The osmotic pressure of a dilute solution is 7 × 10⁵ Pa at 273 K. Osmotic pressure of the same solution at 283 K is _________ × 10⁴ Nm⁻².

Solution

Chemistry ma’am · 4 steps

Same solution means the same concentration, so osmotic pressure just scales with absolute temperature.

1. Fix the concentration. Van't Hoff's equation is π = CRT. The solution does not change, so C stays the same, and R is a constant. That leaves π ∝ T.

   π₂/π₁ = T₂/T₁ ⇒ π₂ = 7 × 10⁵ × 283/273 Pa

2. Put in numbers. 283/273 = 1.0366, so π₂ = 7 × 10⁵ × 1.0366 = 7.256 × 10⁵ Pa.
3. Match the units. 1 Pa = 1 N m⁻², so π₂ = 7.256 × 10⁵ N m⁻² = 72.56 × 10⁴ N m⁻².
4. So. Rounding to the nearest integer, the blank is 73.

The common slip: 68. Multiplying by 273/283 instead of 283/273 gives 6.75 × 10⁵ Pa, or 68. A higher temperature must give a higher osmotic pressure.

The idea to keep. For the same solution at two temperatures, π₁/T₁ = π₂/T₂. Always use kelvin, and check the power of ten the answer blank asks for.

Answer from the NTA final answer key. Solution by PrepWiser.