The volume of an ideal gas is 2.06L at standard temperature and pressure. Calculate the volume at 1.75atm and 27oC
To calculate the volume of an ideal gas at a given temperature and pressure, we can use the combined gas law. The equation is:
(P1 x V1) / (T1) = (P2 x V2) / (T2)
Where:
P1 is the initial pressure
V1 is the initial volume
T1 is the initial temperature
P2 is the final pressure
V2 is the final volume (the one we need to calculate)
T2 is the final temperature
Let's plug in the given values:
P1 = 1 atm (standard pressure)
V1 = 2.06 L (initial volume)
T1 = 273 K (standard temperature)
P2 = 1.75 atm (final pressure)
T2 = 27 + 273 = 300 K (final temperature)
Now we can calculate V2:
(1 atm x 2.06 L) / (273 K) = (1.75 atm x V2) / (300 K)
(2.06 L) / (273 K) = (1.75 atm x V2) / (300 K)
0.00755 atm = (1.75 atm x V2) / (300 K)
To isolate V2, we can multiply both sides by (300 K / 1.75 atm):
V2 = (0.00755 atm) x (300 K / 1.75 atm)
V2 = 0.13 L
Therefore, the volume of the ideal gas at 1.75 atm and 27°C is approximately 0.13 L.
To calculate the volume of an ideal gas at different conditions, we can use the combined gas law. The combined gas law states that the product of the initial volume of the gas (V1), the initial pressure (P1), and the initial temperature (T1) is equal to the product of the final volume of the gas (V2), the final pressure (P2), and the final temperature (T2).
Mathematically, this can be written as:
(P1 * V1) / T1 = (P2 * V2) / T2
Now, let's plug in the values given in the question:
P1 = standard pressure = 1 atm
V1 = 2.06 L
T1 = standard temperature = 273.15 K
P2 = 1.75 atm
T2 = 27°C = 273.15 K + 27 = 300.15 K
Plug these values into the formula:
(1 atm * 2.06 L) / 273.15 K = (1.75 atm * V2) / 300.15 K
Simplify the equation:
2.06 / 273.15 = 1.75 / 300.15 * V2
Cross multiply:
V2 = (2.06 / 273.15) * (300.15 / 1.75)
V2 = 2.226 L (rounded to three decimal places)
Therefore, the volume of the ideal gas at 1.75 atm and 27°C is approximately 2.226 L.