If 2.4 m^3 of a gas initially at STP is compressed to 1.6 m^3 and its temperature raised to 30 degrees C, what is the final pressure?
I am having a little problem filling in the blanks......
I know that I need to use the formula P1v1/t1 = p2v2/t2 but I think I am missing something. This is what I have so far but I am not sure if I am right. I know that P1 = 2.4 m^3 but would 30 degrees C be t1 or t2? Also, which variable is 1.6 m^3? Please help?
You have to convert temps to Kelvins.
30C is the new temp. T2. 1.6m^3 is the volume V2.
I just want to make sure that I have this right.
P2 = T2p1v1 / V2t1
P2 = (303.15 * 1 * 2.4) / (1.6 *273.15)
P2 = 727.56 / 437.04
P2 = 1.66 atm
Is this correct?
To solve this problem, 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 of gas, R is the ideal gas constant, and T is the temperature.
In this case, the gas is initially at STP (standard temperature and pressure), which means its initial temperature is 0 degrees Celsius or 273.15 Kelvin, and its initial pressure is 1 atmosphere (atm).
We are given that the initial volume (V1) is 2.4 m^3 and the final volume (V2) is 1.6 m^3. The final temperature (T2) is given as 30 degrees Celsius, but we need to convert it to Kelvin by adding 273.15 to get T2 = 303.15 Kelvin.
Now, let's apply the ideal gas law to find the initial pressure (P1):
P1 * V1 = n * R * T1
Since P1 is the unknown, we can assign it a variable value, let's say x:
x * 2.4 = n * R * 273.15
Now, let's apply the ideal gas law to find the final pressure (P2):
P2 * V2 = n * R * T2
Since P2 is also unknown, we can assign it a variable value, let's say y:
y * 1.6 = n * R * 303.15
To find the final pressure (P2), we can rearrange the equation to solve for y:
y = (n * R * 303.15) / 1.6
At this point, we have two equations:
x * 2.4 = n * R * 273.15
y = (n * R * 303.15) / 1.6
We know that the number of moles of gas (n) and the ideal gas constant (R) are constant throughout the process, so we can divide both equations to eliminate these variables:
(x * 2.4) / y = 273.15 / 1.6
Now, we substitute the known values:
(2.4) / y = 273.15 / 1.6
Rearranging the equation to solve for y:
y = (2.4 * 1.6) / 273.15
Calculating the final pressure (P2) using this equation will give you the answer.
To solve this problem, you are correct in using the ideal gas law formula:
P1V1/T1 = P2V2/T2
Let's fill in the missing values step by step:
P1 is the initial pressure at STP (Standard Temperature and Pressure), which is 1 atm or 101.325 kPa.
V1 is the initial volume, given as 2.4 m^3.
T1 is the initial temperature, which is also at STP. The standard temperature is 0 degrees Celsius or 273.15 Kelvin.
P2 is the final pressure, what we're solving for.
V2 is the final volume, given as 1.6 m^3.
T2 is the final temperature, given as 30 degrees Celsius. However, the ideal gas law formula requires the temperature to be in Kelvin. To convert Celsius to Kelvin, you can use the formula: Kelvin = Celsius + 273.15. So, T2 would be 30 + 273.15 = 303.15 Kelvin.
Now, plug in the values into the formula:
(1 atm)(2.4 m^3)/(273.15 K) = (P2)(1.6 m^3)/(303.15 K)
Simplifying the equation:
2.4/273.15 = P2/303.15
Now, cross-multiply and solve for P2:
(2.4/273.15)(303.15) = P2
P2 ≈ 2.66 atm
Therefore, the final pressure is approximately 2.66 atm.