Question

Seawater contains $3.4\mathrm{g}$ of salts for every liter of solution. Assuming that the solute consists entirely of $\mathrm{NaCl}$ (over $90\mathrm{\%}$ is), calculate the osmotic pressure of seawater at ${20}^{\circ }\mathrm{C}$.

Short answer

The osmotic pressure of seawater at ${20}^{\circ }\mathrm{C}$, assuming the solute consists entirely of $\mathrm{NaCl}$, is approximately 2.81 atm.

Step-by-step solution

Calculate the molarity of the NaCl solution

Begin by converting the given mass of NaCl to moles. To do this, divide the mass of NaCl by its molar mass (58.44 g/mol): $$\text{moles of NaCl}=\frac{3.4\mathrm{g}}{58.44\mathrm{g}/\mathrm{mol}}=0.0582\mathrm{mol}$$ Next, divide the moles of NaCl by the volume of the solution (1 L) to find the molarity (M): $$\text{Molarity (M)}=\frac{0.0582\mathrm{mol}}{1\mathrm{L}}=0.0582\mathrm{M}$$

Convert the temperature to Kelvin

The van 't Hoff equation requires the temperature to be in Kelvin. To convert the given temperature (20°C) to Kelvin, just add 273.15: $$T(K)={20}^{\circ }\mathrm{C}+273.15=293.15\mathrm{K}$$

Use the van 't Hoff equation to find the osmotic pressure

Now that we have the molarity and the temperature in Kelvin, we can use the van 't Hoff equation to find the osmotic pressure (Π). The equation is as follows: $$\begin{array}{rl}\mathrm{\Pi }& =(\mathrm{i})\times (\mathrm{M})\times (\mathrm{R})\times (\mathrm{T})\end{array}$$ where - i = the number of particles produced upon dissolving the solute (for NaCl, it is 2, as NaCl dissociates into Na+ and Cl- ions) - M = the molarity of the solute - R = the ideal gas constant (0.0821 L atm/mol K) - T = the temperature in Kelvin Plugging in the values, we get: $$\begin{array}{rl}\mathrm{\Pi }& =2\times 0.0582\mathrm{M}\times 0.0821\mathrm{L}\mathrm{atm}/\mathrm{mol}\mathrm{K}\times 293.15\mathrm{K}\\ & =2.81\mathrm{atm}\end{array}$$

State the final answer

The osmotic pressure of seawater at ${20}^{\circ }\mathrm{C}$, assuming the solute consists entirely of $\mathrm{NaCl}$, is approximately 2.81 atm.