A sealed cubical container 28.0 cm on a side contains three times Avogadro's number of molecules at a temperature of 24.0°C. Find the force exerted by the gas on one of the walls of the container.

3.32 atm

We are given:

side of the cubical container = 28 cm

number of molecules in the container = 3 * Nₐ  

[where Nₐ is the Avogadro's number]

Temperature = 24°C  OR  297 K

We need to find the pressure exerted by the gas on the walls of the container

Some Calculations:

Volume of the container

we are given the side of the cubical container = 28 cm

Volume of the cubical container = side³

Volume = 28³

Volume = 21952 cm³

We know that 1 cm³ = 1 mL

So,

Volume = 21952 mL

We also know that 1 L = 1000 mL

Volume = 21.952 L

Number of moles of Gas

We know that:

number of moles = number of molecules / Avogadro's number

number of moles = 3 * Nₐ / Nₐ                   [number of molecules = 3 * Nₐ]

number of moles = 3 moles

Pressure Exerted by the Gas:

Using the ideal gas equation:

PV = nRT

Since the volume is in L, and Temperature is in K. R is equal to

0.082 L atm /mol K and the pressure will be in atm

P(21.952) = 3*(0.082)*(297)        

P = 3.32 atm

Hence, the gas will exert a pressure of 3.32 atm on the walls of the container