Question

At same temperature which pair of the following solutions are isotonic? (if all are 100% ionised)

• A. $0.2MBaC{l}_2$ and $0.2MUrea$
• B. $0.1MUrea$ and $0.1MNaCl$
• C. $0.1MNaCl$ and $0.1M{K}_{2}S{O}_4$
• D. $0.1MBa(N{O}_3{)}_2$ and $0.1MN{a}_{2}S{O}_4$

Answer 1

The correct option is D $0.1MBa(N{O}_3{)}_2$ and $0.1MN{a}_{2}S{O}_4$

Isotonic solutions are solutions having same osmotic pressure.
Osmotic pressure of a solution can be given by,
$\pi =iCRT$
$\pi$ = Osmotic pressure
C = Concentration ($mol/L$)
R = Gas constant ($Latmmo{l}^{-1}{K}^{-1}$)
T = Temperature ($K$)
$i$ = van't Hoff factor

(a)
$BaC{l}_2\to B{a}^{2+}+2C{l}^{-}$
$\therefore$ $i=3$
${\pi }_{BaC{l}_2}=3\times 0.2RT$
Urea is a non-electrolyte so, $i=1$
${\pi }_{Urea}=0.2RT$

(b)
${\pi }_{Urea}=0.1RT$
$NaCl\to N{a}^{+}+C{l}^{-}$
$\therefore$ $i=2$
${\pi }_{NaCl}=2\times 0.1RT$

(c)
${\pi }_{NaCl}=2\times 0.1RT$
$K_{2}S{O}_4\to 2K^{+}+S{O}_4^{2-}$
$\therefore$ $i=3$
${\pi }_{K_{2}S{O}_4}=3\times 0.1RT$

(iv)
$Ba(N{O}_3{)}_2\to B{a}^{2-}+2N{O}_3^{-}$
$\therefore$ $i=3$
${\pi }_{Ba(N{O}_3{)}_2}=3\times 0.1RT$
$N{a}_{2}S{O}_4\to 2N{a}^{+}+S{O}_4^{2-}$
$\therefore$ $i=3$
${\pi }_{N{a}_{2}S{O}_4}=3\times 0.1RT$

Thus, option (d) is correct.