in a lab experiment, 133mL of gas was collected over water at 24 degrees Celsius and 742 torr. Calculate the volume that the dry gas would occupy at STP.
(P1V1/T1) = (P2V2/T2)
P1 = 742-vapor pressure H2O @ 24C. You find vp H2O in tables. I'm sure your text has one.
To calculate the volume that the dry gas would occupy at STP (Standard Temperature and Pressure), you can use the Ideal Gas Law equation, which is:
PV = nRT
Where:
P = Pressure
V = Volume
n = Number of moles
R = Ideal Gas Constant
T = Temperature
At STP, the temperature is 0 degrees Celsius (273.15 Kelvin), and the pressure is 1 atmosphere (760 torr).
First, we need to calculate the number of moles of gas using the given conditions:
Convert the temperature from Celsius to Kelvin:
T1 = 24 degrees Celsius + 273.15 = 297.15 Kelvin
Convert the pressure from torr to atmosphere:
P1 = 742 torr / 760 torr/atm = 0.976 atm
Next, we can use the Ideal Gas Law equation to find the number of moles (n) of the gas:
PV = nRT
n = PV / RT
Since we are looking for the volume at STP, we assume that the number of moles remains constant:
n1 = n2
Therefore, we can rewrite the equation as:
P1V1 / T1 = P2V2 / T2
Since T2 = 273.15 K (STP), we can rearrange the equation to solve for V2 (the volume at STP):
V2 = (P1V1T2) / (P2T1)
Plugging in the values:
V2 = (0.976 atm)(133 mL)(273.15 K) / (1 atm)(297.15 K)
V2 = 44.48 mL
Therefore, the volume that the dry gas would occupy at STP is 44.48 mL.
To calculate the volume that the dry gas would occupy at STP (Standard Temperature and Pressure), we need to use the ideal gas law equation, which 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
Given:
Volume of gas collected over water = 133 mL
Temperature = 24 degrees Celsius = 24 + 273.15 = 297.15 K
Pressure = 742 torr
First, we need to convert the collected volume of the gas from milliliters (mL) to liters (L), as the ideal gas law equation requires volume in liters:
133 mL = 133/1000 L = 0.133 L
Now, we can rearrange the ideal gas law equation to solve for the unknown volume of gas at STP:
V1/T1 = V2/T2
Where:
V1 = Volume of the gas at given conditions
T1 = Temperature of the gas at given conditions
V2 = Volume of the gas at STP (what we want to find)
T2 = Temperature at STP (which is 0 degrees Celsius = 273.15 K)
Rearranging the equation gives us:
V2 = (V1 * T2) / T1
Now we can substitute the values into the equation:
V2 = (0.133 L * 273.15 K) / 297.15 K
Calculating the value gives us:
V2 ≈ 0.122 L
Therefore, the volume that the dry gas would occupy at STP is approximately 0.122 liters.