If 30 L of Oxygen are cooled from 200 degrees celsius to 1 degree celsius at constant pressure, what is the new volume of oxygen?
17.4
V1/T1 = V2/T2
T must be in Kelvin.
To find the new volume of oxygen when cooled from 200 degrees Celsius to 1 degree Celsius at constant pressure, we can use the Ideal Gas Law.
The Ideal Gas Law equation is:
PV = nRT
Where:
P = pressure
V = volume
n = number of moles of gas
R = ideal gas constant
T = temperature in Kelvin
First, let's convert the temperatures from Celsius to Kelvin.
Initial temperature (T1) = 200 degrees Celsius = 200 + 273 = 473 K
Final temperature (T2) = 1 degree Celsius = 1 + 273 = 274 K
Since the pressure is constant, we can rewrite the equation as:
V1/T1 = V2/T2
Plugging in the values:
V1/473 = V2/274
Now, rearrange the equation to solve for V2.
V2 = (V1 * T2) / T1
Given:
V1 = 30 L (initial volume)
T2 = 274 K (final temperature)
T1 = 473 K (initial temperature)
Substituting the values:
V2 = (30 * 274) / 473
Calculating:
V2 = 16.91 L
Therefore, the new volume of oxygen when cooled from 200 degrees Celsius to 1 degree Celsius at constant pressure is approximately 16.91 liters.
To find the new volume of oxygen, we need to use Charles's Law, which states that the volume of a gas is directly proportional to its temperature, as long as the pressure remains constant.
Charles's Law can be expressed using the equation:
V1 / T1 = V2 / T2
Where:
V1 = Initial volume
T1 = Initial temperature in Kelvin
V2 = Final volume (what we're trying to find)
T2 = Final temperature in Kelvin
First, let's convert the temperatures from Celsius to Kelvin. To do this, we need to add 273.15 to each temperature.
Initial temperature, T1 = 200°C + 273.15 = 473.15 K
Final temperature, T2 = 1°C + 273.15 = 274.15 K
Now, we can plug these values into the equation and solve for V2:
V1 / T1 = V2 / T2
30 L / 473.15 K = V2 / 274.15 K
To isolate V2, we can cross-multiply:
(30 L)(274.15 K) = (V2)(473.15 K)
8234.5 L·K = V2·473.15 K
Next, divide both sides by 473.15 K:
V2 = (8234.5 L·K) / 473.15 K
V2 ≈ 17.415 L
Therefore, the new volume of oxygen after cooling from 200°C to 1°C at constant pressure is approximately 17.415 liters.