Could someone please help guide me through this question:
A 1.047 g sample of He(g) is found to occupy a volume of 8.446 L when collected over hexane at 25.0 ∘C and 739.6 mmHg barometric pressure. Use these data to determine the vapor pressure of hexane at 25 ∘C.
Use 1.047 g to calculate mols He. mols = grams/atomic mass.
Then use PV = nRT and solve for P. This will be in atm; I would conert that to mm Hg. atm x 760 = pHe in mmHg.
Then Ptotal = pHe + phexane
You know Ptotal = 739.6 mm
You know PHe from PV = nRT; solve for phexane.
To determine the vapor pressure of hexane at 25 °C, we'll use Dalton's Law of Partial Pressures. Dalton's Law states that the total pressure exerted by a mixture of non-reacting gases is equal to the sum of the partial pressures of each component.
Here's the step-by-step approach to solving this problem:
Step 1: Convert the temperature to Kelvin.
To convert from Celsius to Kelvin, you add 273.15. Therefore, 25 °C + 273.15 = 298.15 K.
Step 2: Convert the pressure to atmospheres.
The given pressure is in mmHg. To convert to atm, divide by 760 (since 1 atm = 760 mmHg).
739.6 mmHg ÷ 760 = 0.972 atm.
Step 3: Calculate the partial pressure of helium.
Given that the He(g) sample occupies a volume of 8.446 L, we can use the ideal gas law to find the partial pressure of helium.
PV = nRT
Where:
P = pressure (in atm)
V = volume (in L)
n = number of moles
R = ideal gas constant (0.0821 L·atm/mol·K)
T = temperature (in K)
We need to find n (number of moles) first.
To find the number of moles of helium, we'll use the molar mass of helium (He).
Molar mass of He = 4.003 g/mol
n = mass / molar mass
n = 1.047 g / 4.003 g/mol
n = 0.2614 mol
Now we can plug in the values into the ideal gas law equation:
P × 8.446 L = 0.2614 mol × 0.0821 L·atm/mol·K × 298.15 K
P = (0.2614 mol × 0.0821 L·atm/mol·K × 298.15 K) / 8.446 L
P = 0.0093 atm
Therefore, the partial pressure of helium is 0.0093 atm.
Step 4: Apply Dalton's Law of Partial Pressures.
According to Dalton's Law, the total pressure (0.972 atm) is equal to the sum of the partial pressures of each component.
Total pressure = Pressure of helium + Vapor pressure of hexane
We can rearrange the formula to solve for the vapor pressure of hexane:
Vapor pressure of hexane = Total pressure - Pressure of helium
Vapor pressure of hexane = 0.972 atm - 0.0093 atm
Vapor pressure of hexane = 0.9627 atm
Therefore, the vapor pressure of hexane at 25 °C is approximately 0.9627 atm.
To determine the vapor pressure of hexane at 25 °C using the given data, we can apply Dalton's Law of Partial Pressures. Dalton's Law states that the total pressure exerted by a mixture of non-reacting gases is equal to the sum of the partial pressures of the individual gases.
In this case, the total pressure is given as 739.6 mmHg, and the gas collected over hexane is helium (He). We need to determine the partial pressure of helium in order to find the vapor pressure of hexane.
First, we calculate the number of moles of helium gas using the ideal gas law:
PV = nRT
Where:
P = Pressure (in atm or mmHg)
V = Volume (in liters)
n = Number of moles
R = Gas constant (0.0821 L•atm/(mol•K)) [if using atm] or (62.36 mmHg•L/(mol•K)) [if using mmHg]
T = Temperature (in Kelvin)
Converting the given pressure from mmHg to atm:
739.6 mmHg ÷ 760 mmHg/atm = 0.9726 atm
Now, let's rearrange the ideal gas law equation to solve for n:
n = PV / RT
n = (0.9726 atm) * (8.446 L) / [(0.0821 L•atm/(mol•K)] * (25 + 273.15 K) [Converting 25 °C to Kelvin]
Simplifying the calculation:
n = 0.9726 * 8.446 / [0.0821 * (25 + 273.15)]
n = 0.9726 * 8.446 / (0.0821 * 298.15)
n = 0.838 mol
So, the sample contains 0.838 moles of helium gas.
According to Dalton's Law of Partial Pressures, the partial pressure of helium (P_He) is equal to the mole fraction of helium (X_He) multiplied by the total pressure (P_total).
Mole fraction (X_He) = Moles of helium (n_He) / Total moles of the mixture (n_total)
Since the sample only contains helium gas, the mole fraction of helium is 1.
Therefore, P_He = X_He * P_total = 1 * 0.9726 atm = 0.9726 atm
Now, we can find the partial pressure of hexane (P_hexane) by subtracting the partial pressure of helium (P_He) from the total pressure (P_total):
P_hexane = P_total - P_He = 0.9726 atm - 0.9726 atm = 0 atm
Hence, the vapor pressure of hexane at 25 °C is 0 atm, indicating that at this temperature, hexane does not have a significant vapor pressure and does not contribute to the total pressure in the mixture.
Note: The given data provided the necessary information for calculating the partial pressure of helium and the vapor pressure of hexane.