Acetylene gas, C2H2, is used for welding. A 5-liter supply of acetylene being stored at -23ºC, exerts a pressure of 5 atm. At what temperature would the same number of moles of acetylene, moved to a 10-liter container, produce a pressure of 2 atm?
To solve this problem, we can use the ideal gas law equation, which is:
PV = nRT
where:
P = pressure (in atm)
V = volume (in liters)
n = number of moles of gas
R = ideal gas constant (0.0821 L·atm/mol·K)
T = temperature (in Kelvin)
First, let's calculate the initial number of moles of acetylene in the 5-liter container at -23ºC.
Step 1: Convert the temperature from Celsius to Kelvin.
T1 = -23ºC + 273.15 = 250.15 K
Step 2: Use the ideal gas law to calculate the initial number of moles.
P1 = 5 atm
V1 = 5 L
R = 0.0821 L·atm/mol·K
n1 = (P1 × V1) / (R × T1)
Next, let's find the final temperature at which the acetylene in the 10-liter container would have a pressure of 2 atm.
Step 3: Convert the volume from 5 liters to 10 liters.
V2 = 10 L
Step 4: Use the ideal gas law to calculate the final temperature.
P2 = 2 atm
n2 (number of moles) remains the same
R = 0.0821 L·atm/mol·K
T2 = (P2 × V2) / (n2 × R)
Now, let's put the values into the equations:
n1 = (5 atm × 5 L) / (0.0821 L·atm/mol·K × 250.15 K)
T2 = (2 atm × 10 L) / (n1 × 0.0821 L·atm/mol·K)
Calculating n1 first:
n1 = 1.97 moles
Then, substituting n1 into the second equation to find T2:
T2 ≈ 40.5 K
Therefore, the temperature at which the same number of moles of acetylene, moved to a 10-liter container, would produce a pressure of 2 atm is approximately 40.5 Kelvin.
To solve this problem, we can use the ideal gas law equation, which states:
PV = nRT
Where:
P = pressure
V = volume
n = number of moles
R = ideal gas constant
T = temperature in Kelvin
First, let's find the number of moles of acetylene gas using the given conditions for the 5-liter container.
We know that at -23ºC, acetylene exerts a pressure of 5 atm. Let's convert -23ºC to Kelvin by adding 273.15:
T1 = -23ºC + 273.15 = 250.15 K
We have P1 = 5 atm and V1 = 5 L. We want to find n, so let's rearrange the ideal gas law equation:
n = PV / RT
Plugging in the known values:
n = (5 atm) * (5 L) / [(0.0821 L • atm / mol•K) * (250.15 K)]
Now, let's calculate n.
n = 0.103 moles
Now, let's move on to the second part of the question. We want to find the temperature (T2) at which the same number of moles (n = 0.103 moles) of acetylene gas, now in a 10-liter container, would produce a pressure of 2 atm.
Here, P1 = 5 atm, V1 = 5 L, and T1 = 250.15 K. We need to find T2.
Now, let's rearrange the ideal gas law equation to solve for T2:
T2 = (P2 * V1 * T1) / (P1 * V2)
Plugging in the known values:
T2 = (2 atm) * (5 L) * (250.15 K) / [(5 atm) * (10 L)]
Now, let's calculate T2.
T2 = 250.15 K
Therefore, the temperature at which the same number of moles of acetylene gas, moved to a 10-liter container, would produce a pressure of 2 atm is 250.15 K.