To determine the condition at which the density of neon will be highest, we can use the ideal gas law and the relationship between density, pressure, and temperature.
### Step-by-Step Solution:
1. **Understand the Ideal Gas Law**: The ideal gas law is given by the equation:
\[
PV = nRT
\]
where \( P \) is the pressure, \( V \) is the volume, \( n \) is the number of moles, \( R \) is the ideal gas constant, and \( T \) is the temperature in Kelvin.
2. **Relate Moles to Mass**: The number of moles \( n \) can be expressed in terms of mass \( W \) and molar mass \( m \):
\[
n = \frac{W}{M}
\]
where \( M \) is the molar mass of neon.
3. **Express Density**: Density \( D \) is defined as mass per unit volume:
\[
D = \frac{W}{V}
\]
From the ideal gas law, we can rearrange to find \( V \):
\[
V = \frac{nRT}{P}
\]
Substituting the expression for \( n \):
\[
V = \frac{WRT}{MP}
\]
Therefore, substituting \( V \) back into the density equation gives:
\[
D = \frac{W}{\frac{WRT}{MP}} = \frac{MP}{RT}
\]
4. **Analyze the Density Equation**: From the equation \( D = \frac{MP}{RT} \), we can see that:
- Density \( D \) is directly proportional to pressure \( P \).
- Density \( D \) is inversely proportional to temperature \( T \).
5. **Determine Conditions for Maximum Density**: To maximize density:
- Increase pressure \( P \) (higher pressure leads to higher density).
- Decrease temperature \( T \) (lower temperature leads to higher density).
6. **Evaluate Given Options**:
- **STP (Standard Temperature and Pressure)**: \( P = 1 \, \text{atm}, T = 273 \, \text{K} \)
- **Option 2**: \( 0^\circ C (273 \, \text{K}), P = 2 \, \text{atm} \)
- **Option 3**: \( P = 273 \, \text{atm} \) (very high pressure)
- **Option 4**: \( 0^\circ C (273 \, \text{K}), P = 2 \, \text{atm} \) (same as option 2)
7. **Select the Highest Density Condition**: Among the options, the condition with the highest pressure and lowest temperature will yield the highest density. The second option (0°C and 2 atm) and the fourth option (0°C and 2 atm) both provide a higher pressure than STP, which will result in a higher density.
### Conclusion:
The density of neon will be highest at **0°C and 2 atm**.
