What is the van't Hoff factor for a binary ionic compound $MX$ $"MX"$ for which ion pairing has led to a percent dissociation of $50 %$ $50%$ ?

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What is the van't Hoff factor for a binary ionic compound $MX$ $"MX"$ for which ion pairing has led to a percent dissociation of $50 %$ $50%$ ?

I'm asking this as a fun question. I know it's supposed to be $1.5$ $1.5$ .

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Answer 1 · 2018-05-14T21:10:54

The dissociation of $MX$ $"MX"$ in water would be:

$MX (a q) \to M_{+}^{z_{+}} (a q) + A_{-}^{z_{-}} (a q)$ $"MX"(aq) -> "M"^(z_+)(aq) + "A"^(z_-)(aq)$

A $100 %$ $100%$ dissociation would lead to a van't Hoff factor of $2$ $2$ , since the total concentration would just be that of the two ions produced per one solute particle.
A $0 %$ $0%$ dissociation would obviously lead to a van't Hoff factor of $1$ $1$ .

So the quick answer is just $i = 1.5$ $i = 1.5$ . (This is only that easy because the coefficients are all $1$ $1$ . If they were not, it would not be $1.5$ $1.5$ per se.)

A full ICE table would also yield the same result.

$MX (a q) \to M_{+}^{z_{+}} (a q) + A_{-}^{z_{-}} (a q)$ $"MX"(aq) " " -> " ""M"^(z_+)(aq) + "A"^(z_-)(aq)$

$I {[MX]}_{i} 00$ $"I"" "["MX"]_i" "" "" "" "0" "" "" "" "0$
$C - \frac{{[MX]}_{i}}{2} + \frac{{[MX]}_{i}}{2} + \frac{{[MX]}_{i}}{2}$ $"C"" "-["MX"]_i/2" "+["MX"]_i/2" "+["MX"]_i/2$
$E \frac{{[MX]}_{i}}{2} \frac{{[MX]}_{i}}{2} \frac{{[MX]}_{i}}{2}$ $"E"" "["MX"]_i/2" "" "" "["MX"]_i/2" "" "["MX"]_i/2$

From this, the total ion concentration is:

$[ions] = \frac{{[MX]}_{i}}{2} + \frac{{[MX]}_{i}}{2} + \frac{{[MX]}_{i}}{2} = 1.5 {[MX]}_{i}$ $["ions"] = ["MX"]_i/2 + ["MX"]_i/2 + ["MX"]_i/2 = 1.5["MX"]_i$

So, the van't Hoff factor is

$i = \frac{total concentration}{undissociated concentration}$ $color(blue)(i) = "total concentration"/"undissociated concentration"$

$= \frac{1.5 {[MX]}_{i}}{{[MX]}_{i}} = 1.5$ $= (1.5["MX"]_i)/(["MX"]_i) = color(blue)(1.5)$

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What is the van't Hoff factor for a binary ionic compound $MX$ $"MX"$ for which ion pairing has led to a percent dissociation of $50 %$ $50%$ ?

I'm asking this as a fun question. I know it's supposed to be $1.5$ $1.5$ .

1 Answer

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What is the van't Hoff factor for a binary ionic compound "MX"MX"MX" for which ion pairing has led to a percent dissociation of 50%50%50%?

I'm asking this as a fun question. I know it's supposed to be 1.51.51.5.

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Impact of this question

What is the van't Hoff factor for a binary ionic compound $MX$ $"MX"$ for which ion pairing has led to a percent dissociation of $50 %$ $50%$ ?

I'm asking this as a fun question. I know it's supposed to be $1.5$ $1.5$ .