# What is the boiling point of an aqueous solution of #"CaCl"_2# with a molal concentration of 1.56 mol/kg?

The boiling point of the solution is 108.705 °C.

where

In this problem,

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To find the boiling point elevation of an aqueous solution of CaCl₂ with a molal concentration of (1.56 , \text{mol/kg}), we can use the boiling point elevation equation:

[ \Delta T_b = i \cdot K_b \cdot m ]

where:

- (\Delta T_b) is the boiling point elevation,
- (i) is the van't Hoff factor (the number of particles the solute splits into or generates in the solution),
- (K_b) is the ebullioscopic constant of the solvent (water, in this case, with (K_b = 0.512 , \text{°C·kg/mol})),
- (m) is the molal concentration of the solution.

For (CaCl_2), which dissociates into (Ca^{2+}) and (2Cl^{-}), the van't Hoff factor (i = 3) (since it dissociates into 3 ions).

Given:

- (i = 3),
- (K_b = 0.512 , \text{°C·kg/mol}),
- (m = 1.56 , \text{mol/kg}).

Substituting these values into the equation:

[ \Delta T_b = 3 \cdot 0.512 , \text{°C·kg/mol} \cdot 1.56 , \text{mol/kg} ]

[ \Delta T_b = 1.54 \cdot 1.56 ]

[ \Delta T_b = 2.40 , \text{°C} ]

The normal boiling point of water is (100.00 , \text{°C}). Therefore, the boiling point of the solution is:

[ 100.00 , \text{°C} + 2.40 , \text{°C} = 102.40 , \text{°C} ]

The boiling point of the aqueous solution of (CaCl_2) with a molal concentration of (1.56 , \text{mol/kg}) is (102.40 , \text{°C}).

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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