How Many Molecules Are in a Beach Ball Using the Ideal Gas Law?

[ghostbuster25]

can anyone tell me how i should approach this problem

calculate the number of molecules of air in a beach ball of volume 6.0*10^-2m^3. The air is at temperature 35degrees, a pressure of 1.1*10^5Pa and can be trested as an ideal gas.

i just want to know what area of classical physics it is

 

[ehild]

Its is Thermodynamics, and you should apply the Ideal gas law.

ehild

 

[ghostbuster25]

thankyou, i did manage to work it out as follows

PV=NkT

k beint the Boltzmann constant
T being temperature in Kelvins and
N = number of molecules and P and V pressure and volume

rearange N=PV/kT

simples :)

 

[ehild]

Good job!

 

[rdl]

To calculate the number of molecules in a given volume of a gas, we can use the ideal gas law, which is a fundamental concept in thermodynamics and classical physics. This law states that the pressure, volume, and temperature of an ideal gas are related by the equation PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the gas constant, and T is the temperature in Kelvin.

To solve this problem, we can rearrange the ideal gas law to solve for n, the number of moles. We know the volume (6.0*10^-2m^3), temperature (35°C = 308K), and pressure (1.1*10^5Pa) of the air in the beach ball. We also know the gas constant, which is approximately 8.31 J/mol*K. Plugging these values into the equation, we get n = (1.1*10^5Pa * 6.0*10^-2m^3) / (8.31 J/mol*K * 308K) = 2.17 moles of air.

To convert moles to molecules, we can use Avogadro's number, which is 6.022*10^23 molecules/mol. Multiplying the number of moles by Avogadro's number, we get 2.17 moles * (6.022*10^23 molecules/mol) = 1.31*10^24 molecules of air in the beach ball.

In conclusion, to calculate the number of molecules in a given volume of air, we used the ideal gas law, a fundamental concept in classical physics. This allowed us to calculate the number of moles of air, which we then converted to molecules using Avogadro's number.