The presence of a non-volatile solute lowers the vapor pressure of the solvent compared to that of the pure solvent.

Using Raoult's Law, the vapor pressure of the solution is P_total = (0.6 * 100) + (0.4 * 50) = 60 + 20 = 80 mmHg.

The total vapor pressure of a solution is the sum of the partial vapor pressures of its components: 80 mmHg + 20 mmHg = 100 mmHg.

In an ideal solution, the enthalpy of mixing is zero, indicating no heat is absorbed or released during mixing.

Expanding gives 3x - 3 = 2x + 8. Rearranging gives x = 11.

Dividing both sides by 3 gives x - 2 = 4, thus x = 6.

Subtracting 3x from both sides gives 2x + 2 = 10, then subtracting 2 gives 2x = 8, leading to x = 4.

The equation factors to (x - 3)(x + 3) = 0, giving solutions x = 3 and x = -3.

Subtracting 8 from both sides gives 4y = 16, then dividing by 4 gives y = 4.

For both roots to be negative, the sum of roots (4) must be positive and the product (k) must be positive, hence k > 0.

For both roots to be positive, k must be greater than the square of half the coefficient of x: k > (6/2)^2 = 9.

Using Vieta's formulas, sum of roots = 1 + 2 = 3 = -(-4)/2 => k = 2*1*2 = 4.

Raoult's Law states that the vapor pressure of a solvent in a solution is directly proportional to the mole fraction of the solvent.

The boiling point of a solvent increases when a non-volatile solute is added due to boiling point elevation.

The freezing point of a solvent decreases when a non-volatile solute is added, a phenomenon known as freezing point depression.

As the concentration of a non-volatile solute increases, the vapor pressure of the solution decreases according to Raoult's Law.

The vapor pressure of a solvent decreases when a non-volatile solute is added due to the solute particles occupying space at the surface.

The addition of a volatile solute decreases the vapor pressure of the solvent due to the presence of solute molecules.

Raoult's Law states that the vapor pressure of a solvent in a solution is directly proportional to the mole fraction of the solvent.

Raoult's Law states that the vapor pressure of a solvent in a solution is directly proportional to the mole fraction of the solvent.

Boiling point elevation = i * K_b * m = 2 * 0.512 * 1 = 1.024 °C (i = 2 for NaCl)

Boiling point elevation = i * K_b * m = 2 * 0.512 * 0.5 = 0.512 °C; Boiling point = 100 + 0.512 = 100.512 °C

Mass of KCl = 0.5 moles × 74.5 g/mol = 37.25 g. Concentration = 37.25 g / 1.5 L = 24.83 g/L.

Molality (m) = moles of solute / kg of solvent = 5 moles / 3 kg = 1.67 m.

Molarity (M) = moles of solute / liters of solution = 0.5 moles / 1.5 L = 0.33 M.

PPM = (mass of solute in grams / volume of solution in liters) * 10^6 = (1 g / 1 L) * 10^6 = 1000 ppm.

Molarity (M) = moles of solute / liters of solution = (10 g / 58.5 g/mol) / 0.5 L = 0.34 M.

The addition of a non-volatile solute raises the boiling point of the solvent, a phenomenon known as boiling point elevation.

Adding a non-volatile solute decreases the vapor pressure of the solvent due to the reduction in the mole fraction of the solvent.

Increasing temperature generally increases the vapor pressure of a solution due to increased kinetic energy of the molecules.