A sample of gas has a volume of 8.00 L at 20.0 degrees celcius and 700. torr. What will be it's volume at STP?
To find the volume of the gas at STP (Standard Temperature and Pressure), you can use the combined gas law equation:
P1V1 / T1 = P2V2 / T2
Where:
P1 = initial pressure of the gas
V1 = initial volume of the gas
T1 = initial temperature of the gas
P2 = final pressure (at STP, the pressure is 1 atm)
V2 = final volume (what we want to find)
T2 = final temperature (at STP, the temperature is 0 degrees Celsius or 273.15 Kelvin)
Given:
P1 = 700. torr
V1 = 8.00 L
T1 = 20.0 degrees Celsius = 293.15 Kelvin
P2 = 1 atm
T2 = 0 degrees Celsius = 273.15 Kelvin
Now, substitute the given values into the equation:
(700. torr) * (8.00 L) / (293.15 K) = (1 atm) * (V2) / (273.15 K)
Simplifying the equation:
(700. torr * 8.00 L * 273.15 K) / (293.15 K) = V2
V2 = (1918800 torr * L) / (293.15 K) ≈ 6542 L
Therefore, the volume of the gas at STP will be approximately 6542 L.
To calculate the volume of the gas at STP (Standard Temperature and Pressure), you need to use the ideal gas law equation, which is as follows:
PV = nRT
Where:
P = Pressure
V = Volume
n = Number of moles
R = Ideal gas constant
T = Temperature
STP is defined as a temperature of 273.15 Kelvin (0 degrees Celsius) and a pressure of 1 atmosphere (atm) or 760 torr.
To solve the problem, follow these steps:
Step 1: Convert the temperature from Celsius to Kelvin.
Add 273.15 to the given temperature to convert it to Kelvin.
Thus, 20.0 degrees Celsius = (20.0 + 273.15) Kelvin = 293.15 Kelvin.
Step 2: Convert the pressure from torr to atmospheres.
Divide the given pressure by 760.
Thus, 700 torr = (700 ÷ 760) atm = 0.9211 atm.
Step 3: Calculate the volume of the gas at STP.
Since n, R, and T are constant for the same gas, the equation can be simplified to:
V1/T1 = V2/T2.
V1 = 8.00 L (initial volume)
T1 = 293.15 K (initial temperature)
P1 = 0.9211 atm (initial pressure)
T2 = 273.15 K (STP temperature)
P2 = 1 atm (STP pressure)
V2 = ? (final volume)
Rearrange the equation to solve for V2:
V2 = V1 × (T2 / T1) × (P1 / P2).
V2 = 8.00 L × (273.15 K / 293.15 K) × (0.9211 atm / 1 atm)
V2 = 7.06 L (rounded to two decimal places)
Therefore, the volume of the gas at STP will be approximately 7.06 L.
Note the correct spelling of celsius.
Use (P1V1/T1) = (P2V2/T2)