established these variables, let’s dive deeper into how they affect our calculation:
- Boyle’s Law: According to Boyle’s law, pressure and volume are inversely proportional at a constant temperature. So, if we know one variable (pressure or volume) and keep everything else constant, we can calculate how changes in one factor affect another.
- Charles’ Law: Charles’ law states that at constant pressure, volume and temperature are directly proportional. This means that when we change either variable while keeping everything else constant, there will be a corresponding change in the other factor.