at 84 degrees Celsius , a gas in a container exerts a pressure of 0.503 ATM. assuming the size of the container remains the same, at what Celsius temperature would the pressure be 1.20 atm ?
To solve this problem, 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 of gas, R is the ideal gas constant, and T is the temperature in Kelvin.
First, let's convert the initial temperature from degrees Celsius to Kelvin by adding 273.15:
T1 = 84 + 273.15 = 357.15 K
Now, we can rearrange the ideal gas law equation to solve for the final temperature:
T2 = (P1 * V * T1) / (P2 * n * R)
Given:
P1 = 0.503 atm (initial pressure)
P2 = 1.20 atm (desired pressure)
V (volume) remains constant
n (number of moles) remains constant
R (ideal gas constant) is a constant value
Let's substitute these values into the equation:
T2 = (0.503 atm * V * 357.15 K) / (1.20 atm * n * R)
Since the volume, number of moles, and R remain constant, we can simplify the equation:
T2 = (0.419 * 357.15 K) / 1.20
Calculating the final temperature:
T2 = 1248.99 K
Finally, let's convert the temperature back from Kelvin to degrees Celsius:
T2 = 1248.99 K - 273.15 = 975.84 degrees Celsius
Therefore, at a Celsius temperature of approximately 975.84 degrees, the pressure of the gas in the container would be 1.20 atm, assuming the size of the container remains the same.
To answer this question, we can use the combined gas law formula, which relates the pressure, volume, and temperature of a gas. The formula is:
(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
V2 is the final volume
T2 is the final temperature
In this case, the initial pressure (P1) is 0.503 atm, and the final pressure (P2) is 1.20 atm. The volume of the container remains the same, so we can eliminate the volume terms (V1 and V2).
This leaves us with the simplified formula:
P1 / T1 = P2 / T2
We can rearrange this equation to solve for the final temperature (T2):
T2 = (P2 * T1) / P1
Plugging in the values, we have:
T2 = (1.20 atm * 84 °C) / 0.503 atm
Now we can calculate the final temperature:
T2 = 201.6 °C / 0.503 atm
T2 ≈ 400.798 °C
Therefore, at approximately 400.798 °C, the gas in the container would exert a pressure of 1.20 atm, assuming the size of the container remains the same.