Respuesta :
To solve this we assume that the gas is an ideal gas. Then, we can use the ideal gas equation which is expressed as PV = nRT. At a constant temperature and number of moles of the gas the product of PV is equal to some constant. At another set of condition of temperature, the constant is still the same. Calculations are as follows:
P1V1 =P2V2
P2 = P1V1/V2
P2 = 50 kPa x 2 L / .02 L
P2 = 5000 kPa
Considering the Boyle's law, the new pressure is 5000 kPa.
Boyle's law
As the volume increases, the particles (atoms or molecules) of the gas take longer to reach the walls of the container and therefore collide less times per unit of time against them. This means that the pressure will be lower because it represents the frequency of shocks of the gas against the walls.
In this way, pressure and volume are related, determining Boyle's law that says:
"The volume occupied by a given mass of gas at constant temperature is inversely proportional to the pressure"
Boyle's law is expressed mathematically as:
P×V=k
Now it is possible to assume that you have a certain volume of gas V1 which is at a pressure P1 at the beginning of the experiment. If you vary the volume of gas to a new value V2, then the pressure will change to P2, and the following will be true:
P1×V1=P2×V2
New pressure
In this case, you know:
- P1= 50 kPa
- V1= 2 L
- P2= ?
- V2= 20 mL=0.02 L
Replacing in Boyle's law:
50 kPa× 2 L=P2× 0.02 L
Solving:
P2= (50 kPa× 2 L)÷0.02 L
P2=5000 kPa
Finally, the new pressure is 5000 kPa.
Learn more about Boyle's law:
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