Problem 78 - Chemistry The Central Science

Question

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

Step-by-Step Solution

Answer

The osmotic pressure of seawater at \(20^{\circ} \mathrm{C}\), assuming the solute consists entirely of \(\mathrm{NaCl}\), is approximately \(1.41 \mathrm{~atm}\).

Step 1: Convert Given Information to Appropriate Units

First, we will convert the given concentration of salts (3.4 g per liter) into moles per liter (mol/L) using the molar mass of NaCl (58.44 g/mol). Moles of NaCl per liter = (3.4 g of NaCl) / (58.44 g/mol of NaCl) Next, convert the given temperature of 20°C to Kelvin. Temperature in Kelvin (T) = 20°C + 273.15 = 293.15 K

Step 2: Apply the Osmotic Pressure Formula

Now that we have the concentration and temperature in appropriate units, we can apply the osmotic pressure formula: Osmotic Pressure (π) = n/V * R * T where n/V is the moles per liter (mol/L), R is the universal gas constant (0.0821 L atm / K mol), and T is the temperature in Kelvin. Using the values calculated in Step 1: π = (3.4 g of NaCl / 58.44 g/mol of NaCl) * (0.0821 L atm / K mol) * (293.15 K)

Step 3: Calculate the Osmotic Pressure

Now we can calculate the osmotic pressure by solving the equation: π = (0.0582 mol/L) * (0.0821 L atm / K mol) * (293.15 K) π ≈ 1.41 atm The osmotic pressure of seawater at 20°C, assuming the solute consists entirely of NaCl, is approximately 1.41 atm.

Key Concepts

Molarity

Molarity, often represented by the symbol 'M,' is a measure of the concentration of a solute in a solution. It is defined as the number of moles of a substance per liter of solution. Understanding molarity is critical when it comes to calculating osmotic pressure since it directly influences the number of solute particles in a solution.

To find the molarity, you divide the mass of the solute (in grams) by its molar mass (the mass of one mole of the substance, in grams per mole) and then divide that by the volume of the solution (in liters). In the case of the seawater exercise, we're looking at the concentration of dissolved salts, presumed to be sodium chloride (NaCl), in the solution. The formula this exercise employs is:
\[ \text{Molarity (M)} = \frac{\text{Mass of solute (g)}}{\text{Molar mass (g/mol)} \times \text{Volume of solution (L)}} \]
Once the molarity is determined, it becomes easier to plug this value into the osmotic pressure formula.

Osmotic Pressure Formula

Osmotic pressure can be likened to the 'pulling' force exerted by a solution to draw water across a semipermeable membrane. The osmotic pressure formula is derived from the principles of thermodynamics and is instrumental in predicting the movement of water in biological systems and industrial processes.

The formula to calculate osmotic pressure (π) is:
\[ \pi = \frac{n}{V} \times R \times T \]
where \(\frac{n}{V}\) is the molarity (the number of moles of solute per liter of solution, \(mol/L\)), \(R\) is the ideal gas constant and \(T\) is the absolute temperature in Kelvin (K). This formula assumes ideal behavior and that the solute does not ionize or dissociate.

In our seawater example, sodium chloride dissociates into sodium and chloride ions, which would actually double the number of particles. However, for simplicity, the exercise assumes it doesn't dissociate. This is important to consider in a real-world scenario, as it affects osmotic pressure.

Unit Conversion

Unit conversion is fundamental in chemistry calculations, as you often need to convert units to ensure consistency within formulas. For osmotic pressure calculations, it's crucial to convert the temperature to Kelvin, as the gas constant \(R\) is defined using this unit.

To convert from Celsius to Kelvin, you simply add 273.15 to the Celsius temperature. The step-by-step solution displays the importance of unit conversion:
\[ T(\text{K}) = T(\text{°C}) + 273.15 \]
Additionally, the grams of the solute need to be converted to moles, which requires the use of the molar mass of the solute as a conversion factor. Understanding how to manipulate units correctly ensures accuracy in the calculation of osmotic pressure and in chemistry as a whole.