A gas such as carbon monoxide would be most likely to obey the ideal gas law at

Options

A. (a) high temperatures and low pressures
B. (b) low temperatures and high pressures
C. (c) high temperatures and high pressures
D. (d) low temperatures and low pressures

Explanation

To determine the conditions under which carbon monoxide (CO) behaves like an ideal gas, we need to analyze the ideal gas law and the behavior of real gases.

### Step-by-Step Solution:

1. **Understanding the Ideal Gas Law**:
The ideal gas law is represented 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.

2. **Identifying Real Gas Behavior**:
Carbon monoxide is a real gas, which means it does not always follow the ideal gas law. Real gases deviate from ideal behavior under certain conditions, particularly at high pressures and low temperatures.

3. **Conditions Favoring Ideal Gas Behavior**:
- **High Temperature**: At high temperatures, the kinetic energy of gas molecules increases. This means that the molecules move faster and are less affected by intermolecular forces. As a result, the attractive forces between molecules become negligible.
- **Low Pressure**: At low pressures, the volume of the gas is large. This means that the volume occupied by the gas molecules themselves (which is represented by the term \( nB \) in the van der Waals equation) becomes insignificant compared to the total volume. Thus, the volume occupied by the gas molecules can be neglected.

4. **Applying the Van der Waals Equation**:
The van der Waals equation for real gases is given by:
\[ \left(P + \frac{a n^2}{V^2}\right)(V - nB) = nRT \]
Here, \( a \) and \( b \) are constants that account for the intermolecular forces and the volume occupied by the gas molecules, respectively.

5. **Neglecting Terms**:
- At high temperatures, the term \( \frac{a n^2}{V^2} \) becomes small compared to \( P \) because the pressure is not significantly affected by the attractive forces.
- At low pressures, the term \( nB \) becomes small compared to \( V \) because the volume is large.

6. **Resulting Ideal Gas Equation**:
Under these conditions (high temperature and low pressure), the van der Waals equation simplifies to the ideal gas equation:
\[ PV = nRT \]

7. **Conclusion**:
Therefore, carbon monoxide would be most likely to obey the ideal gas law at high temperatures and low pressures.

### Final Answer:
The correct option is **A: High temperatures and low pressures**.