Out of the three states of matter, only the gases have most of the physical properties common. They neither have definite shapes nor volumes. Upon mixing they form homogeneous mixture irrespective of their nature and can also be compressed on applying pressure. In addition to these, the gases obey different gas laws such as boyle's Law, Charles's Law, Dalton's Law of partial pressures, Graham's Law of diffusion etc. Based upon these laws, ideal gas equation `PV = nRT` has been derived.
When the product of pressure and volume is plotted against pressure for a given amount of a gas, the obtained is

Options

A. parallel to X-axis
B. parallel to Y-axis
C. linear with positive slope
D. linear with negative slope

Explanation

To solve the question, we need to analyze the relationship between pressure (P), volume (V), and the product of pressure and volume (PV) for a given amount of gas, based on Boyle's Law.

### Step-by-Step Solution:

1. **Understanding Boyle's Law**:
- Boyle's Law states that for a given amount of gas at constant temperature, the pressure (P) of the gas is inversely proportional to its volume (V). Mathematically, this can be expressed as:
\[ PV = k \]
where \(k\) is a constant.

2. **Rearranging the Equation**:
- From Boyle's Law, we can express the relationship as:
\[ V = \frac{k}{P} \]
- This indicates that as pressure increases, volume decreases, and vice versa.

3. **Plotting the Graph**:
- We are asked to plot the product of pressure and volume (PV) against pressure (P).
- Since \(PV = k\) is constant, we can say that:
\[ PV = k \]
- Therefore, if we plot \(PV\) on the y-axis and \(P\) on the x-axis, we will have a horizontal line at the value of \(k\).

4. **Conclusion**:
- The graph of the product of pressure and volume (PV) against pressure (P) will be a straight line parallel to the x-axis, indicating that \(PV\) remains constant regardless of changes in pressure.

### Final Answer:
When the product of pressure and volume is plotted against pressure for a given amount of gas, the obtained graph is a horizontal line parallel to the x-axis.