IMO Practice Test — States of Matter
14 Questions • 15 min • Olympiad level
15:00
Question 1 of 14
At constant temperature, a gas at 6 atm occupies 2 L. If compressed to 0.5 L, the pressure is:
12 atm
18 atm
24 atm
3 atm
Explanation: $P_2=\frac{P_1V_1}{V_2}=\frac{6\times2}{0.5}=24\ \text{atm}$.
Question 2 of 14
A gas at 300 K is heated until its volume doubles at constant pressure. The new temperature is:
150 K
300 K
600 K
900 K
Explanation: Charles’ law: $V\propto T$, so doubling $V$ doubles $T$ to $600\ \text{K}$.
Question 3 of 14
Two flasks of equal volume at the same $T$ hold $\text{H}_2$ and $\text{O}_2$ at equal pressure. The ratio of numbers of molecules $\text{H}_2:\text{O}_2$ is:
16:1
1:16
1:1
2:1
Explanation: By Avogadro’s law equal $V,T,P$ means equal numbers of molecules, so $1:1$.
Question 4 of 14
The ratio $u_{rms}$ of $\text{H}_2$ to $\text{O}_2$ at the same temperature is:
1:4
4:1
1:16
16:1
Explanation: $\frac{u_{H_2}}{u_{O_2}}=\sqrt{\frac{32}{2}}=\sqrt{16}=4$, so $4:1$.
Question 5 of 14
If the rms speed of a gas at 27°C is $v$, its rms speed at 927°C is:
$2v$
$3v$
$4v$
$\sqrt{2}\,v$
Explanation: $T_1=300$ K, $T_2=1200$ K; $\frac{v_2}{v_1}=\sqrt{\frac{1200}{300}}=2$.
Question 6 of 14
For a real gas at very high pressure, $Z=\frac{PV}{nRT}$ is generally:
less than 1
equal to 1
greater than 1
zero
Explanation: Finite molecular volume dominates at high pressure, giving $Z>1$.
Question 7 of 14
For 2 mol of a gas at 500 K and 8.21 atm occupying 10 L, $Z$ is approximately ($R=0.0821$):
0.5
1.0
1.25
2.0
Explanation: $Z=\frac{8.21\times10}{2\times0.0821\times500}=\frac{82.1}{82.1}=1.0$.
Question 8 of 14
A gas has van der Waals constants $a=4.0$, $b=0.05\ \text{L/mol}$. Its critical volume per mole is:
0.05 L
0.10 L
0.15 L
0.20 L
Explanation: $V_c=3b=3\times0.05=0.15\ \text{L/mol}$.
Question 9 of 14
Which gas is the easiest to liquefy?
$\text{He}$
$\text{H}_2$
$\text{N}_2$
$\text{NH}_3$
Explanation: $\text{NH}_3$ has hydrogen bonding, hence the strongest attractions and the highest $T_c$.
Question 10 of 14
A mixture has equal masses of $\text{He}$ ($M=4$) and $\text{CH}_4$ ($M=16$). The mole ratio $\text{He}:\text{CH}_4$ is:
1:4
4:1
1:1
2:1
Explanation: For equal mass $m$, moles $=\frac{m}{M}$, so ratio $=\frac{1/4}{1/16}=4:1$.
Question 11 of 14
A 1 L vessel holds $\text{N}_2$ at 0.6 atm and $\text{O}_2$ at 0.4 atm. The mole fraction of $\text{N}_2$ is:
0.4
0.6
1.0
0.24
Explanation: Total $=1.0$ atm; $x_{\text{N}_2}=\frac{p_{\text{N}_2}}{P_{total}}=\frac{0.6}{1.0}=0.6$.
Question 12 of 14
For the Maxwell distribution, raising the temperature keeps which quantity constant?
the most probable speed
the peak height
the total area under the curve
the width of the curve
Explanation: The area equals the total number of molecules, which is conserved; only the shape shifts.
Question 13 of 14
A gas obeys $PV=nRT$ best under conditions of:
high P, low T
low P, high T
high P, high T
low P, low T
Explanation: At low pressure and high temperature, molecular volume and attractions are negligible, so $Z\to1$.
Question 14 of 14
If the average KE of gas molecules is doubled, the absolute temperature is:
halved
unchanged
doubled
quadrupled
Explanation: $\overline{KE}=\frac{3}{2}k_BT\propto T$, so doubling KE doubles $T$.