Choose the compound with the larger positional probability...

Choose the compound with the larger positional probability in each case. a. $1 \mathrm{~mol} \mathrm{H}_{2}$ (at STP) or $1 \mathrm{~mol} \mathrm{H}_{2}$ (at $\left.100^{\circ} \mathrm{C}, 0.5 \mathrm{~atm}\right)$ b. $1 \mathrm{~mol} \mathrm{~N}_{2}$ (at STP) or $1 \mathrm{~mol} \mathrm{~N}_{2}$ (at $\left.100 \mathrm{~K}, 2.0 \mathrm{~atm}\right)$ c. $1 \mathrm{~mol} \mathrm{H}_{2} \mathrm{O}(s)\left(\right.$ at $\left.0^{\circ} \mathrm{C}\right)$ or $1 \mathrm{~mol} \mathrm{H}_{2} \mathrm{O}(l)\left(\right.$ at $\left.20^{\circ} \mathrm{C}\right)$

Choose the compound with the larger positional probability in each case.
a. $1 \mathrm{~mol} \mathrm{H}_{2}$ (at STP) or $1 \mathrm{~mol} \mathrm{H}_{2}$ (at $\left.100^{\circ} \mathrm{C}, 0.5 \mathrm{~atm}\right)$
b. $1 \mathrm{~mol} \mathrm{~N}_{2}$ (at STP) or $1 \mathrm{~mol} \mathrm{~N}_{2}$ (at $\left.100 \mathrm{~K}, 2.0 \mathrm{~atm}\right)$
c. $1 \mathrm{~mol} \mathrm{H}_{2} \mathrm{O}(s)\left(\right.$ at $\left.0^{\circ} \mathrm{C}\right)$ or $1 \mathrm{~mol} \mathrm{H}_{2} \mathrm{O}(l)\left(\right.$ at $\left.20^{\circ} \mathrm{C}\right)$

Key Concepts

States of Matter

The state of matter—whether a substance is a gas, liquid, or solid—plays a key role in its molecular distribution. Gases have high positional probability spread over a larger volume due to greater particle mobility, while liquids and solids have molecules that are more closely packed and hence a different positional probability profile.

Molar Volume

Molar volume is the volume occupied by one mole of a substance at given conditions of temperature and pressure. Differences in molar volume determine the density of molecules, which directly influences the positional probability in a system, especially when comparing gases under different thermodynamic conditions.

Positional Probability

This concept refers to the likelihood of finding a particle in a specific region of space. It is influenced by factors such as the number of particles, the volume available for distribution, and the state of matter. In gases, for instance, where particles are widely separated, the probability is spread out over a larger volume compared to condensed phases.

Ideal Gas Law

The ideal gas law (PV = nRT) explains the relationship between pressure, volume, and temperature for a given number of moles of a gas. It is crucial for comparing conditions under which gases are held since variations in these parameters affect the molecular spacing and thus the positional probability of the gas molecules.

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