IMO Practice Test — Solutions
14 Questions • 15 min • Olympiad level
15:00
Question 1 of 14
A 2 M solution of a substance (M = 60) has density $1.08\ \text{g mL}^{-1}$. Its molality is closest to:
1.9 m
2.1 m
2.5 m
1.5 m
Explanation: Mass of solute $=120$ g; solution mass $=1080$ g; water $=960$ g $=0.96$ kg; $m=2/0.96=2.08\approx2.1$ m.
Question 2 of 14
If $K_H$ of N$_2$ is greater than $K_H$ of O$_2$ at the same temperature, then in water:
N$_2$ is more soluble
O$_2$ is more soluble
both equally soluble
neither dissolves
Explanation: Larger $K_H$ means lower solubility, so O$_2$ (smaller $K_H$) is more soluble.
Question 3 of 14
For an ideal binary solution with $p_A^0=120$ and $p_B^0=80$ (mm Hg) at $x_A=0.25$, $p_{total}$ is:
80 mm Hg
90 mm Hg
100 mm Hg
110 mm Hg
Explanation: $p=120(0.25)+80(0.75)=30+60=90$ mm Hg.
Question 4 of 14
For the solution in the previous question, the mole fraction of A in the vapour is closest to:
0.25
0.33
0.50
0.67
Explanation: $y_A=p_A/p_{total}=30/90=0.33$.
Question 5 of 14
Equal masses of two non-electrolytes (M = 100 and M = 200) are dissolved separately in equal water. The ratio of $\Delta T_f$ values is:
1:1
1:2
2:1
4:1
Explanation: $\Delta T_f$ is proportional to moles, hence to $1/M$; ratio $=200/100=2:1$.
Question 6 of 14
$\text{K}_2\text{SO}_4$ dissociates completely. Its limiting van't Hoff factor is:
2
3
4
1
Explanation: $\text{K}_2\text{SO}_4$ gives $2\text{K}^++\text{SO}_4^{2-}$, three ions, so $i=3$.
Question 7 of 14
At 27 degrees C, a solution exerts an osmotic pressure of 4.98 bar. Its molar concentration is ($R=0.083$):
0.1 M
0.2 M
0.3 M
0.5 M
Explanation: $C=\Pi/(RT)=4.98/(0.083\times300)=0.2$ M.
Question 8 of 14
A maximum-boiling azeotrope forms when a solution shows:
positive deviation
ideal behaviour
negative deviation
zero vapour pressure
Explanation: Negative deviation gives a vapour-pressure minimum and a boiling-point maximum.
Question 9 of 14
0.1 m solutions of glucose, NaCl, and CaCl$_2$ are arranged by freezing point. The correct order (lowest first) is:
glucose < NaCl < CaCl$_2$
CaCl$_2$ < NaCl < glucose
NaCl < CaCl$_2$ < glucose
glucose < CaCl$_2$ < NaCl
Explanation: More particles (i) means greater depression and lower freezing point: CaCl$_2$ (i=3) lowest, glucose (i=1) highest.
Question 10 of 14
Relative lowering of vapour pressure for 1 mol solute in 9 mol solvent is:
0.05
0.10
0.11
0.90
Explanation: $x_{solute}=1/(1+9)=0.10$.
Question 11 of 14
A weak acid HA in water shows $i=1.3$. Its degree of dissociation ($n=2$) is:
0.13
0.30
0.65
0.70
Explanation: $\alpha=(i-1)/(n-1)=0.3/1=0.30$.
Question 12 of 14
Acetic acid dimerises in benzene with 80% association. Its van't Hoff factor is:
0.6
0.8
1.2
1.6
Explanation: $i=1-\alpha/2=1-0.40=0.60$ for dimerisation.
Question 13 of 14
The boiling-point elevation of 0.5 m sucrose in water ($K_b=0.512$) is:
0.128 K
0.256 K
0.512 K
1.024 K
Explanation: $\Delta T_b=K_b m=0.512\times0.5=0.256$ K.
Question 14 of 14
If 1 g of a polymer (M = 50000) is dissolved in 100 mL water at 300 K, the osmotic pressure ($R=0.083$) is closest to:
$5\times10^{-3}$ bar
$5\times10^{-2}$ bar
$5\times10^{-1}$ bar
5 bar
Explanation: $C=(1/50000)/0.1=2\times10^{-4}$ M; $\Pi=2\times10^{-4}\times0.083\times300=4.98\times10^{-3}$ bar.