Normality (N) = number of equivalents / liters of solution. H2SO4 has 2 equivalents per mole, so 4 moles = 8 equivalents. Normality = 8 equivalents / 2 L = 4 N.

Normality (N) = Molarity (M) x number of equivalents. H2SO4 has 2 acidic protons, so 1 M x 2 = 2 N.

Osmotic pressure = iCRT = 2 * 0.2 * 0.0821 * 298 = 4.92 atm (i = 2 for NaCl)

Osmotic pressure = (n/V)RT = (0.2/1) * 0.0821 * 298 = 4.92 atm.

Osmotic pressure (π) = nRT/V = (0.5 moles * 0.0821 * 298) / 1 = 12.3 atm.

Osmotic pressure (π) = nRT/V = (0.5 mol)(0.0821 L·atm/(K·mol))(298 K) = 12.3 atm.

Osmotic pressure (π) = iCRT = 1 * 0.5 * 0.0821 * 298 = 12.3 atm.

Osmotic pressure (π) = nRT/V = (0.5 moles)(0.0821 L·atm/(K·mol))(298 K) = 12.3 atm.

Osmotic pressure (π) = (n/V)RT = (0.5/2) * 0.0821 * 298 = 6.14 atm.

Osmotic pressure (π) = nRT/V = (0.5 moles)(0.0821 L·atm/(K·mol))(298 K) / 2 L = 6.13 atm.

Osmotic pressure (π) = nRT/V = (0.5 moles * 0.0821 * 298) / 2 = 12.21 atm.

Osmotic pressure (π) = nRT/V = (1 mol)(0.0821 L·atm/(K·mol))(298 K) / 2 L = 0.82 atm.

Osmotic pressure is directly proportional to both the temperature and the concentration of solute.

Percentage by mass = (mass of solute / mass of solution) * 100 = (20 g / (20 g + 180 g)) * 100 = 20%.

Percentage by mass = (mass of solute / total mass) × 100 = (5 g / (5 g + 95 g)) × 100 = 5%.

Colligative properties depend primarily on the concentration of solute particles in a solution.

The elevation of boiling point occurs because the presence of solute lowers the vapor pressure of the solvent, requiring a higher temperature to reach boiling.

The presence of solute particles reduces the number of solvent molecules at the surface, leading to a lower vapor pressure.

Boiling point elevation is directly proportional to the molality of the solution.

The equation has no real solutions; the solutions are x = i and x = -i.

The equation factors to (x + 2)^2 = 0, giving a double root x = -2.

The equation factors to (x-2)(x-3) = 0, giving solutions x = 2 and x = 3.

Dividing both sides by 2 gives x - 1 = 2, thus x = 3.

Subtract 1 from both sides: 4x = 8. Then divide by 4: x = 2.

Adding 7 to both sides gives 5x = 10, then dividing by 5 gives x = 2.

Factoring gives (x - 2)(x + 2) = 0, leading to solutions x = 2 and x = -2.

The absolute value equation gives two cases: x - 3 = 5 or x - 3 = -5, leading to x = 8 or x = -2.

If the roots are reciprocals, then k = sum of roots = 0 and product = 1. Thus, k = 2.

For equal roots, the discriminant must be zero: (-4)^2 - 4*1*k = 0 => 16 - 4k = 0 => k = 4.

For equal roots, the discriminant must be zero: k^2 - 4*1*16 = 0 => k^2 = 64 => k = 8 or k = -8.