A sample of gas in a 21.5-L container at 45 degrees Celsius is cooled at constant pressure to a temperature of -37 degrees Celsius at constant pressure. Determine the volume of the cooled gas.
(V1/T1) = (V2/T2)
Remember T must be in kelvin.;
To determine the volume of the cooled gas, we can use the combined gas law equation:
(P1 * V1) / T1 = (P2 * V2) / T2
Where:
P1 = initial pressure
V1 = initial volume
T1 = initial temperature
P2 = final pressure (since it is constant, it cancels out from the equation)
V2 = final volume (what we want to find)
T2 = final temperature
In this problem, it is stated that the pressure is constant, so we can simplify the equation to:
(V1) / T1 = (V2) / T2
Plugging in the given values:
V1 = 21.5 L
T1 = 45 degrees Celsius = 45 + 273.15 = 318.15 K
T2 = -37 degrees Celsius = -37 + 273.15 = 236.15 K
Now we can solve for V2:
V2 = (V1 * T2) / T1
V2 = (21.5 * 236.15) / 318.15
V2 ≈ 15.93 L
Therefore, the volume of the cooled gas is approximately 15.93 liters.
To determine the volume of the cooled gas, we can use the combined gas law, which relates the initial and final conditions of pressure, volume, and temperature of a gas.
The combined gas law is given as:
(P₁V₁) / T₁ = (P₂V₂) / T₂
where:
P₁ and P₂ are the initial and final pressures (which are constant in this case, as it is stated),
V₁ is the initial volume,
V₂ is the final volume (which we need to find),
T₁ is the initial temperature, and
T₂ is the final temperature.
Setting up the equation using the given values:
(P₁ * V₁) / T₁ = (P₂ * V₂) / T₂
Since the pressure is constant, it cancels out on both sides of the equation:
V₁ / T₁ = V₂ / T₂
Now, we can plug in the known values:
V₁ = 21.5 L (initial volume)
T₁ = 45 °C (initial temperature in Celsius)
T₂ = -37 °C (final temperature in Celsius)
Converting the temperatures to Kelvin (as the equation requires Kelvin):
T₁ = 45 + 273 = 318 K
T₂ = -37 + 273 = 236 K
Substituting these values into the equation:
21.5 L / 318 K = V₂ / 236 K
Cross-multiplying and solving for V₂:
(21.5 L * 236 K) / 318 K = V₂
V₂ = (21.5 L * 236 K) / 318 K
V₂ ≈ 15.9 L
Therefore, the volume of the gas after being cooled to -37 degrees Celsius is approximately 15.9 liters.