Questions: Four 0.6 mol samples of argon gas are described in the table below. Rank these samples in order of decreasing rate of collisions between atoms. That is, select " 1 " next to the sample with the most collisions per second between Ar atoms and the walls of the container. Select " 2 " next to the sample with the next most collisions per second between Ar atoms and the walls of the container, and so on. sample volume temperature collisions per second A 42 L -44 °C B 34 L -27 °C C 38 L -27 °C D 42 L -27 °C

Four 0.6 mol samples of argon gas are described in the table below. Rank these samples in order of decreasing rate of collisions between atoms.
That is, select " 1 " next to the sample with the most collisions per second between Ar atoms and the walls of the container. Select " 2 " next to the sample with the next most collisions per second between Ar atoms and the walls of the container, and so on.
sample volume temperature collisions per second
A 42 L -44 °C
B 34 L -27 °C
C 38 L -27 °C
D 42 L -27 °C

Transcript text: Four 0.6 mol samples of argon gas are described in the table below. Rank these samples in order of decreasing rate of collisions between atoms. That is, select " 1 " next to the sample with the most collisions per second between Ar atoms and the walls of the container. Select " 2 " next to the sample with the next most collisions per second between Ar atoms and the walls of the container, and so on. sample & volume & temperature & collisions per second A & $42 . \mathrm{L}$ & $-44 .{ }^{\circ} \mathrm{C}$ & $\square$ B & $34 . \mathrm{L}$ & $-27 .{ }^{\circ} \mathrm{C}$ & $\square$ C & $38 . \mathrm{L}$ & $-27 .{ }^{\circ} \mathrm{C}$ & $\square$ D & $42 . \mathrm{L}$ & $-27 . .^{\circ} \mathrm{C}$ & $\square$

Solution

Solution Steps

Step 1: Convert Temperatures to Kelvin

First, we need to convert the given temperatures from Celsius to Kelvin using the formula: \[ T(K) = T(°C) + 273.15 \]

For sample A: \[ T_A = -44 + 273.15 = 229.15 \, \text{K} \]
For sample B, C, and D (all have the same temperature): \[ T_B = T_C = T_D = -27 + 273.15 = 246.15 \, \text{K} \]

Step 2: Understand the Relationship Between Collisions and Conditions

The rate of collisions in a gas is influenced by both the temperature and the volume of the container. Higher temperatures increase the kinetic energy of the gas molecules, leading to more frequent collisions. Smaller volumes also lead to more frequent collisions due to the reduced space for the gas molecules to move.

Step 3: Rank Based on Temperature

Since samples B, C, and D have a higher temperature (246.15 K) compared to sample A (229.15 K), they will have more collisions per second. Therefore, sample A will have the least collisions.

Step 4: Rank Based on Volume

Among samples B, C, and D, the volume will determine the ranking:

Sample B has the smallest volume (34 L), leading to the most collisions.
Sample C has a volume of 38 L, leading to the next most collisions.
Sample D has the largest volume among the three (42 L), leading to the least collisions among them.

Final Answer

\[ \begin{array}{|c|c|c|c|} \hline \text{sample} & \text{volume} & \text{temperature} & \text{collisions per second} \\ \hline \text{A} & 42 \, \text{L} & -44 \, ^{\circ} \text{C} & \boxed{4} \\ \hline \text{B} & 34 \, \text{L} & -27 \, ^{\circ} \text{C} & \boxed{1} \\ \hline \text{C} & 38 \, \text{L} & -27 \, ^{\circ} \text{C} & \boxed{2} \\ \hline \text{D} & 42 \, \text{L} & -27 \, ^{\circ} \text{C} & \boxed{3} \\ \hline \end{array} \]

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