A 0.245-L flask contains 0.467 mol CO 2 at 159 ^ C. Calculate the pressure: (a) using the ideal gas law (b) using the van der Waals equation (c) Explain the reason for the difference. (d) Identify which correction (that for \(\mathrm{P}\) or \(\mathrm{V}\) ) is dominant and why.

The ideal gas law is a fundamental equation that relates the pressure, volume, temperature, and amount of an ideal gas. With this equation, chemists and physicists can calculate the behavior of gases under different conditions. The ideal gas law is represented as:
\( PV = nRT \)
where \( P \) is pressure, \( V \) is volume, \( n \) represents the moles of gas, \( R \) is the gas constant, and \( T \) stands for temperature in Kelvin. This equation assumes that gas particles are point particles that do not interact with one another and that the space they take up is insignificant. In practice, we use the ideal gas law to calculate one property of a gas when the other three are known. For students working on exercises involving this law, it is important to first ensure all units are consistent, like converting temperature to Kelvin and volume to liters, before applying the equation.

Assessing gas pressure accurately is essential for scientists to predict gas behavior in various conditions. In exercises concerning gas pressure calculation, the ideal gas law serves as the starting point. After ensuring that all units are consistent and plugging the known values into the equation (\( P = \frac{nRT}{V} \) ), the pressure \( P \) can be determined. It is vital to remember that our result from this calculation describes an 'ideal' scenario without considering real-life deviations like intermolecular forces and the actual volume taken up by the gas particles. Hence, while the ideal gas law provides a good approximation, real gases often require more complex models such as the van der Waals equation to adjust for these factors and yield a more accurate pressure value.

While the ideal gas law overlooks them, intermolecular forces—the attractive and repulsive forces between molecules—are significant in understanding real gas behavior. When using the van der Waals equation, adjustments are made to take these forces into account. Specifically, the equation includes an 'a' term (\( \frac{[n^2a]}{V^2} \)), which corrects for the attraction between gas molecules. This term is crucial as it explains why real gases often show less pressure than ideal gases under the same conditions—the attraction can pull molecules together, reducing their impacts with the walls of their container.
Understanding intermolecular forces is especially important for students exploring why real gases deviate from ideal behavior. These forces vary depending on the type of gas and can significantly impact calculations. By comparing corrections for pressure (intermolecular forces) and volume (occupied by gas molecules) in the van der Waals equation, students can determine which factor has a greater effect on gas behavior in a given context.