In the northeastern United States during freezing weather, CaCl2 is spread on icy highways to melt the ice. Calculate the freezing point of a solution containing 0.50 mole of CaCl2 in 1 kg of water.

Question

In the northeastern United States during freezing weather, [latex]CaCl_{2}[/latex] is spread on icy highways to melt the ice. Calculate the freezing point of a solution containing 0.50 mole of [latex]CaCl_{2}[/latex] in 1 kg of water.

Accepted Answer

STEP 1 State the given and needed quantities.

ANALYZE THE PROBLEM	Given	Need	Connect
	0.50 mole of [latex]CaCl_{2}[/latex] 1 kg of water	freezing point of solut ion	[latex]CaCl_{2}[/latex] strong electrolyte, 1 mole/kg lowers freezing point 1.86 °C

STEP 2 Determine the number of moles of solute particles.

[latex] CaCl_{2}(s) → Ca^{2+}(aq) + 2Cl^{-}(aq) [/latex]= 3 moles of solute particles

[latex] \begin{array}{r c}\boxed{\begin{matrix} 1 mole of CaCl_{2} = 3 moles of solute particles \\frac{ 3 moles solute particles}{1 mole CaCl_{2} } ext{ and } \frac{1 mole CaCl_{2}}{ 3 moles solute particles} \end{matrix}} \end{array} [/latex]

STEP 3 Determine the temperature change using the moles of solute particles and the degrees Celsius change per mole of particles.

[latex] \begin{array}{r c}\boxed{\begin{matrix} 1 mole of solute particles = 1.86 °C\\frac{1.86 °C}{1 moles solute particles } ext{ and } \frac{1 moles solute particles}{1.86 °C} \end{matrix}}\end{array} [/latex]

Temperature change = [latex] 0.50 \cancel{mole CaCl_{2}} imes \boxed{\frac{3 \cancel{moles solute particles}}{1 \cancel{mole CaCl_{2}}} } imes \boxed{\frac{1.86 °C}{1 \cancel{ moles solute particles}} } [/latex]

[latex] =2.8 °C[/latex]

STEP 4 Subtract t he temperature change from the freezing point. The temperature change, ΔT, is subtracted from 0.00 °C to obtain the new freezing point of the [latex]CaCl_{2}[/latex] solution.

[latex] T_{solution} = T_{water} - ΔT = 0.00 °C - 2.8 °C = -2.8 °C [/latex]

Question 9.16: In the northeastern United States during freezing weather, C...

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