Question

A graph is plotted between pressure and volume at different temperatures. On the basis of the graph what changes will you observe in the volume if (i) the pressure is increased at constant temperature. (ii) the temperature is decreased at constant pressure. (a) volume increases in both the cases (b) volume decreases in both the cases (c) volume increases in (i) and decreases in (ii) (d) volume decreases in (i) and increases in (ii).

Short answer

Volume decreases in both (i) and (ii); hence, the correct answer is (b) volume decreases in both the cases.

Step-by-step solution

Understanding Boyle's Law

First, interpret the given situation using Boyle's Law for case (i), where at constant temperature, pressure is inversely proportional to volume. This means if pressure is increased, volume must decrease.

Understanding Charles' Law

Next, consider Charles' Law for case (ii), which states that at constant pressure, volume is directly proportional to temperature. Thus, if the temperature decreases, the volume will also decrease.

Combining Observations

Combine the observations from Boyle's Law and Charles' Law to determine the overall impact on volume. From (i) volume decreases with increased pressure, and from (ii) volume decreases with decreased temperature.

Key concepts

Pressure-volume relationship

In the study of gases, one of the fundamental concepts is the pressure-volume relationship, known to many as Boyle's Law. This principle tells us about how gases behave when we change their pressure while keeping their temperature constant. Simply put, Boyle's Law states that for a given mass of an ideal gas, the pressure (\( P \text{ in Pascals (Pa)} \) is inversely proportional to its volume (\( V \text{ in liters (L)} \). This means that if you increase the pressure applied to a gas, its volume will decrease, as long as the temperature doesn't change. We can represent this law mathematically as: \[ P_1 \times V_1 = P_2 \times V_2 \] where \( P_1 \text{ and } V_1 \) are the initial pressure and volume, and \( P_2 \text{ and } V_2 \) are the pressure and volume after the change. This formula helps students understand that if we double the pressure, the volume will halve, assuming that we're dealing with an ideal gas under ideal conditions.

To aid in understanding, imagine squeezing a balloon. The harder you squeeze, the smaller the balloon becomes – that's Boyle's Law in action. However, real gases may deviate from this behavior under extreme conditions, which is a little reminder that while Boyle's Law gives us a good approximation, nature often has nuances.

Temperature-volume relationship

Another key concept in understanding the behavior of gases is the relationship between temperature and volume, often illustrated by Charles' Law. The law unfolds the direct proportionality between volume and temperature when we keep the pressure constant. In practice, this means if a gas is heated up, its volume will expand, assuming the pressure remains unchanged.

Charles' Law is mathematically expressed as \( \frac{V_1}{T_1} = \frac{V_2}{T_2} \), where \( V \text{ and } T \) represent the volume and absolute temperature, respectively. It's vital to note that the temperature must be measured in Kelvin (\( K \) for Charles' Law to be accurate. If we take a balloon and heat it, as per Charles' Law, the balloon grows larger because the molecules inside move more vigorously, needing more space. Conversely, cooling the gas results in a reduction of volume. It’s a simple yet powerful concept which helps us explain everyday phenomena like why a balloon might shrivel on a cold day.

Gas laws in chemistry

Understanding gas laws is crucial in the field of chemistry as they provide a foundational understanding of how gaseous substances interact with their surroundings. Boyle's Law and Charles' Law are part of a broader collection of empirical laws that describe the behavior of ideal gases. These gas laws help chemists and scientists predict the behavior of gases in various chemical reactions and conditions, from inflating airbags to the production of industrial gases.

It's crucial to learn these gas laws not just independently, but also how they integrate with each other, forming combined gas laws and eventually leading to the Ideal Gas Law. This integration allows for more complex calculations and predictions. For instance, when studying chemical kinetics or the conditions required for a reaction to occur, knowing the behavior of gases at different pressures, volumes, and temperatures can be key to experimental success. Students should concentrate on the refined application of these laws, ensuring they recognize when conditions depart from the ideal and how real gases might behave differently.

Graphical interpretation of gas laws

The graphical interpretation of the gas laws provides a visual understanding of these principles. For Boyle's Law, a graph of pressure versus volume at constant temperature will yield a curve that shows an inverse relationship—a hyperbola. As the pressure increases, the volume decreases, reflecting the 'squeeze the balloon' analogy. On the Charles' Law front, a graph of volume against temperature at constant pressure displays a direct relationship, constructing a straight line that goes through the origin. The steeper the slope, the more significant the change in volume with temperature.

These graphical representations are not just visual aids but powerful tools to predict gas behavior under given conditions. They also serve as a means to confirm the accuracy of collected data against theoretical expectations. Educators often encourage students to graph these relationships in laboratory settings to solidify their understanding and witness the laws in action. If discrepancies arise, it's an excellent opportunity to discuss real gas behavior, experimental error, or measurement techniques. Grasping these graphical relationships is a foundational skill in chemistry, revealing how variables interrelate in the real world.