A 200-mL sample of Oxygen gas is collected at 26 degrees C and a pressure of 690 torr. What volume will the gas occupy at STP (0 degree C and 760 torr)
Use (P1V1/T1) = (P2V2/T2)
T1 and T2 must be in kelvin.
Well, if we're talking about oxygen gas, we better make sure it's not going to knock us out with its amazing charm! Alright, let's dive into this puzzle.
To find the volume of the gas at STP, we can use the combined gas law equation:
(P1 * V1) / (T1) = (P2 * V2) / (T2)
Now let's plug in the given values:
P1 = 690 torr
V1 = 200 mL
T1 = 26°C + 273 = 299 K
P2 = 760 torr
T2 = 0°C + 273 = 273 K
Now we can solve for V2, the volume of the gas at STP.
(690 torr * 200 mL) / (299 K) = (760 torr * V2) / (273 K)
Cross-multiplying, we get:
(690 torr * 200 mL * 273 K) = (760 torr * V2 * 299 K)
Dividing both sides by 760 torr * 299 K, we find:
V2 = (690 torr * 200 mL * 273 K) / (760 torr * 299 K)
Calculating that out, we get V2 ≈ 171 mL.
So, bow down to the charm of oxygen gas! At STP, it will occupy a volume of approximately 171 mL, ready to fill our lungs with laughter.
To find the volume of the gas at STP, we can use the combined gas law equation:
(P1 * V1) / (T1) = (P2 * V2) / (T2)
Where:
P1 = initial pressure of the gas
V1 = initial volume of the gas
T1 = initial temperature of the gas (in Kelvin)
P2 = final pressure (STP pressure, 760 torr)
V2 = final volume (what we want to find)
T2 = final temperature (STP temperature, 0 degrees Celsius)
First, let's convert the temperatures to Kelvin:
T1 = 26 degrees C + 273.15 = 299.15 K
T2 = 0 degrees C + 273.15 = 273.15 K
Next, we can substitute the given values into the equation:
(690 torr * 200 mL) / (299.15 K) = (760 torr * V2) / (273.15 K)
Simplifying and solving for V2:
(690 torr * 200 mL * 273.15 K) = (760 torr * V2 * 299.15 K)
138.06 * 10^4 torr * mL * K = 227.71 * 10^4 torr * V2 * K
138.06 * mL = 227.71 * V2
V2 = (138.06 * mL) / (227.71)
Now we can substitute the given volume and solve for V2:
V2 = (138.06 * 200 mL) / (227.71)
V2 ≈ 113.66 mL
Therefore, the gas will occupy approximately 113.66 mL at STP.
To find the volume of the gas at STP, we can use the combined gas law formula, which relates the initial conditions (temperature and pressure) to the final conditions.
The combined gas law formula is:
(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. To convert from degrees Celsius to Kelvin, use the following formula:
Kelvin = Celsius + 273.15
So, for the initial temperature (26 degrees C), we have:
T1 = 26 + 273.15 = 299.15 K
For the final temperature (0 degrees C), we have:
T2 = 0 + 273.15 = 273.15 K
Now, let's substitute the given values into the combined gas law:
(690 torr * V1) / (299.15 K) = (760 torr * V2) / (273.15 K)
Next, let's rearrange the equation to solve for V2 (the final volume):
V2 = (690 torr * V1 * 273.15 K) / (760 torr * 299.15 K)
Now, substitute the known values:
V2 = (690 torr * 200 mL * 273.15 K) / (760 torr * 299.15 K)
Now, we can calculate the final volume:
V2 = (690 * 200 * 273.15) / (760 * 299.15)
≈ 155.67 mL
Therefore, the volume of the gas at STP (0 degrees C and 760 torr) is approximately 155.67 mL.