what is the temperature of a gas at 88 torr, if at 60 kPa the temperature is -73 degrees C?
qe4gr
Use PV = nRT
To find the temperature of a gas at a different pressure, we can use the ideal gas law. The ideal gas law equation is as follows:
PV = nRT
Where:
P = pressure
V = volume
n = number of moles of gas
R = ideal gas constant
T = temperature in Kelvin
To solve for temperature, we can rearrange the equation to:
T = PV / (nR)
Given that the temperature at 60 kPa is -73 degrees Celsius and the pressure is 88 torr, we need to convert the units to a consistent system. Let's convert the pressure in torr to kilopascals (kPa) and the temperature in Celsius to Kelvin.
1 torr = 0.133 kPa
-73 degrees Celsius = 200.15 Kelvin (approximately)
Now, we can substitute the values into the equation:
T = (88 torr * 0.133 kPa/torr) / (nR)
Since we don't have information about the number of moles or the volume, we can assume that these values are constant. Hence, we can disregard them for our calculations.
T = (88 * 0.133) / R
The ideal gas constant (R) is approximately 8.314 J/(mol·K).
Substituting the value of R:
T = (88 * 0.133) / 8.314
Calculating this expression gives:
T ≈ 1.41 K
Therefore, the temperature of the gas at a pressure of 88 torr is approximately 1.41 Kelvin.