Use the graph of pressure versus inverse volume and explain the trend of the graph and indicate mathematical relationship of the variables of the graph for grade 11 practical worksheet term 3 verify Boyle's law

Answer 1

Certainly! Boyle's Law is a fundamental principle in gas physics that states that the pressure of a gas is inversely proportional to its volume when the temperature and the amount of gas are constant. This relationship can be observed and verified through an experiment that involves measuring pressure versus volume of a gas.

Graph Description

1. Graph Type: The graph depicts pressure (P) on the y-axis and inverse volume (1/V) on the x-axis.

2. Trend: As the inverse volume (1/V) increases, the pressure (P) also increases. This indicates a direct relationship between pressure and the inverse of volume. The graph should show a straight line that slopes upwards, suggesting that higher pressures correspond to lower volumes.

Mathematical Relationship

According to Boyle's Law, the relationship can be mathematically expressed as:

\[ PV = k \]

Where:

• \( P \) is the pressure of the gas,
• \( V \) is the volume of the gas,
• \( k \) is a constant for a given quantity of gas at a constant temperature.

In terms of the variables plotted on the graph:

\[ P = k \times \frac{1}{V} \quad \text{or} \quad P \propto \frac{1}{V} \]

This reflects the inverse relationship between pressure and volume. When plotted as pressure (P) against inverse volume (1/V), we can infer that:

\[ P = m \left( \frac{1}{V} \right) + b \]

Where \( m \) is the slope of the line and \( b \) is the y-intercept. Ideally, if we eliminate measurement errors and maintain constant temperature, you will find that \( b \) is close to zero for an ideal gas.

Practical Worksheet Tasks

1. Data Collection: Measure the pressure of a gas at various inverse volumes. Record the data in a table format.

2. Graph Plotting: Plot the data points on the graph with pressure (P) on the y-axis and inverse volume (1/V) on the x-axis.

3. Trend Analysis: Describe the trend observed in the graph and how it supports Boyle’s Law. Discuss how increasing the inverse volume leads to a proportional increase in pressure.

4. Calculate and Interpret: Determine the slope (m) of the line and interpret its physical significance in the context of Boyle’s Law.

5. Conclude: Write a conclusion summarizing how the experimental results confirm Boyle’s Law, including any deviations that may have been observed and potential sources of error in the experiment.

This framework provides a solid grounding for students to understand and verify Boyle's Law through practical experimentation and data analysis.