A sample of oxygen is collected in a 387 mL container over water at 15◦C, and the barom- eter reads 738 torr. What volume would the dry gas occupy at 781 torr and 15◦C? Water’s partial pressure at 15◦C is 12.8 torr.
Answer in units of mL
Use (P1V1/T1) = (P2V2/T2)
V1 = 387 mL
P1 = 738mm-12.8 = ?
To find the volume of the dry gas, we need to use Dalton's law of partial pressures, which states that the total pressure of a mixture of gases is equal to the sum of the pressures of each individual gas.
First, let's calculate the partial pressure of the oxygen gas. Since the barometer reads 738 torr and the partial pressure of water vapor at 15◦C is 12.8 torr, we can subtract the water vapor pressure from the total pressure to find the partial pressure of the dry gas:
Partial pressure of oxygen = Total pressure - Water vapor pressure
Partial pressure of oxygen = 738 torr - 12.8 torr
Partial pressure of oxygen = 725.2 torr
Now we can use the ideal gas law to find the volume of the dry gas. The ideal gas law equation is:
PV = nRT
Where:
P = pressure (in atm)
V = volume (in liters)
n = number of moles
R = ideal gas constant (0.0821 L.atm/mol.K)
T = temperature (in Kelvin)
We need to convert the given temperatures from degrees Celsius to Kelvin:
Temperature in Kelvin = Temperature in Celsius + 273.15
Given that the temperature is 15◦C, the temperature in Kelvin is:
Temperature in Kelvin = 15◦C + 273.15 = 288.15 K
Now we can set up our equation for the ideal gas law:
(P1)(V1) / (T1) = (P2)(V2) / (T2)
Where:
P1 = initial pressure (partial pressure of oxygen) = 725.2 torr
V1 = initial volume = 387 mL (converted to liters by dividing by 1000)
T1 = initial temperature = 288.15 K
P2 = final pressure = 781 torr
V2 = final volume (what we want to find)
T2 = final temperature = 288.15 K
Plugging in the values, we get:
(725.2 torr)(387 mL / 1000) / 288.15 K = (781 torr)(V2) / 288.15 K
Now we can solve for V2:
V2 = [(725.2 torr)(387 mL / 1000) / 288.15 K] * (288.15 K / 781 torr)
Calculating this expression will give us the final volume of the dry gas. The answer should be in mL, so remember to convert it back.