Question
Asked Feb 7, 2020
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A mixture of table salt and ice is used to chill the contents of hand-operated ice-cream makers. What is the melting point of a mixture of 2.00 lb of NaCl and 12.00 lb of ice if exactly half of the ice melts? Assume that all the NaCl dissolves in the melted ice and that the van't Hoff factor for the resulting solution is 1.44.

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Expert Answer

Step 1

Given, the van't hoff factor for the resulting solution = 1.44

The amount of NaCl = 2.0 lb

The amount of ice (H2O) =12.00 lb

The amount of NaCl in terms of kilogram is represented as -

1 lb = 0.4535 Kg

2.0 lb = 2.0 x 0.4535 Kg

          = 0.907 Kg

It is given that exactly half of the ice melts. Therefore, the amount of ice (H2O) is expressed as -

Chemistry homework question answer, step 1, image 1

The amount of ice (H2O) in terms of kilogram is represented as -

1 lb = 0.4535 Kg

6.0 lb = 6.0 x 0.4535 Kg

          = 2.721 Kg

Step 2

The change in freezing point (ΔTf) is represented as -

Chemistry homework question answer, step 2, image 1

Now we will calculate the molality -

Chemistry homework question answer, step 2, image 2

The number of moles (n) of NaCl is calculated by the formula -

Chemistry homework question answer, step 2, image 3

Molar mass of NaCl = 58.44 g/mol

Substituting the given mass and molar mass,

Chemistry homework question answer, step 2, image 4

Step 3

The given mass of solute ice (H2O) = 2.721 Kg

Chemistry homework question answer, step 3, image 1

The value of freezing point depression constant = 1.86°C/m

...

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