Question

Most pasta recipes instruct you to add a teaspoon of salt to a pot

of boiling water. Does this have a significant effect on the boiling temperature?

Justify your answer with a rough numerical estimate.

Short answer

There is hardly any effect on the boiling temperature of water.

Step-by-step solution

Given information

Addition of salt effects the boiling temperature of water. The shift in the boiling temperature is given by

$$\begin{gathered} T-T_{\circ }=\frac{n_{B}R{T^2}_{\circ }}{L} \\ Here,T_{o}isboilingtemperatureofwaterwithoutanysolute; \\ {n}_{B}isno.ofmolesofsolute; \\ Lislatentheatoffusion. \end{gathered}$$

Effect of adding salt

We are adding a tablespoon of salt.

Assuming a tablespoon of salt = 6g

$$\begin{gathered} n=\frac{m}{M} \\ M=58.44\raisebox{1ex}{$g$}\!\left/ \!\raisebox{-1ex}{$mol$}\right. \\ m=6g \\ n=\frac{6}{58.44} \\ n=0.1026\raisebox{1ex}{$g$}\!\left/ \!\raisebox{-1ex}{$mol$}\right. \end{gathered}$$

substituting the values

T_o = 373 K

n = 0.1026

R = 8.3 1$\raisebox{1ex}{$J$}\!\left/ \!\raisebox{-1ex}{$$}\right.K-mol$

L = $2.26\times {10}^{6}J$

localid="1647192130510" $$\begin{gathered} T-T_o=\frac{0.1026\times 8.31\times {\left(373\right)}^2}{2.26\times {10}^6} \\ T-T_o=0.053K \\ T=373+0.053 \\ =373.053K \end{gathered}$$

This change is hardly significant.