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Which sample has particles with the lowest average kinetic energy? $\newline$ ( $1$ ) $1.0 \mathrm{~g}$ of $\mathrm{I}_{2}$ at $50 .^{\circ} \mathrm{C}$ $\newline$ ( $3$ ) $7.0 \mathrm{~g}$ of $\mathrm{I}_{2}$ at $40 .{ }^{\circ} \mathrm{C}$ $\newline$ ( $2$ ) $2.0 \mathrm{~g}$ of $\mathrm{I}_{2}$ at $30 .{ }^{\circ} \mathrm{C}$ $\newline$ ( $4$ ) $9.0 \mathrm{~g}$ of $\mathrm{I}_{2}$ at $\mathrm{I}_{2}$ $1$ $\newline$ $1$ $\newline$ $2$ $\newline$ $3$ $\newline$ $4$

Full solution

Q. Which sample has particles with the lowest average kinetic energy?

\newline

(

1

)

1.0 \mathrm{~g}

\mathrm{I}_{2}

50 .^{\circ} \mathrm{C}

\newline

(

3

)

7.0 \mathrm{~g}

\mathrm{I}_{2}

40 .{ }^{\circ} \mathrm{C}

\newline

(

2

)

2.0 \mathrm{~g}

\mathrm{I}_{2}

30 .{ }^{\circ} \mathrm{C}

\newline

(

4

)

9.0 \mathrm{~g}

\mathrm{I}_{2}

\mathrm{I}_{2}

1

\newline

1

\newline

2

\newline

3

\newline

4

Temperature and Kinetic Energy Relationship: The average kinetic energy of particles in a sample is directly related to temperature; the lower the temperature, the lower the average kinetic energy, regardless of the mass of the sample. So, we just need to compare the temperatures given for each sample.
Comparison of Sample Temperatures: Sample $(1)$ is at $50\,^\circ\mathrm{C}$ , sample $(2)$ is at $30\,^\circ\mathrm{C}$ , sample $(3)$ is at $40\,^\circ\mathrm{C}$ , and sample $(4)$ is at $20\,^\circ\mathrm{C}$ . We can see that sample $(4)$ has the lowest temperature.
Identifying Sample with Lowest Temperature: Since sample $4$ has the lowest temperature, it means that the particles in this sample have the lowest average kinetic energy.