A sample of gas collected at 21.0 oC and a pressure of 660.0 torr has a volume of 1.83 liters. What volume in liters will the gas occupy at 38.0 oC under a pressure of 500.0 torr?
(P1V1/T1)=(P2V2/T2)
Don't forget T is in kelvin.
2.20
To solve this problem, we can use the combined gas law equation:
(P₁ * V₁) / (T₁) = (P₂ * V₂) / (T₂)
where:
P₁ = initial pressure
V₁ = initial volume
T₁ = initial temperature (in Kelvin)
P₂ = final pressure
V₂ = final volume
T₂ = final temperature (in Kelvin)
First, let's convert the temperatures to Kelvin by adding 273.15:
T₁ = 21.0 + 273.15 = 294.15 K
T₂ = 38.0 + 273.15 = 311.15 K
Next, let's substitute the given values into the combined gas law equation:
(660.0 torr * 1.83 L) / (294.15 K) = (500.0 torr * V₂) / (311.15 K)
Now, we can solve for V₂ by rearranging the equation:
V₂ = (660.0 torr * 1.83 L * 311.15 K) / (500.0 torr * 294.15 K)
V₂ = 371234.55 torr⋅L / 147075 torr
V₂ = 2.52 L (rounded to two decimal places)
Therefore, the gas will occupy a volume of 2.52 liters at 38.0°C under a pressure of 500.0 torr.
To solve this problem, we can use the combined gas law equation, which relates the initial and final conditions of temperature, pressure, and volume. The equation is given by:
(P1 * V1) / (T1) = (P2 * V2) / (T2)
Where:
P1 and P2 are the initial and final pressures
V1 and V2 are the initial and final volumes
T1 and T2 are the initial and final temperatures
Given:
P1 = 660.0 torr
V1 = 1.83 liters
T1 = 21.0 oC = 21.0 + 273.15 K (temperature in Kelvin conversion)
We need to find:
V2
Step 1: Convert the initial temperature to Kelvin:
T1 = 21.0 + 273.15 = 294.15 K
Step 2: Plug in the values into the combined gas law equation:
(P1 * V1) / T1 = (P2 * V2) / T2
Step 3: Convert the final temperature to Kelvin:
T2 = 38.0 + 273.15 = 311.15 K
Step 4: Rearrange the equation to solve for V2:
V2 = (P2 * V1 * T2) / (P1 * T1)
Step 5: Substitute the given values into the equation:
V2 = (500.0 torr * 1.83 liters * 311.15 K) / (660.0 torr * 294.15 K)
Step 6: Calculate the value of V2:
V2 ≈ 0.988 liters (rounded to three decimal places)
Therefore, the gas will occupy approximately 0.988 liters at 38.0 oC under a pressure of 500.0 torr.