Calculating Helium Gas Amount in a Balloon: An Application of the Ideal Gas Law

Helmets and pressure vessels are often filled with helium gas for various purposes, from scientific research to weather balloons. Determining the amount of helium gas in such a vessel requires a straightforward application of the Ideal Gas Law. In this article, we will walk through the process of calculating the amount of helium gas present in a 740.0 cm3 balloon at 145 PSI and 25.0°C, providing a step-by-step guide and emphasizing the importance of unit conversion in such calculations.

What is the Ideal Gas Law?

The Ideal Gas Law is a mathematical equation that describes the behavior of an ideal gas. The law is given by:

PV nRT
The symbols in the equation represent:

P - Pressure (in atm) V - Volume (in L) n - Number of moles of the gas R - Universal gas constant (0.0821 L atm / (mol K) or 8.314 J / (mol K)) T - Temperature (in K)

The Universal Gas Constant (R) can be adapted to different units. In this problem, the units need to be consistent.

Problem: Helium Gas in a Balloon

We are asked to find the amount of helium gas present in a 740.0 cm3 balloon at 145 PSI and 25.0°C. The Ideal Gas Law will solve this problem for us.

Step-by-Step Solution

Step 1: Convert Units to Standard Form

The given values are:

P 145 PSI V 740.0 cm3 T 25.0°C

First, convert the pressure from PSI to atm:

P 145 psi × 0.06805 atmpsi 9.867 atm

Next, convert the volume from cm3 to L:

V 740.0 cm3L 0.7400 L

Finally, convert the temperature from Celsius to Kelvin:

T 25.0 °C 273.15 298.2 K

Step 2: Apply the Ideal Gas Law

Now that the units are consistent, apply the Ideal Gas Law to find the number of moles of helium gas:

n PVRT 9.867 atm × 0.7400 L0.08206 L atm mol K L atm × 298.2 K 0.298 mol

We have now calculated that there are approximately 0.298 moles of helium gas in the balloon.

Additional Considerations: Calculating Mass of Helium

Knowing the number of moles of helium, it is also possible to calculate the mass of the helium using its molar mass. The molar mass of helium (He) is approximately 4.00 g/mol.

Calculating Mass of Helium

The formula for mass is:

m n × M
Where:

m - Mass of the helium gas (in grams) n - Number of moles of helium (0.298 mol) M - Molar mass of helium (4.00 g/mol)

Substitute the values:

m 0.298 mol × 4.00 gmol 1.192 g

Therefore, the mass of helium in the balloon is approximately 1.192 grams.

Conclusion

Understanding and applying the Ideal Gas Law is crucial in many fields, including chemistry, physics, and engineering. By converting the given units to a consistent system and following the steps outlined in the Ideal Gas Law, one can accurately determine the amount of gas present in a given volume under specific conditions. In this case, we found that a 740.0 cm3 balloon at 145 PSI and 25.0°C contains approximately 0.298 moles, or 1.192 grams, of helium gas.