Sea water is found to contain 5.85%NaCl and 9.5% MgCl2 by wt of soln. Calculate its normal Boiling Pt assuming 80% ionisation for NaCl and 50% ionisation of MgCl2.

Given Kb for H2O is 0.51 KgK/mol

To determine the normal boiling point of seawater with the given concentrations of NaCl and MgCl2, we need to consider the colligative properties of solutions, specifically boiling point elevation. This phenomenon occurs when a solute is added to a solvent, raising the boiling point of the solvent. The formula for boiling point elevation is:

Boiling Point Elevation Formula

The boiling point elevation can be calculated using the formula:

ΔT_b = i * K_b * m

• ΔT_b = change in boiling point
• i = van 't Hoff factor (number of particles the solute breaks into)
• K_b = ebullioscopic constant of the solvent (for water, K_b = 0.51 °C kg/mol)
• m = molality of the solution

Step 1: Calculate the Molality of the Solution

First, we need to find the molality of the solution. Molality (m) is defined as the number of moles of solute per kilogram of solvent. We will calculate the molality for both NaCl and MgCl2 separately.

NaCl Calculation

Given that seawater contains 5.85% NaCl by weight, we can assume we have 1000 g of seawater for simplicity. Thus, the mass of NaCl is:

Mass of NaCl = 5.85 g

To find the number of moles of NaCl:

Molar mass of NaCl = 58.44 g/mol

Moles of NaCl = 5.85 g / 58.44 g/mol ≈ 0.100 mol

Assuming the density of seawater is approximately 1.025 g/mL, the mass of the solvent (water) in 1000 g of seawater is:

Mass of water = 1000 g - 5.85 g = 994.15 g ≈ 0.994 kg

Molality of NaCl = 0.100 mol / 0.994 kg ≈ 0.101 mol/kg

MgCl2 Calculation

Next, for MgCl2, which is present at 9.5% by weight:

Mass of MgCl2 = 9.5 g

Molar mass of MgCl2 = 95.21 g/mol

Moles of MgCl2 = 9.5 g / 95.21 g/mol ≈ 0.100 mol

Using the same mass of water (0.994 kg), we find the molality of MgCl2:

Molality of MgCl2 = 0.100 mol / 0.994 kg ≈ 0.101 mol/kg

Step 2: Determine the van 't Hoff Factors

Next, we need to consider the ionization of the solutes:

• NaCl ionizes into Na⁺ and Cl^-, so with 80% ionization: i_NaCl = 2 * 0.80 = 1.6
• MgCl2 ionizes into Mg²⁺ and 2 Cl^-, so with 50% ionization: i_MgCl2 = 3 * 0.50 = 1.5

Step 3: Calculate the Total Molality

The total molality of the solution is the sum of the molalities of NaCl and MgCl2:

Total molality = 0.101 mol/kg + 0.101 mol/kg = 0.202 mol/kg

Step 4: Calculate the Boiling Point Elevation

Now we can calculate the boiling point elevation:

ΔT_b = (i_NaCl + i_MgCl2) * K_b * m

ΔT_b = (1.6 + 1.5) * 0.51 °C kg/mol * 0.202 mol/kg

ΔT_b = 3.1 * 0.51 * 0.202 ≈ 0.323 °C

Step 5: Determine the New Boiling Point

The normal boiling point of pure water is 100 °C. Therefore, the boiling point of seawater is:

Boiling Point = 100 °C + ΔT_b = 100 °C + 0.323 °C ≈ 100.32 °C

In summary, the normal boiling point of seawater, considering the specified concentrations and ionization rates of NaCl and MgCl2, is approximately 100.32 °C. This slight increase in boiling point is due to the presence of dissolved salts, which affect the physical properties of the water.