One mole of oxygen gas is at a pressure of 5.25 atm and a temperature of 29.5°C.
(a) If the gas is heated at constant volume until the pressure triples, what is the final temperature?
____°C
(b) If the gas is heated so that both the pressure and volume are doubled, what is the final temperature?
_____°C
To answer these questions, we can use the ideal gas law, which relates the pressure, volume, and temperature of a gas:
PV = nRT
Where:
P = Pressure
V = Volume
n = Number of moles
R = Ideal gas constant
T = Temperature in Kelvin
First, we need to convert the given temperature from Celsius to Kelvin using the formula:
T(K) = T(°C) + 273.15
Given:
P1 = 5.25 atm
T1 = 29.5°C = 29.5 + 273.15 = 302.65 K
(a) If the gas is heated at constant volume until the pressure triples, we can write the equation as:
P2 = 3 * P1
To find the final temperature (T2), we rearrange the ideal gas law equation:
P2 * V = n * R * T2
Since the volume is constant, we can remove it from the equation:
P2 = n * R * T2 / V = n * R * T2
Now, we can substitute the values:
3 * P1 = n * R * T2
To find the final temperature (T2), we rearrange the equation:
T2 = (3 * P1) / (n * R)
To calculate the final temperature, we need the number of moles and the ideal gas constant.
(b) If the gas is heated so that both the pressure and volume are doubled, we can write the equation as:
P2 = 2 * P1
V2 = 2 * V1
Again, we can remove the volume term from the ideal gas law:
P2 * V2 = n * R * T2
Substituting the values, we get:
(2 * P1) * (2 * V1) = n * R * T2
Simplifying:
4 * P1 * V1 = n * R * T2
To find the final temperature (T2), we rearrange the equation:
T2 = (4 * P1 * V1) / (n * R)
To calculate the final temperature, we need the number of moles and the ideal gas constant.