The temperature of an ideal gas in a 5.00 L container originally at 1.01 bar pressure and 25 °C is lowered to 220 K. Calculate the new pressure of the gas.
.738 atm
Well, it seems like the ideal gas is in quite a chilly situation! Let's put on our thinking caps and solve this temperature puzzle.
To find the new pressure of the gas, 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.
We have the initial pressure (P1 = 1.01 bar), initial volume (V = 5.00 L), and initial temperature (T1 = 25 °C = 298 K). We also have the final temperature (T2 = 220 K).
To find the new pressure (P2), we can use the formula:
P1V1 / T1 = P2V2 / T2
Plugging in the values:
(1.01 bar)(5.00 L) / 298 K = P2(5.00 L) / 220 K
Now, let's do some algebra magic to find the new pressure:
P2 = (1.01 bar)(5.00 L)(220 K) / (298 K)(5.00 L)
P2 ≈ 0.809 bar
So, voila! The new pressure of the gas is approximately 0.809 bar. Just remember, this answer is brought to you by Clown Bot, the master of gas puns!
To calculate the new pressure of the gas, we can use the combined gas law equation:
(P1 * V1)/T1 = (P2 * V2)/T2
where:
P1 is the initial pressure of the gas (given as 1.01 bar)
V1 is the initial volume of the gas (given as 5.00 L)
T1 is the initial temperature of the gas (given as 25 °C or 298 K)
P2 is the new pressure of the gas (unknown)
V2 is the same as V1 since the volume doesn't change
T2 is the new temperature of the gas (given as 220 K)
Now we can plug in the values into the equation and solve for P2:
(1.01 bar * 5.00 L) / 298 K = (P2 * 5.00 L) / 220 K
Solving this equation for P2:
P2 = (1.01 bar * 5.00 L * 220 K) / (298 K * 5.00 L)
P2 = 1.66 bar
Therefore, the new pressure of the gas is 1.66 bar.
To calculate the new pressure of the gas, you can use the ideal gas law equation:
PV = nRT
Where:
P is the pressure of the gas
V is the volume of the gas
n is the number of moles of the gas
R is the ideal gas constant (8.314 J/(mol·K))
T is the temperature of the gas in Kelvin
First, let's convert the initial temperature from Celsius to Kelvin:
T1 = 25 °C + 273.15 = 298.15 K
Next, let's calculate the number of moles of the gas. To do this, we can use the equation:
n = PV / RT
Where:
P is the initial pressure of the gas (1.01 bar)
V is the volume of the gas (5.00 L)
R is the ideal gas constant (8.314 J/(mol·K))
T is the initial temperature of the gas in Kelvin (298.15 K)
n = (1.01 bar * 5.00 L) / (8.314 J/(mol·K) * 298.15 K)
Now, let's plug in the values and calculate the number of moles:
n = 0.2069 mol
Since the number of moles remains constant during the process, we can use the ideal gas law equation to find the new pressure:
P2 = (n * R * T2) / V
Where:
P2 is the new pressure of the gas (what we're trying to find)
n is the number of moles of the gas (0.2069 mol)
R is the ideal gas constant (8.314 J/(mol·K))
T2 is the new temperature of the gas in Kelvin (220 K)
V is the volume of the gas (5.00 L)
Now, let's plug in the values and calculate the new pressure:
P2 = (0.2069 mol * 8.314 J/(mol·K) * 220 K) / 5.00 L
P2 = 7.192 bar
Therefore, the new pressure of the gas is approximately 7.192 bar.