Question ce84d

Oct 4, 2017

The answer is (C) ${\text{329 g mol}}^{- 1}$.

Explanation:

The idea here is that the minimum molar mass of the compound will correspond to a salt that contains $1$ mole of sodium.

In other words, the minimum molar mass occurs when $1$ mole of this salt contains $1$ mole of sodium.

Now, let's assume that we're dealing with a sample of this salt that contains exactly $1$ mole of sodium. This implies that the sample will also contain $1$ mole of salt.

As you know, sodium has a molar mass of about ${\text{23.0 g mol}}^{- 1}$. This means that this sample, which contains $1$ mole of sodium, will contain $\text{23.0 g}$ of sodium.

By definition, you know that the salt is 7% by mass sodium, which means that every $\text{100 g}$ of salt contains $\text{7 g}$ of sodium. This implies that the mass of the sample will be

23.0 color(red)(cancel(color(black)("g Na"))) * "100 g salt"/(7color(red)(cancel(color(black)("g Na")))) = "328.57 g salt"

Since we've established that this sample contains $1$ mole of salt, you can say that the molar mass of the salt is

M_ ("M salt") = "328.57 g"/"1 mole" ~~ color(darkgreen)(ul(color(black)("329 g mol"^(-1))))#

This represents the minimum molar mass of the salt because it corresponds to $1$ mole of sodium per mole of salt.