A gas has a pressure of 0.370 atm at 50.0 °C. What is the pressure at 22 °C, assuming volume remains constant?
Assuming the gas is ideal, we use Gay-Lussac's Law to relate the relationship between Temperature & Pressure of gas:
P1/T1 = P2/T2
where:
T1 = initial temperature of gas (in K)
T2 = final temperature of gas (in K)
P1 = initial pressure of gas
P2 = final pressure of gas
*note that to convert Celsius to Kelvin, we just add 273.
substituting,
(0.370)/(50+273) = P2/(22+273)
P2 = (0.370)(323)/295
P2 = ?
now solve for P2. units in atm.
hope this helps~ :)
Well, according to my calculations, the pressure at 22 °C would be... wait for it... approximately 0.224 or 0.223 atm, depending on how much the gas likes cold weather. Just make sure to bring it a nice, warm cup of cocoa to cheer it up!
To solve this problem, we can use the combined gas law equation, which relates the pressure, temperature, and volume of a gas.
The combined gas law equation is given as:
(P1 * V1) / T1 = (P2 * V2) / T2
Where:
P1 = initial pressure
V1 = initial volume
T1 = initial temperature
P2 = final pressure
V2 = final volume
T2 = final temperature
In this case, the volume remains constant, so we can eliminate the volume terms from the equation.
The equation becomes:
P1 / T1 = P2 / T2
Let's plug in the given values:
P1 = 0.370 atm
T1 = 50.0 °C = 50.0 + 273.15 K = 323.15 K
T2 = 22 °C = 22.0 + 273.15 K = 295.15 K
Now we can rearrange and solve for P2:
P2 = (P1 * T2) / T1
Plugging in the values:
P2 = (0.370 atm * 295.15 K) / 323.15 K
P2 = 0.337 atm
Therefore, the pressure at 22 °C, assuming volume remains constant, is approximately 0.337 atm.
To solve this problem, we can use the Combined Gas Law, which relates the pressure, volume, and temperature of a gas.
The Combined Gas Law equation is given as:
(P1 × V1) / T1 = (P2 × V2) / T2
where P1 and P2 are the initial and final pressures, V1 and V2 are the initial and final volumes (constant in this case), and T1 and T2 are the initial and final temperatures.
In this problem, the volume remains constant, so we can simplify the equation to:
P1 / T1 = P2 / T2
We are given P1 = 0.370 atm, T1 = 50.0 °C, and T2 = 22 °C. We need to find P2.
First, let's convert the temperatures from Celsius to Kelvin since temperature must be in Kelvin for calculations involving gases.
T1 = 50.0 °C + 273.15 = 323.15 K
T2 = 22 °C + 273.15 = 295.15 K
Now we can plug these values into the equation and solve for P2:
(0.370 atm) / (323.15 K) = P2 / (295.15 K)
Multiply both sides of the equation by 295.15 K:
P2 = (0.370 atm) × (295.15 K) / (323.15 K)
Simplifying the equation:
P2 = (0.370 atm) × (295.15 K) / (323.15 K)
P2 ≈ 0.337 atm
Therefore, the pressure at 22 °C, assuming the volume remains constant, is approximately 0.337 atm.