How many grams of salt must be added to 300g of water to increase its boiling point by 5°C?

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Answer 1 · 2016-12-22T23:04:51

You must add 86 g of salt.

The formula for boiling point elevation is

$color(blue)(|bar(ul(ΔT_"b" = iK_"b"m)|)$

where

We can solve the equation for the molality of the solution.

$m = (ΔT_"b")/(iK_"b")$

In this problem,

$ΔT_"b" = "5 °C"$
$i = 2$ , because 1 mol of $"NaCl"$ gives 2 mol of particles in solution.
$K_"b" = "0.512 °C·kg·mol"^"-1"$

∴ $m = (5 color(red)(cancel(color(black)("°C"))))/(2 × 0.512 color(red)(cancel(color(black)("°C")))·"kg·mol"^"-1") = "4.88 mol·kg"^"-1"$

Next, we calculate the moles of $"NaCl"$ .

The formula for molality is

$color(blue)(bar(ul(|color(white)(a/a) "Molality" = "moles of solute"/"kilograms of solvent"color(white)(a/a)|)))" "$

∴ $"Moles of NaCl" = 0.300 color(red)(cancel(color(black)("kg"))) × "4.88 mol"·color(red)(cancel(color(black)("kg"^"-1"))) = "1.46 mol"$

Finally, convert moles of $"NaCl"$ to grams of $"NaCl"$ .

$"Mass of NaCl" = 1.46 color(red)(cancel(color(black)("mol NaCl"))) × "58.44 g NaCl"/(1 color(red)(cancel(color(black)("mol NaCl")))) = "86 g NaCl"$