(P1V1/T1) = (P2V2/T2)
P1 = 742-vapor pressure H2O @ 24C. You find vp H2O in tables. I'm sure your text has one.
P1 = 742-vapor pressure H2O @ 24C. You find vp H2O in tables. I'm sure your text has one.
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.
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.