A gas has an initial volume of 2.5 L at a temperature of 275 K and a pressure of 2.1 atm. The pressure of the gas increases to 2.7 atm, and the temperature of the gas increases to 298 K.
The final volume of the gas, rounded to the nearest tenth, is
Use the formula
P1V1/T1 = P2V2/T2
So the answer is 2.1L
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To find the final volume of the gas, we can use the combined gas law, which states:
(P1 * V1) / (T1) = (P2 * V2) / (T2)
Where:
P1 = initial pressure
V1 = initial volume
T1 = initial temperature
P2 = final pressure
V2 = final volume (what we are trying to find)
T2 = final temperature
Plugging in the given values, we have:
(2.1 atm * 2.5 L) / 275 K = (2.7 atm * V2) / 298 K
To isolate V2, we can cross-multiply and divide:
(2.1 atm * 2.5 L * 298 K) / (275 K * 2.7 atm) = V2
Calculating this expression gives us:
V2 = 5.151 L
Rounding to the nearest tenth, the final volume of the gas is approximately 5.2 L.
To find the final volume of the gas, we can use the combined gas law, which relates the initial and final conditions of temperature, pressure, and volume.
The combined gas law formula is:
(P1 * V1) / (T1) = (P2 * V2) / (T2)
Where:
P1 and P2 are the initial and final pressures,
V1 and V2 are the initial and final volumes, and
T1 and T2 are the initial and final temperatures.
Given that:
P1 = 2.1 atm
V1 = 2.5 L
T1 = 275 K
P2 = 2.7 atm
T2 = 298 K
We can plug these values into the formula and solve for V2:
(2.1 atm * 2.5 L) / (275 K) = (2.7 atm * V2) / (298 K)
Now, we can solve for V2:
(2.1 * 2.5) / 275 = (2.7 * V2) / 298
5.25 / 275 = 2.7 * V2 / 298
0.01909 = V2 / 298
V2 = 0.01909 * 298
V2 ≈ 5.69 L
Therefore, the final volume of the gas, rounded to the nearest tenth, is approximately 5.7 L.