The density of neon will be minimum at

Options

A. STP
B. `0^(@)C, 2 atm`
C. `273^(@)C, 1 atm`
D. `273^(@)C, 2 atm`

Explanation

To determine the conditions under which the density of neon will be minimum, we can use the ideal gas law and the relationship between density, pressure, and temperature. Here’s a step-by-step solution:

### Step-by-Step Solution:

1. **Understand the Ideal Gas Law**:
The ideal gas law is given by the equation:
\[ PV = nRT \]
where \(P\) is pressure, \(V\) is volume, \(n\) is the number of moles, \(R\) is the universal gas constant, and \(T\) is temperature.

2. **Relate Moles to Mass**:
The number of moles \(n\) can be expressed in terms of mass \(m\) and molar mass \(M\):
\[ n = \frac{m}{M} \]

3. **Substitute into the Ideal Gas Law**:
Substituting \(n\) into the ideal gas law gives:
\[ PV = \frac{m}{M}RT \]

4. **Express Density**:
Density (\(\rho\)) is defined as mass per unit volume:
\[ \rho = \frac{m}{V} \]
Rearranging the ideal gas equation to express volume in terms of the other variables:
\[ V = \frac{mRT}{PM} \]
Substituting this into the density equation:
\[ \rho = \frac{m}{\frac{mRT}{P}} = \frac{P M}{RT} \]

5. **Analyze the Density Equation**:
From the equation \(\rho = \frac{PM}{RT}\), we can see that:
- Density (\(\rho\)) is directly proportional to pressure (\(P\)).
- Density (\(\rho\)) is inversely proportional to temperature (\(T\)).

6. **Determine Conditions for Minimum Density**:
To minimize density, we need to:
- Minimize pressure (\(P\)).
- Maximize temperature (\(T\)).

7. **Identify the Conditions**:
Given the options provided in the question (not specified here), select the option where pressure is at its lowest and temperature is at its highest.

8. **Conclusion**:
The density of neon will be minimum at conditions of low pressure and high temperature.