What is the number of molecules in an 80 L gas with a gauge pressure of 2 atm at 300 K?

To determine the number of molecules in an 80 L gas at a gauge pressure of 2 atm and a temperature of 300 K, the ideal gas law can be utilized, which is expressed as:

[ PV = nRT ]

In this equation:

• ( P ) is the absolute pressure,

• ( V ) is the volume,

• ( n ) is the number of moles,

• ( R ) is the ideal gas constant (approximately 0.0821 L·atm/(K·mol)),

• ( T ) is the temperature in Kelvin.

First, it’s important to convert the gauge pressure to absolute pressure. Since gauge pressure measures pressure above atmospheric pressure, we add the atmospheric pressure (approximately 1 atm):

[ P = 2 , \text{atm} + 1 , \text{atm} = 3 , \text{atm} ]

Now substituting the values into the ideal gas law gives us:

[ (3 , \text{atm}) (80 , \text{L}) = n (0.0821 , \text{L·atm/(K·mol)}) (300 , K) ]

Calculating