Helium is a very important element for both industrial and research applications. In its gas form it can be used for welding, and since it has a very low melting point (only 0.95 K under 2.5 MPa) it can be used in liquid form to cool superconducting magnets, such as those found in particle physics experiments. Say we have a cylinder of n = 125 moles of Helium gas at room temperature (T = 20° C). The cylinder has a radius of r = 17 cm and a height h = 1.64 m. What pressure is Helium gas under?

P = 20.1697 atm

Explanation:

In this case we need to use the ideal gas equation which is:

PV = nRT (1)

Where:

P: Pressure (atm)

V: Volume (L)

n: moles

R: universal gas constant (=0.082 L atm / K mol)

T: Temperature

From here, we can solve for pressure:

P = nRT/V  (2)

According to the given data, we have the temperature (T = 20 °C, transformed in Kelvin is 293 K), the moles (n = 125 moles), and we just need the volume. But the volume can be calculated using the data of the cylinder dimensions.

The volume for any cylinder would be:

V = πr²h  (3)

Replacing the data here, we can solve for the volume:

V = π * (17)² * 164

V = 148,898.93 cm³

This volume converted in Liters would be:

V = 148,898.93 mL * 1 L / 1000 mL

V = 148.899 L

Now we can solve for pressure:

P = 125 * 0.082 * 293 / 148.899