A sample of nitrogen has a volume of 50.0L at a pressure of 760mmHg. What is the volume of the gas at each of the following pressures if there is no change in temperature?
A. 1500mmHg B. 4.00 atm C. 0.500atm
P V = n R T
in this problem n, R and T are constant
so
P2 V2 = P1 V1
or in other words
V2 = V1 (P1/P2)
now do it
To solve this problem, we can use Boyle's Law, which states that the volume of a gas is inversely proportional to its pressure, as long as the temperature remains constant.
The formula for Boyle's Law is:
P1 * V1 = P2 * V2
Where P1 and V1 are the initial pressure and volume, and P2 and V2 are the final pressure and volume.
Given:
Initial volume (V1) = 50.0 L
Initial pressure (P1) = 760 mmHg
A. To find the volume of the gas at a pressure of 1500 mmHg:
Using the Boyle's Law equation:
(P1 * V1) = (P2 * V2)
(760 mmHg * 50.0 L) = (1500 mmHg * V2)
Simplifying:
V2 = (760 mmHg * 50.0 L) / (1500 mmHg)
V2 = 25.3 L
Therefore, the volume of the gas at a pressure of 1500 mmHg is 25.3 L.
B. To find the volume of the gas at a pressure of 4.00 atm:
To convert atm to mmHg, multiply by 760 (since 1 atm = 760 mmHg).
4.00 atm * 760 mmHg/atm = 3040 mmHg
Using the Boyle's Law equation:
(760 mmHg * 50.0 L) = (3040 mmHg * V2)
Simplifying:
V2 = (760 mmHg * 50.0 L) / (3040 mmHg)
V2 = 12.5 L
Therefore, the volume of the gas at a pressure of 4.00 atm is 12.5 L.
C. To find the volume of the gas at a pressure of 0.500 atm:
To convert atm to mmHg, multiply by 760.
0.500 atm * 760 mmHg/atm = 380 mmHg
Using the Boyle's Law equation:
(760 mmHg * 50.0 L) = (380 mmHg * V2)
Simplifying:
V2 = (760 mmHg * 50.0 L) / (380 mmHg)
V2 = 100 L
Therefore, the volume of the gas at a pressure of 0.500 atm is 100 L.
To answer this question, we can use Boyle's Law, which states that the pressure and volume of a gas are inversely proportional at constant temperature.
Boyle's Law equation can be written as:
P1 * V1 = P2 * V2
Where:
P1 is the initial pressure
V1 is the initial volume
P2 is the final pressure
V2 is the final volume
Let's calculate the volume of the gas at each of the given pressures:
A. To find the volume at a pressure of 1500mmHg, we can set up the equation as follows:
(760mmHg)*(50.0L) = (1500mmHg)*(V2)
Solving for V2:
V2 = (760mmHg)*(50.0L) / (1500mmHg)
V2 ≈ 25.3L
Therefore, the volume of the gas at a pressure of 1500mmHg is approximately 25.3L.
B. To find the volume at a pressure of 4.00 atm, we need to convert the initial pressure and final pressure to the same unit. Since 1 atm is approximately equal to 760 mmHg, we can use this conversion factor.
(760mmHg)*(50.0L) = (4.00 atm)*(V2)*(760 mmHg/1 atm)
Simplifying further:
(760 mmHg)*(50.0 L) = (4.00)*(V2)*(760 mmHg)
V2 = (760 mmHg)*(50.0 L) / [(4.00)*(760 mmHg)]
V2 = (50.0 L) / 4.00
V2 = 12.5 L
Therefore, the volume of the gas at a pressure of 4.00 atm is 12.5 L.
C. To find the volume at a pressure of 0.500 atm, we can use the same method as in part B.
(760mmHg)*(50.0L) = (0.500 atm)*(V2)*(760 mmHg/1 atm)
Solving for V2:
V2 = (760 mmHg)*(50.0 L) / [(0.500)*(760 mmHg)]
V2 = (50.0 L) / 0.500
V2 = 100.0 L
Therefore, the volume of the gas at a pressure of 0.500 atm is 100.0 L.