A solution contains naphthalene dissolved in hexane at a concentration of 10.40% naphthalene by mass. Calculate the vapor pressure of hexane above the solution, given that the vapor pressure of pure hexane at this temperature is 151 torr.
Convert 10.4% naphthalene in hexane to Xnaph and Xhexane.
Tben Phexane = Xhexane*Pohexane.
how do i convert so? 10.4gNaphx1mol/128.18gNaphx86.2gHexane/1mol=6.99molHexane?
6.99mol*151torr=1056.08?
To calculate the vapor pressure of hexane above the solution, we can use Raoult's Law. According to Raoult's Law, the vapor pressure of a component in a solution is directly proportional to its mole fraction in the solution.
First, we need to find the mole fraction of hexane in the solution. The mole fraction of hexane (X_hexane) is given by the ratio of the grams of hexane (m_hexane) to the grams of the solution (m_solution):
X_hexane = m_hexane / m_solution
We are given that the concentration of naphthalene in the solution is 10.40% by mass. So, the mass of hexane in the solution is 100% - 10.40% = 89.60%:
m_hexane = 89.60% of m_solution
Next, we convert the mass percentages to grams:
m_hexane = 0.8960 * m_solution
Now, we can substitute this value into the equation for mole fraction:
X_hexane = 0.8960 * m_solution / m_solution
Simplifying:
X_hexane = 0.8960
Since we know the mole fraction of hexane in the solution, we can apply Raoult's Law to calculate the vapor pressure of hexane above the solution. According to Raoult's Law, the vapor pressure of hexane (P_hexane) is the product of the mole fraction of hexane (X_hexane) and the vapor pressure of pure hexane (P_hexane°):
P_hexane = X_hexane * P_hexane°
Given that the vapor pressure of pure hexane (P_hexane°) is 151 torr and X_hexane is 0.8960, we can substitute these values into the equation:
P_hexane = 0.8960 * 151 torr
Calculating:
P_hexane ≈ 135.70 torr
Therefore, the vapor pressure of hexane above the solution is approximately 135.70 torr.