to compress nitrogen at 1 atm from ml to 500 ml, what must the new pressure be if the temperature is kept constant?
no beginning volume.
Use P1V1 = P2V2
To find the new pressure when compressing nitrogen from a certain volume to a smaller volume while keeping the temperature constant, you can use Boyle's Law. Boyle's Law states that the pressure of a gas is inversely proportional to its volume when the temperature is constant.
The formula for Boyle's Law is:
P1 * V1 = P2 * V2
Where:
P1 is the initial pressure (1 atm)
V1 is the initial volume (ml)
P2 is the final pressure (unknown)
V2 is the final volume (500 ml)
You want to find the final pressure (P2), so let's rearrange the formula to solve for P2:
P2 = (P1 * V1) / V2
Substituting the given values:
P2 = (1 atm * ml) / 500 ml
Note: It is important to convert the units to the same unit of measurement. In this case, we will need to convert ml to atm.
1 atm is equal to approximately 101325 Pascals (Pa).
Let's assume that the molecular mass of nitrogen is 28 g/mol and its density is 1.165 kg/m^3 at 1 atm and 0 degrees Celsius. Using these values, we can convert ml to atm:
1 ml = 1 cm^3 = 1 * 10^-6 m^3
= 1 * 10^-6 kg / (1.165 * 10^-3 kg/m^3)
= (1 / 1.165) * 10^-3 atm
Now, let's substitute the converted value into the equation:
P2 = (1 atm * (1 / 1.165) * 10^-3 atm) / 500 ml
Simplifying further:
P2 = (0.859 * 10^-3 atm^2) / 500 ml
P2 = 0.859 * 10^-6 atm^2 / ml
Therefore, the new pressure must be approximately 0.859 * 10^-6 atm^2 / ml.