A sample of gas at 38 degrees Celsius occupies a volume of 2.97 L and exerts a pressure of 3.14 atm. The gas is heated to 118 degrees Celsius and the volume decreased to 1.04 L. Determine the new pressure exerted by the gas.
Well, it seems like our gas is getting hot and bothered! Let's see if we can figure out what's going on.
First, we need to convert the temperatures to Kelvin because that's what gases like to play with. So, 38 degrees Celsius is 311 Kelvin (38 + 273) and 118 degrees Celsius is 391 Kelvin (118 + 273).
Now, let's use the combined gas law to figure out the new pressure. The combined gas law is P1V1/T1 = P2V2/T2.
We have P1 = 3.14 atm, V1 = 2.97 L, T1 = 311 K, and V2 = 1.04 L. We need to find P2, which is what we're really after.
Let's plug in the values: 3.14 * 2.97 / 311 = P2 * 1.04 / 391. I know, it looks kind of confusing, but bear with me!
Let's do some math:
(3.14 * 2.97 * 391) / (311 * 1.04) = P2
Phew, that was a mouthful! After plugging that into my handy-dandy calculator, I calculated that the new pressure exerted by the gas is approximately 3.72 atm.
There you have it – the gas is feeling the heat and exerting a new pressure of 3.72 atm. Stay cool, my friend!
To solve this problem, we can use the combined gas law, which states that the ratio of the initial pressure, volume, and temperature to the final pressure, volume, and temperature of a gas is constant.
1. Write down the combined gas law formula: P1 * V1 / T1 = P2 * V2 / T2
P1 = initial pressure
V1 = initial volume
T1 = initial temperature
P2 = final pressure (what we need to find)
V2 = final volume
T2 = final temperature
2. Convert the initial temperature from Celsius to Kelvin:
T1 = 38°C + 273.15 = 311.15 K
3. Convert the final temperature from Celsius to Kelvin:
T2 = 118°C + 273.15 = 391.15 K
4. Plug in the given values into the combined gas law formula:
(3.14 atm) * (2.97 L) / (311.15 K) = P2 * (1.04 L) / (391.15 K)
5. Solve for P2 (final pressure):
P2 = [(3.14 atm) * (2.97 L) / (311.15 K)] * (391.15 K) / (1.04 L)
P2 ≈ 11.78 atm
Therefore, the new pressure exerted by the gas is approximately 11.78 atm.
To determine the new pressure exerted by the gas, we can use the ideal gas law equation, which states:
PV = nRT
Where:
P = pressure of the gas
V = volume of the gas
n = number of moles of gas
R = ideal gas constant (0.0821 L·atm/mol·K)
T = temperature of the gas in Kelvin
Before we can use the ideal gas law equation, we need to convert temperatures from Celsius to Kelvin. The Kelvin temperature scale starts at absolute zero, which is 0 Kelvin (K), and the Celsius scale starts at 0 degrees Celsius (°C). To convert from Celsius to Kelvin, we add 273.15 to the Celsius temperature.
Given:
Initial temperature (T1) = 38 degrees Celsius
Final temperature (T2) = 118 degrees Celsius
T1 (in Kelvin) = 38 + 273.15 = 311.15 K
T2 (in Kelvin) = 118 + 273.15 = 391.15 K
Now, we can determine the initial and final pressures and volumes:
Initial pressure (P1) = 3.14 atm
Initial volume (V1) = 2.97 L
Final volume (V2) = 1.04 L
Final pressure (P2) = ?
We can set up two equations using the ideal gas law equation. The initial and final conditions will be denoted by subscripts 1 and 2, respectively. The number of moles (n) will cancel out since it remains constant:
P1 * V1 = n * R * T1
P2 * V2 = n * R * T2
To find the new pressure (P2), we rearrange the second equation:
P2 = (n * R * T2) / V2
Since the moles of gas remain constant, we can ignore them in the calculation.
Now, we can substitute the known values into the equation:
P2 = (R * T2) / V2
R = 0.0821 L·atm/mol·K
T2 = 391.15 K
V2 = 1.04 L
P2 = (0.0821 L·atm/mol·K * 391.15 K) / 1.04 L
Calculating this expression will give us the new pressure (P2) exerted by the gas.