Using Raoult's law, the vapor pressure of the solution = (moles of solvent / total moles) * P0 = (9 / 10) * P0 = 0.9 P0.

Vapor pressure lowering = (moles of solute / total moles) = 2 / (2 + 4) = 2/6 = 1/3. Thus, vapor pressure is 1/2 of pure solvent.

Vapor pressure = (moles of solvent / total moles) * P0 = (4 / (2 + 4)) * P0 = (4/6) * P0 = 0.67 P0.

The vertex can be found using the formula x = -b/2a. Here, x = 2, and substituting back gives y = -1.

The vertex can be found using the formula x = -b/2a = 6/2 = 3. Substituting x = 3 into the equation gives y = -1.

Using Ohm's law, V = I * R = 2A * 10Ω = 20V.

Using Ohm's law, V = IR = 3A * 10Ω = 30V.

Using Ohm's law, V = IR = 1.5A * 12Ω = 18V.

Using Ohm's law, V = IR = 3A * 12Ω = 36V.

Using Ohm's law, V = IR = 3A * 5Ω = 15V.

Using Ohm's law, V = IR = 3A * 5Ω = 15V.

Using Ohm's law, V = I * R = 2A * 10Ω = 20V.

Using Ohm's law, V = I * R = 4A * 3Ω = 12V.

Using the formula M1V1 = M2V2, (0.1 M)(0.25 L) = (0.2 M)(V2). V2 = 0.125 L = 125 mL.

Volume = moles / molarity = 0.5 moles / 1 M = 0.5 L.

At STP, 1 mole of an ideal gas occupies 22.4 liters.

Volume (L) = moles / molarity = 4 moles / 2 M = 2 L.

Volume = side³ = 3³ = 27 cubic units.

Volume = side³ = 4³ = 64 cubic units.

Volume = πr²h = π(2²)(5) = 20π cubic units.

Volume = πr²h = π(3²)(5) = 45π cubic units.

Volume = (4/3)πr³ = (4/3)π(5)³ = (4/3)π(125) = 500/3π cubic units.

Using the Rydberg formula, the wavelength for the transition from n=3 to n=1 can be calculated to be approximately 102.6 nm.

Using the Rydberg formula, the wavelength for the transition from n=4 to n=2 can be calculated to be approximately 486 nm.

Using the formula λ = d sin θ / m, where d = 0.1 mm, θ = 30°, and m = 1, we find λ = 0.1 mm * sin(30°) = 0.1 mm * 0.5 = 0.05 mm = 0.2 mm.

Work = F × d × cos(θ) = 15 N × 4 m × cos(60°) = 15 × 4 × 0.5 = 30 J.

Work done (W) = P * ΔV = 3 atm * (5 L - 2 L) = 3 atm * 3 L = 9 atm·L = 15 J (1 atm·L = 101.325 J)

The work done by an ideal gas during an isobaric (constant pressure) expansion is given by W = PΔV.

The work done during an isothermal expansion is given by W = nRT ln(V2/V1).

For an ideal gas undergoing isothermal expansion, the work done is given by W = nRT ln(Vf/Vi).