Question

How much salt would one need to add to 1 kg water to change the boiling temperature by 5°C (in grams)(Kb = 0.51 Ckg/mol) for water and i = 2 for NaCl.)

Answer 1

Answer

286.356 grams of salt (NaCl) needed to be added.

Explanation

Given:

ΔTb = 5 °C

i = 2, because 1 mol of NaCl gives 2 mol of particles in solution.

Kb = 0.51 °Ckg/mol

What to find:

To find how much salt in grams would one need to add to 1 kg of water to change the boiling temperature by 5°C.

Step-by-step solution:

Step 1: Determine the molality of the solution.

The formula for boiling point elevation is:

$\Delta T_b=iK_bm$

Where

$\begin{gathered} \Delta T_b\text{ }is\text{ }the\text{ }boiling\text{ }point\text{ }elevation \\ \\ i\text{ }is\text{ }the\text{ }van^{\prime}t\text{ }Hoff\text{ }factor \\ \\ K_b\text{ }is\text{ }the\text{ }boiling\text{ }point\text{ }elevation\text{ }constant \\ \\ m\text{ }is\text{ }the\text{ }molality\text{ }of\text{ }the\text{ }solution \end{gathered}$

Therefore, the molality of the solution is:

$m=\frac{\Delta T_b}{iK_b}=\frac{5\degree C}{2\times0.51\degree C\cdot kg\text{/}mol}=4.90\text{ }mol\text{/}kg$

Step 2: Determine the moles of NaCl in 4.90 mol/kg of NaCl.

The formula for molality is:

$\begin{gathered} Molality=\frac{moles\text{ }of\text{ }solute}{kilogram\text{ }of\text{ }solvent} \\ \\ \Rightarrow Moles\text{ }of\text{ }solute=Molality\times kilogram\text{ }of\text{ }solvent \\ \\ Moles\text{ }of\text{ }solute=4.90\text{ }mol\text{/}kg\times1\text{ }kg \\ \\ Moles\text{ }of\text{ }solute=4.90\text{ }mol \end{gathered}$

Step 3: Convert moles of NaCl in step 2 to grams of NaCl.

Finally, we can convert the moles of NaCl in step 2 to grams of NaCl using the mole formula below:

$Moles=\frac{Mass}{Molar\text{ }mass}$

Putting moles of NaCl as 4.90 mol and the molar mass of NaCl as 58.44 g/mol, the mass of NaCl in grams is:

$\begin{gathered} Mass\text{ }of\text{ }NaCl=Moles\times Molar\text{ }mass \\ \\ Mass\text{ }of\text{ }NaCl=4.90\text{ }mol\times58.44\text{ }g\text{ /}mol \\ \\ Mass\text{ }of\text{ }NaCl=286.356\text{ }grams \end{gathered}$

Hence, 286.356 grams of salt (NaCl) is needed to be added to 1 kg of water to change the boiling temperature by 5°C.

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