Question

Calculate the mass % of naphthalene (C10H8) in 50.0 g of methanol to obtain a vapor pressure of 118 mmHg. The vapor pressure of methanol, at 298 K, is 123.8 mmHg.

Answer 1

Answer 2

To calculate the mass percentage of naphthalene (C10H8) in the mixture, we need to determine the number of moles of naphthalene and methanol present.

First, we calculate the moles of methanol (CH3OH) in the mixture:

Mass of methanol = 50.0 g Molar mass of methanol = 32.04 g/mol

Moles of methanol = mass/molar mass = 50.0 g / 32.04 g/mol = 1.5607 mol

Next, we calculate the moles of naphthalene (C10H8) in the mixture. Since we don't have the mass of naphthalene provided, we need additional information to determine its moles.

To find the mole fraction of methanol in the vapor phase, we use Raoult's Law:

Pmethanol = Xmethanol * P°methanol

Where: Pmethanol = vapor pressure of methanol in the mixture = 118 mmHg Xmethanol = mole fraction of methanol in the mixture (unknown) P°methanol = vapor pressure of pure methanol = 123.8 mmHg

Using the equation, we can solve for Xmethanol:

Xmethanol = Pmethanol / P°methanol = 118 mmHg / 123.8 mmHg = 0.9511

The mole fraction of naphthalene can be calculated as:

Xnaphthalene = 1 - Xmethanol = 1 - 0.9511 = 0.0489

Now, we can calculate the moles of naphthalene:

Moles of naphthalene = Xnaphthalene * Moles of methanol = 0.0489 * 1.5607 mol = 0.0762 mol

Finally, we can calculate the mass percentage of naphthalene in the mixture:

Mass of naphthalene = Moles of naphthalene * Molar mass of naphthalene = 0.0762 mol * 128.17 g/mol (molar mass of naphthalene) = 9.773 g

Mass percentage of naphthalene = (Mass of naphthalene / Mass of mixture) * 100 = (9.773 g / 50.0 g) * 100 = 19.55%

Therefore, the mass percentage of naphthalene in the mixture is approximately 19.55%.