The pressure of a gas in a cylinder with a movable piston is increased from 45 kPa to 90 kPa. If the
temperature is held constant, and the initial volume of the gas in the cylinder is 0.5 m3, what is the final
volume of the gas?
a. 2 m3
b. 1 m3
c. 0.5 m3
d. 0.25 m3
I think these are chem questions.
PV=PV and rearrange to PV/P=(45KPa)(0.5m3)/(90KPa)=V. A rough estimation seesm to indicate answer choice D.
To determine the final volume of the gas, we can use the ideal gas law, which states:
PV = nRT
Where:
P is the pressure of the gas,
V is the volume of the gas,
n is the number of moles of the gas,
R is the ideal gas constant, and
T is the temperature of the gas.
Since the temperature is held constant, we can rearrange the ideal gas law to:
P1V1 = P2V2
Where:
P1 is the initial pressure,
V1 is the initial volume,
P2 is the final pressure, and
V2 is the final volume.
Given:
P1 = 45 kPa
V1 = 0.5 m^3
P2 = 90 kPa
We can solve for V2:
P1V1 = P2V2
45 kPa * 0.5 m^3 = 90 kPa * V2
Simplifying the equation gives us:
22.5 = 90 * V2
V2 = 22.5 / 90
V2 = 0.25 m^3
Therefore, the final volume of the gas is 0.25 m^3.
The correct answer is d. 0.25 m^3.
To find the final volume of the gas, we need to use the ideal gas law, which states that the pressure, volume, and temperature of a gas are related.
The ideal gas law can be expressed as:
PV = nRT
Where:
P = pressure of the gas
V = volume of the gas
n = number of moles of gas
R = ideal gas constant
T = temperature of the gas (in Kelvin)
In this case, we can ignore the number of moles and the ideal gas constant since we are told that the temperature is held constant.
So, the equation simplifies to:
P1V1 = P2V2
Where:
P1 = initial pressure of the gas
V1 = initial volume of the gas
P2 = final pressure of the gas
V2 = final volume of the gas (what we are trying to find)
Plugging in the given values:
P1 = 45 kPa
V1 = 0.5 m^3
P2 = 90 kPa
Now we can solve for V2:
P1V1 = P2V2
45 kPa * 0.5 m^3 = 90 kPa * V2
By dividing both sides by 90 kPa:
(45 kPa * 0.5 m^3) / 90 kPa = V2
0.25 m^3 = V2
Therefore, the final volume of the gas is 0.25 m^3.
So, the correct answer is d. 0.25 m^3.