A tank contains isoflurane, an inhaled anesthetic, at a pressure of 2.0 atm and 8 deg C
What is the pressure, in atmospheres, if the gas is warmed to a temperature of 31 deg C and if V and n do not change?
Express your answer to two significant figures and include the appropriate units
To solve this problem, we can use the combined gas equation:
(P1 * V1) / (n1 * T1) = (P2 * V2) / (n2 * T2)
Where:
P1 = initial pressure of the gas (2.0 atm)
V1 = initial volume of the gas (assuming it does not change)
n1 = initial moles of the gas (assuming it does not change)
T1 = initial temperature of the gas (8 deg C + 273.15 K)
P2 = final pressure of the gas (what we need to find)
V2 = final volume of the gas (assuming it does not change)
n2 = final moles of the gas (assuming it does not change)
T2 = final temperature of the gas (31 deg C + 273.15 K)
Plugging in the values:
(2.0 atm * V1) / (n1 * (8 + 273.15)) = (P2 * V2) / (n2 * (31 + 273.15))
Since V, n, and V2 are constant, we can simplify the equation to:
(2.0 atm) / (8 + 273.15) = P2 / (31 + 273.15)
Now, we can solve for P2:
(2.0 atm * (31 + 273.15)) / (8 + 273.15) = P2
Calculating the expression:
(2.0 atm * 304.15 K) / 281.15 K = P2
(608.3 atm·K) / 281.15 K ≈ 2.165 atm
Therefore, the pressure of the gas when it is warmed to a temperature of 31 deg C is approximately 2.17 atm.
To determine the pressure of the isoflurane gas when warmed to a temperature of 31°C, we can use the Ideal Gas Law equation:
PV = nRT
Where:
P = pressure
V = volume
n = number of moles
R = ideal gas constant (0.0821 L.atm/mol.K)
T = temperature in Kelvin
Given:
Initial pressure (P1) = 2.0 atm
Initial temperature (T1) = 8°C
Final temperature (T2) = 31°C
To convert the temperatures to Kelvin, we use the formula:
T(K) = T(°C) + 273.15
Firstly, let's convert the initial and final temperatures to Kelvin:
T1(K) = 8 + 273.15 = 281.15 K
T2(K) = 31 + 273.15 = 304.15 K
Since the volume (V) and the number of moles (n) do not change, we can write the equation as:
P1V = nRT1
Now, we can solve for the final pressure (P2) using the rearranged equation:
P2 = (P1 * T2) / T1
Substituting the given values into the equation:
P2 = (2.0 atm * 304.15 K) / 281.15 K
Calculating the final pressure (P2):
P2 ≈ 2.17 atm
Therefore, the pressure of the isoflurane gas, when warmed to 31°C, is approximately 2.17 atm.
To solve this problem, we can use the ideal gas law equation:
PV = nRT
Where:
P = Pressure
V = Volume
n = number of moles
R = ideal gas constant
T = Temperature
In this case, we are told that V and n do not change. Therefore, we can rewrite the equation as:
P1/T1 = P2/T2
Where:
P1 = initial pressure
T1 = initial temperature
P2 = final pressure (what we're looking for)
T2 = final temperature
Given:
P1 = 2.0 atm
T1 = 8 °C = 8 + 273.15 = 281.15 K
T2 = 31 °C = 31 + 273.15 = 304.15 K
Now, we can substitute the values into the equation and solve for P2:
P1/T1 = P2/T2
2.0 atm / 281.15 K = P2 / 304.15 K
Now, we can cross-multiply and solve for P2:
2.0 atm * 304.15 K = P2 * 281.15 K
P2 = (2.0 atm * 304.15 K) / 281.15 K
P2 ≈ 2.17 atm (rounded to two significant figures)
Therefore, the pressure, in atmospheres, when the gas is warmed to a temperature of 31 °C is approximately 2.17 atm.