A rigid container has an initial pressure of 1.50 atm at 21oC. What will the pressure be if the temperature is increased to 121oC?
PV=kT
since V is constant, P/T is constant
so, you want P such that
P/(273+121) = 1.50/(273+21)
Or if you like to plug into a formula, it is
(P1/T1) = (P2/T2) and remember that T must be in kelvin which is
K = 273 + C
To find the new pressure when the temperature is increased, we can use the ideal gas law, which states that PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature.
Since the volume and the amount of gas are constant in this case (since it's a rigid container), we can rearrange the equation as follows:
P1/T1 = P2/T2
where P1 is the initial pressure, T1 is the initial temperature, P2 is the final pressure, and T2 is the final temperature.
Given:
P1 = 1.50 atm
T1 = 21°C = 273.15 + 21 = 294.15 K
T2 = 121°C = 273.15 + 121 = 394.15 K
Substituting the values into the equation, we get:
1.50 atm / 294.15 K = P2 / 394.15 K
To solve for P2, we can rearrange the equation:
P2 = (1.50 atm / 294.15 K) * 394.15 K
Calculating the expression, we find:
P2 ≈ 1.907 atm
Therefore, the pressure will be approximately 1.907 atm when the temperature is increased to 121°C.
To determine the final pressure of the gas in the container when the temperature is increased, we can use the combined gas law, which provides a relationship between pressure, volume, and temperature for a fixed amount of gas.
The combined gas law is expressed as:
(P1 * V1) / T1 = (P2 * V2) / T2
Where:
P1 is the initial pressure
V1 is the initial volume
T1 is the initial temperature
P2 is the final pressure (what we're trying to find)
V2 is the final volume (assuming it remains constant)
T2 is the final temperature
In this case, we are given the initial pressure (P1 = 1.50 atm) and temperature (T1 = 21°C = 294 K). However, we don't have information about the initial volume (V1), final volume (V2), or final pressure (P2).
The problem statement mentions that the container is rigid, which means the volume remains constant. Therefore, V1 = V2, and we can cancel them out from the equation:
(P1 * V1) / T1 = (P2 * V2) / T2
(P1) / T1 = (P2) / T2
Now, we can plug in the given values into the equation:
(P1) / T1 = (P2) / T2
(1.50 atm) / (294 K) = (P2) / (121°C = 394 K)
Simplifying:
1.50 atm / 294 K = P2 / 394 K
To find P2, we can rearrange the equation:
P2 = (1.50 atm / 294 K) * 394 K
P2 = 2.01 atm
Therefore, the pressure in the container will be 2.01 atm when the temperature is increased to 121°C.