Question

Which of the following pairs of aqueous solutions have roughly the same freezing point depression?

1. (A) 0.100m C6H12O6 and 0.0333m MgCl2

2. (B) 0.100m NaCl and 0.100m C6H12O6

3. (C) 0.200m NaCl and 0.300m Na2SO4

4. (D) 0.100m KCl and 0.0500m MgBr2

5. (E) 0.100m KI and 0.0500m Na3PO4

Answer 1

we know that

freezing point depression(ΔTf) = i * Kf * m

i is vant hoff factor(for non - electrolyte it is 1)

Kf = 1.86°C/m

m is molality

now

(A) 0.100m C6H12O6 and 0.0333m MgCl2

0.100m C6H12O6 (non electrolyte)

i = 1

ΔTf = i * Kf * m

= 1 * 1.86 °C/m * 0.1m

= 0.186 °C

0.0333 m MgCl2

i = 3(1 Mg2+ and 2Cl-)

ΔTf = i * Kf * m

= 3 * 1.86 * 0.0333

= 0.1858 °C

Both are roughly same

(B) 0.100m NaCl and 0.100m C6H12O6

0.100m NaCl

i = 2 ( 1 Na+ and 1 Cl-)

ΔTf = i * Kf * m

= 2 * 1.86 °C/m * 0.1m

= 0.372 °C

0.100m C6H12O6 (non - electrolyte)

i = 1

ΔTf = i * Kf * m

= 1 * 1.86 * 0.1

= 0.186 °C

Both aren't same

(C) 0.200m NaCl and 0.300m Na2SO4

0.200m NaCl

I = 2 ( 1 Na+ and 1 Cl-)

ΔTf = i * Kf * m

= 2 * 1.86 * 0.2

= 0.744 °C

0.300m Na2SO4

i = 3 ( 2 Na+ and SO4^2-)

ΔTf = i * Kf * m

= 3 * 1.86 * 0.3

= 1.674 °C

Both aren't same

(D) 0.100m KCl and 0.0500m MgBr2

0.100m KCl

i = 2 ( 1 K+ and 1 Cl-)

ΔTf = i * Kf * m

= 2 * 1.86 * 0.1

= 0.372 °C

0.0500m MgBr2

i = 3 ( Mg2+ and 2 Br-)

ΔTf = i * Kf * m

= 3 * 1.86 *0.05

= 0. 279 °C

Both aren't same

(E) 0.100m KI and 0.0500m Na3PO4

0.100m KI

i = 2 ( 1 K+ and 1 I-)

ΔTf = i * Kf * m

= 2 * 1.86 * 0. 1

= 0.372 °C

0.0500m Na3PO4

i = 4 ( 3 Na+ and 1 PO4^3-​​​​​​)

ΔTf = i * Kf * m

= 4 * 1.86 * 0.05

= 0.372 °C

Both are same

So

A) and E) pairs of aqueous solutions have roughly the same freezing point depression