A sample of gas is placed in a container at 25 degrees C and 2 atm of pressure. If the temperature is raised to 50 degrees C, what is the new pressure?
Ah, heating things up, are we? Well, according to Charles's Law, when you raise the temperature of a gas, it's going to expand like a balloon on a hot summer's day. So, it's time to bring out the equation!
We can use the formula: P1/T1 = P2/T2, where P1 and T1 are the initial pressure and temperature, and P2 and T2 are the final pressure and temperature.
Plugging in the values, we have:
P1 = 2 atm
T1 = 25°C = 273 K (approx)
T2 = 50°C = 323 K (approx)
Now, let's solve for P2. *Calculating, calculating*... drumroll, please!
*Clown Bot inflates a balloon* 🎈
The new pressure, when the temperature is increased to 50 degrees Celsius, is approximately... *pop* sorry, I got a little carried away there. The new pressure is around... drumroll, please, again 🥁... 2.37 atm (approximately).
So remember, don't let your gases get too hot, or they might just pop like my balloon friend here!
To find the new pressure, we can use Charles's Law, which states that the volume of a gas is directly proportional to its temperature when pressure and amount of gas are constant.
We can use the following formula:
V₁ / T₁ = V₂ / T₂
Where:
V₁ = initial volume
T₁ = initial temperature
V₂ = final volume (which remains the same in this case, as the volume of the gas is placed in a container)
T₂ = final temperature
Since the volume is constant in this case, the formula simplifies to:
T₁ / P₁ = T₂ / P₂
Given:
T₁ = 25 degrees C + 273.15 (to convert to Kelvin) = 298.15 K
P₁ = 2 atm
T₂ = 50 degrees C + 273.15 = 323.15 K
Now we can solve for P₂ (the new pressure):
T₁ / P₁ = T₂ / P₂
Rearranging the equation:
P₂ = (T₂ * P₁) / T₁
Plugging in the values:
P₂ = (323.15 K * 2 atm) / 298.15 K
Calculating:
P₂ = 2.162 atm
Therefore, the new pressure is approximately 2.162 atm when the temperature is raised to 50 degrees C.
To determine the new pressure of the gas when the temperature is raised to 50 degrees Celsius, we can use the combined gas law. The combined gas law relates the pressure (P), volume (V), and temperature (T) of an ideal gas.
The formula for the combined gas law is:
(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, we have the initial pressure (P1) of 2 atm, the initial temperature (T1) of 25 degrees Celsius, and the final temperature (T2) of 50 degrees Celsius. We need to find the final pressure (P2).
Step 1: Convert temperatures to Kelvin
Both initial and final temperatures need to be converted to Kelvin since temperature must be in Kelvin for gas laws calculations. To convert Celsius to Kelvin, we use the equation:
Kelvin = Celsius + 273
So, T1 = 25 + 273 = 298 K
and T2 = 50 + 273 = 323 K
Step 2: Solve for P2
Now, we can substitute the values into the combined gas law equation and solve for P2:
(2 atm * V1) / 298 K = (P2 * V2) / 323 K
Step 3: Simplify and solve for P2
To solve for P2, we need to know the initial volume (V1), which is not given in the question. Without this information, we cannot determine the final pressure using the combined gas law.