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The Baltic Sea has a salinity of \(1.0 \%\), that is, its water contains \(10 \mathrm{~g}\) of salt for every liter of solution. Assuming that the solute consists entirely of \(\mathrm{NaCl}\) (in fact, over \(90 \%\) of the salt is indeed \(\mathrm{NaCl}\), calculate the osmotic pressure of this seawater at \(15^{\circ} \mathrm{C}\).

Short Answer

Expert verified
The osmotic pressure of the Baltic Sea at 15°C is approximately 8.08 atm.

Step by step solution

01

Identify Given Values

We know the salinity is 1.0% which means there are \(10 \text{ g} \text{ NaCl} \text{ per liter of solution}\). The temperature is given as \(15^\circ \text{C}\). Since osmotic pressure depends on the number of particles in solution and not just the mass, we'll need the molar mass of \(\text{NaCl}\) which is \(58.44 \text{ g/mol}\).
02

Convert Grams to Moles

Using the molar mass, convert grams of \(\text{NaCl}\) to moles: \[\text{moles} = \frac{10 \text{ g}}{58.44 \text{ g/mol}} \approx 0.171 \text{ mol}\]
03

Calculate Molarity of NaCl

Since we have 0.171 moles of NaCl in 1 liter, the molarity \(M\) is:\[M = 0.171 \text{ mol/L}\]
04

Determine the Dissociation Factor (i)

Sodium chloride \(\text{NaCl}\) dissociates into \(\text{Na}^+\) and \(\text{Cl}^-\), resulting in 2 ions. Thus, the dissociation factor \(i\) is 2.
05

Apply the Osmotic Pressure Formula

The formula for osmotic pressure is given by:\[\Pi = iMRT\]where \(R\) is the ideal gas constant \(0.0821 \text{ L atm/mol K}\) and \(T\) is the temperature in Kelvin. Convert \(15^\circ \text{C}\) to Kelvin: \[T = 15 + 273.15 = 288.15 \text{ K}\]
06

Calculate Osmotic Pressure

Substitute all the known values into the osmotic pressure formula:\[\Pi = 2 \times 0.171 \text{ mol/L} \times 0.0821 \text{ L atm/mol K} \times 288.15 \text{ K} \approx 8.08 \text{ atm}\]

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Sodium Chloride Dissociation
Sodium chloride, or NaCl, plays a crucial role in many chemical and environmental processes due to its ability to dissociate in water. When NaCl is added to water, it separates into two ions. This process is known as dissociation.
A single molecule of NaCl dissociates into one sodium ion (\( \text{Na}^+ \)) and one chloride ion (\( \text{Cl}^- \)). Sodium ions have a positive charge, while chloride ions are negatively charged. These ions are crucial in biological and chemical reactions because they conduct electricity and take part in various cellular processes.
When calculating osmotic pressure, recognizing that NaCl dissociates into two particles is essential. Hence, the dissociation factor, often denoted as \( i \), is 2, meaning each mole of NaCl yields two moles of ions.
Molarity Calculation
Molarity is a measure of concentration that tells us how many moles of a solute are present in a liter of solution. To find molarity, you need to convert the mass of the solute to moles and then divide by the volume of the solution in liters.
Start by calculating the moles of NaCl using its molar mass. The molar mass of NaCl is \( 58.44 \, \text{g/mol} \) . If you have \( 10 \, \text{g} \) of NaCl dissolved in water, use the formula:
\[moles = \frac{\text{mass of NaCl in grams}}{\text{molar mass of NaCl}} = \frac{10}{58.44} \approx 0.171 \, \text{mol}\]Now, since this amount is dissolved in 1 liter, the molarity \( M \) becomes:\[M = \frac{0.171 \, \text{mol}}{1 \, \text{L}} = 0.171 \, \text{mol/L}\]Molarity is crucial in calculating osmotic pressure because it indicates the concentration of particles in the solution.
Salinity and Molarity
Salinity is a measure of how much salt is present in a given amount of water. In our exercise, the seawater has a salinity of \( 1.0\% \) , meaning there are \( 10 \, \text{g} \) of salt per liter.
This salinity value is directly related to the molarity of the solution when the solute is entirely NaCl. By converting the mass of salt to moles and considering the water volume, we calculate the molarity.
The relationship between salinity and molarity helps to understand different marine and freshwater environments. Areas with different salinities will have various implications for aquatic life and chemical processes within the water. Salinity affects properties like osmotic pressure, which has widespread implications for both plants and animals.
Molar Mass of NaCl
The molar mass of a compound is the mass of one mole of its entities (atoms, molecules, etc.) and is given in grams per mole. To understand and calculate chemical concentrations, knowing the molar mass of substances is crucial.
For sodium chloride (NaCl), its molar mass is the combined molar masses of sodium (Na) and chlorine (Cl). Sodium has an atomic mass of approximately \( 22.99 \, \text{g/mol} \) , and chlorine has \( 35.45 \, \text{g/mol} \). So,\[\text{Molar mass of NaCl} = 22.99 + 35.45 = 58.44 \, \text{g/mol}\]
This value is essential in converting the mass of NaCl to moles when calculating molarity. Without determining the molar mass, it would be challenging to gauge the effect of NaCl in solutions, such as their contribution to osmotic pressure in the ocean or the lab.

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Most popular questions from this chapter

At \(20^{\circ} \mathrm{C}\), the vapor pressure of benzene \(\left(\mathrm{C}_{6} \mathrm{H}_{6}\right)\) is \(10 \mathrm{kPa}\), and that of toluene \(\left(\mathrm{C}_{7} \mathrm{H}_{8}\right)\) is \(2.9 \mathrm{kPa}\). Assume that benzene and toluene form an ideal solution. (a) What is the composition in mole fraction of a solution that has a vapor pressure of \(4.7 \mathrm{kPa}\) at \(20^{\circ} \mathrm{C} ?(\mathbf{b})\) What is the mole fraction of benzene in the vapor above the solution described in part (a)?

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