The density of argon ($p$) at normal temperature and pressure (N.T.P.) can be found using the ideal gas law:

$pV = nRT$

Rearranging to express density in terms of known quantities at N.T.P.:

1. Write the ideal gas law in terms of molar mass and density:

   $PV = nRT \Rightarrow P = \frac{nRT}{V} \Rightarrow p = \frac{M}{V} = \frac{PM}{RT}$

   Here:

   • $p$ is the density,
   • $M$ is the molar mass of argon,
   • $R$ is the gas constant, and
   • $T$ is the temperature at N.T.P.

2. Use the relationship between $C_p$ and $C_v$ for an ideal gas:

   For an ideal gas, the ratio $\gamma = \frac{C_p}{C_v}$ is used to relate $C_p$ and $C_v$.

3. Substitute into the density formula:

   Since we know the values at N.T.P. (where $P$ and $T$ are constants):

   $p = \frac{P \cdot M}{R \cdot T}$

4. Final density expression:

   By substituting the known molar mass for argon and constants $P$ and $T$ at N.T.P., you would arrive at a numerical answer for $p$.

This density calculation assumes you have values for $C_p$ and $C_v$, which relate to the molar mass and specific heat ratio. Would you like the step-by-step computation with specific values?

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1. How does the ideal gas law apply to other noble gases like helium?
2. What role does molar mass play in calculating gas density?
3. How can specific heats $C_p$ and $C_v$ help in understanding gas behavior under different conditions?
4. What are typical values of $C_p$ and $C_v$ for argon, and how do they affect density?
5. How would this calculation change at a different temperature or pressure?

Tip: When using the ideal gas law, remember that it assumes ideal conditions, so deviations can occur at very high pressures or low temperatures.