91Ó°ÊÓ

To find out how many moles of a gas are present in a certain volume and conditions, we use the Ideal Gas Law, which is a fundamental equation in chemistry and physics. This equation is expressed as:\[ PV = nRT \]Here, \( P \) is the pressure, \( V \) is the volume, \( n \) is the number of moles, \( R \) is the ideal gas constant (8.314 J/mol K), and \( T \) is the temperature in Kelvin.
If you need to calculate the number of moles \( n \), you rearrange the formula as:\[ n = \frac{PV}{RT} \]This equation tells you that the number of moles is directly proportional to the pressure and volume, and inversely proportional to the temperature, meaning that if the pressure or volume increases, the number of moles will also increase, while an increase in temperature will decrease the number of moles needed to create the same pressure and volume under ideal conditions.
When working with real-world problems, like in our exercise, make sure you have all values in proper units: Pressure in Pascals (Pa), Volume in cubic meters (m³), and Temperature in Kelvin (K). This ensures the equation works correctly.

Helium is quite unique and has special properties that make it very different from other gasses. Understanding these properties is important when it comes to calculations involving helium, especially in applications such as airships.

• Helium is a lighter-than-air gas, which explains its use in balloons and airships like blimps to provide lift.
• It is non-reactive, meaning it doesn't combust or react with other substances easily.
• Helium has a relatively low molecular weight of 4 g/mol (or 0.004 kg/mol), which contributes to its buoyant properties.

These characteristics make helium stable, safe, and effective for lifting, as it won't ignite or react dangerously even in open air. Its low molecular weight, when compared to other gases, is a crucial factor in determining how many moles to expect in a given volume and ultimately helps us convert moles into mass for practical computations.

Once you have determined the number of moles present in a gas, converting this to mass is straightforward with the help of the molar mass.The molar mass of a substance is the mass of one mole of that substance, which means it is usually expressed in grams per mole (g/mol). In our exercise, we found that helium has a molar mass of 4 g/mol, equivalent to 0.004 kg/mol when converted to kilograms.
The formula you use for calculating the mass \( m \) of a gas is simply:\[ m = n \times M \]Where \( n \) is the number of moles (which we've calculated with the ideal gas law), and \( M \) is the molar mass. Calculating the mass helps in determining how much of the gas is present in terms of weight rather than moles. For instance, in our blimp scenario, multiplying the number of moles by the molar mass of helium gives us a mass of approximately 1016.45 kg.
This conversion from moles to mass is key in practical applications where physical quantities like weight are more useful than moles, such as measuring how much material is needed for lift or how much to transport.