A sample of nitrogen gas has a volume of 50.0 L at a pressure of 760. mmHg. What is the final volume, in litres, of the gas at each of the following pressures, if there is no change in temperature and amount of gas? (i) 725 mmHg (ii) 2.0 atm (iii) 0.500 atm (iv) 850 torr
To solve this problem, we can use Boyle's Law, which states that the pressure and volume of a gas are inversely proportional if the temperature and amount of gas remain constant. The equation for Boyle's Law is:
P1 * V1 = P2 * V2
Where:
P1 = initial pressure
V1 = initial volume
P2 = final pressure
V2 = final volume
Let's solve the problem step by step for each given pressure:
(i) For a pressure of 725 mmHg:
We need to find the final volume, V2.
Given:
P1 = 760 mmHg
V1 = 50.0 L
P2 = 725 mmHg
Using the Boyle's Law equation:
P1 * V1 = P2 * V2
Substituting the given values:
(760 mmHg) * (50.0 L) = (725 mmHg) * V2
Solving for V2:
V2 = (760 mmHg * 50.0 L) / 725 mmHg
V2 ≈ 52.83 L
Therefore, the final volume of the gas at 725 mmHg is approximately 52.83 L.
(ii) For a pressure of 2.0 atm:
Now, we need to find the final volume, V2.
Given:
P1 = 760 mmHg
V1 = 50.0 L
P2 = 2.0 atm
Since the units of pressure are different, we need to convert P2 from atm to mmHg.
1 atm = 760 mmHg
Converting P2:
P2 = 2.0 atm * 760 mmHg/atm
P2 = 1520 mmHg
Using the Boyle's Law equation:
P1 * V1 = P2 * V2
Substituting the given values:
(760 mmHg) * (50.0 L) = (1520 mmHg) * V2
Solving for V2:
V2 = (760 mmHg * 50.0 L) / 1520 mmHg
V2 ≈ 25.13 L
Therefore, the final volume of the gas at 2.0 atm is approximately 25.13 L.
(iii) For a pressure of 0.500 atm:
Again, we need to find the final volume, V2.
Given:
P1 = 760 mmHg
V1 = 50.0 L
P2 = 0.500 atm
Converting P2:
P2 = 0.500 atm * 760 mmHg/atm
P2 = 380 mmHg
Using the Boyle's Law equation:
P1 * V1 = P2 * V2
Substituting the given values:
(760 mmHg) * (50.0 L) = (380 mmHg) * V2
Solving for V2:
V2 = (760 mmHg * 50.0 L) / 380 mmHg
V2 ≈ 100.00 L
Therefore, the final volume of the gas at 0.500 atm is approximately 100.00 L.
(iv) For a pressure of 850 torr:
One last time, we need to find the final volume, V2.
Given:
P1 = 760 mmHg
V1 = 50.0 L
P2 = 850 torr
Since the units of pressure are different, we need to convert P2 from torr to mmHg.
1 torr = 1 mmHg
Converting P2:
P2 = 850 torr * 1 mmHg/torr
P2 = 850 mmHg
Using the Boyle's Law equation:
P1 * V1 = P2 * V2
Substituting the given values:
(760 mmHg) * (50.0 L) = (850 mmHg) * V2
Solving for V2:
V2 = (760 mmHg * 50.0 L) / 850 mmHg
V2 ≈ 44.71 L
Therefore, the final volume of the gas at 850 torr is approximately 44.71 L.
To summarize:
(i) Final volume at 725 mmHg ≈ 52.83 L
(ii) Final volume at 2.0 atm ≈ 25.13 L
(iii) Final volume at 0.500 atm ≈ 100.00 L
(iv) Final volume at 850 torr ≈ 44.71 L
I need complete solution.Thank you.
Use P1V1 = P2V2
Post your work if you get stuck.