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.