find the volume of a gas at STP, if its volume is 80.0 mL at 109 kPa and -12.5 C
Well, if you're asking me to find the volume of a gas at STP, then I have to disappoint you. You see, STP stands for "Standard Temperature and Pressure," which is typically defined as 0 degrees Celsius and 1 atmosphere of pressure. Since you've given me a different temperature and pressure, it's not exactly STP. So, in other words, it's like asking me to find a unicorn in a cabbage patch – possible, but not probable!
To find the volume of a gas at STP (Standard Temperature and Pressure), we can use the Combined Gas Law equation, which states:
(P1 * V1) / (T1) = (P2 * V2) / (T2)
Where:
P1 = initial pressure (in kPa)
V1 = initial volume (in mL)
T1 = initial temperature (in Kelvin)
P2 = final pressure (STP is 101.325 kPa)
V2 = final volume
T2 = final temperature (STP is 273.15 Kelvin)
Let's substitute the given values into the equation:
(P1 * V1) / (T1) = (P2 * V2) / (T2)
P1 = 109 kPa
V1 = 80.0 mL
T1 = -12.5°C = 260.65 Kelvin
P2 = 101.325 kPa (STP)
T2 = 273.15 Kelvin (STP)
(109 * 80.0) / (260.65) = (101.325 * V2) / (273.15)
Now, let's solve for V2:
V2 = (101.325 * V2 * 260.65) / (273.15 * 109 * 80)
V2 = (26065.5725) / (2262960)
V2 ≈ 0.0115 mL
Therefore, the volume of the gas at STP is approximately 0.0115 mL.
To find the volume of a gas at STP (Standard Temperature and Pressure), we need to use the ideal gas law equation. The ideal gas law equation is:
PV = nRT
Where:
P = pressure of the gas
V = volume of the gas
n = number of moles of the gas
R = ideal gas constant
T = temperature of the gas in Kelvin
First, we need to convert the given temperature from Celsius to Kelvin. The Kelvin temperature scale is used in gas calculations as it does not have negative values. The conversion from Celsius to Kelvin is done by adding 273.15 to the Celsius temperature.
T = -12.5°C + 273.15 = 260.65 K
Next, we need to convert the given pressure from kilopascals (kPa) to atmospheres (atm) since STP is defined as 1 atmosphere.
1 atm = 101.325 kPa
P = 109 kPa * (1 atm / 101.325 kPa) = 1.075 atm
Now, we can rearrange the equation PV = nRT to solve for the volume (V).
V = (nRT) / P
At STP, 1 mole of any gas occupies 22.4 liters of volume. We can use this information to calculate the number of moles (n).
n = V / 22.4
Substituting the given values:
n = 80.0 mL / 1000 mL/L = 0.08 L / 22.4 L/mol = 0.00357 mol
Now we can substitute the values back into the equation to find the volume at STP:
V = (nRT) / P
V = (0.00357 mol * 0.0821 L·atm/(mol·K) * 260.65 K) / 1.075 atm
V = 0.592 L or 592 mL
Therefore, the volume of the gas at STP is approximately 592 mL.
PV=kT, so you want V such that
101.325V/273 = 109*80/(273-12.5)