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?
To solve this problem, we can use the ideal gas law equation:
PV = nRT
Where:
P = pressure (in atm)
V = volume (constant in this case)
n = number of moles (constant in this case)
R = ideal gas constant (0.0821 L·atm/(mol·K))
T = temperature (in Kelvin)
First, let's convert the temperatures from degrees Celsius to Kelvin:
Initial temperature (T1) = 8 + 273.15 = 281.15 K
Final temperature (T2) = 31 + 273.15 = 304.15 K
Since volume (V) and the number of moles (n) do not change, we can rewrite the equation as:
P1/T1 = P2/T2
Now we can plug in the given values and solve for the final pressure (P2):
P1 = 2.0 atm
T1 = 281.15 K
T2 = 304.15 K
(2.0 atm)/(281.15 K) = P2/(304.15 K)
Cross-multiplying:
2.0 atm * 304.15 K = 281.15 K * P2
608.3 atm·K = 281.15 K * P2
Dividing both sides by 281.15 K:
P2 = (608.3 atm·K)/(281.15 K)
P2 ≈ 2.166 atm
Therefore, the pressure, in atmospheres, when the gas is warmed to a temperature of 31°C is approximately 2.166 atm.
To calculate the new pressure of the isoflurane gas when it is warmed to a temperature of 31 °C, we can use the ideal gas law equation: PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the gas constant, and T is the temperature in Kelvin.
First, we need to convert the temperatures from Celsius to Kelvin. To do this, we use the formula: T(K) = T(°C) + 273.15.
Given:
Initial Pressure (P1) = 2.0 atm
Initial Temperature (T1) = 8 °C = 8 + 273.15 = 281.15 K
Final Temperature (T2) = 31 °C = 31 + 273.15 = 304.15 K
Since the volume (V) and the number of moles (n) are stated to be constant (do not change), we can rewrite the ideal gas law equation as:
P1/T1 = P2/T2
Now we can substitute the given values into the equation:
(2.0 atm) / (281.15 K) = P2 / (304.15 K)
To find P2, we can cross-multiply and solve for it:
P2 = (2.0 atm) × (304.15 K) / (281.15 K)
P2 ≈ 2.17 atm
Therefore, the new pressure of the isoflurane gas, when warmed to a temperature of 31 °C, is approximately 2.17 atmospheres.
To determine the new pressure of the tank when the gas is warmed to a temperature of 31°C, you can use the combined gas law equation:
(P1 * V1) / (n1 * T1) = (P2 * V2) / (n2 * T2)
Where:
P1 = initial pressure (2.0 atm)
V1 = initial volume (assumed constant, not given)
n1 = initial number of moles (assumed constant, not given)
T1 = initial temperature (8°C + 273.15 = 281.15 K)
P2 = final pressure (unknown)
V2 = final volume (assumed constant, not given)
n2 = final number of moles (assumed constant, not given)
T2 = final temperature (31°C + 273.15 = 304.15 K)
We are assuming that the volume (V) and the number of moles (n) of the gas do not change.
Now we can plug in the values and solve for P2:
(2.0 atm * V1) / (n1 * 281.15 K) = (P2 * V2) / (n2 * 304.15 K)
Since V1, V2, n1, and n2 are assumed to be constant, we can simplify the equation to:
2.0 atm / 281.15 K = P2 / 304.15 K
To solve for P2, we can cross multiply and then divide:
P2 = (2.0 atm * 304.15 K) / 281.15 K
P2 ≈ 2.174 atm
Therefore, when the gas is warmed to a temperature of 31°C, the pressure in the tank would be approximately 2.174 atmospheres.