The ratio of the initial to the final pressure of a given mass of gas...

Explanation

To solve this question, we need to understand the relationship between pressure and volume for a given mass of gas at a constant temperature. This relationship is described by Boyle's Law, which states that the product of pressure and volume is constant for a given mass of gas at constant temperature.

Mathematically, Boyle's Law is represented as:

\[\text{P}_1\text{V}_1 = \text{P}_2\text{V}_2\]

Where \(\text{P}_1\) and \(\text{P}_2\) are the initial and final pressures respectively, and \(\text{V}_1\) and \(\text{V}_2\) are the initial and final volumes respectively.

From the question, we know the ratio of initial to final pressure is 1:1.5, and the initial volume is 300cm\(^3\). Let's denote the initial pressure as \(P\) and the final pressure as \(1.5P\). We can now use Boyle's Law to find the final volume:

\[P \times 300 = 1.5P \times \text{V}_2\]

To find \(\text{V}_2\), we can divide both sides by \(1.5P\):

\[\text{V}_2 = \frac{P \times 300}{1.5P}\]

The \(P\) in the numerator and denominator cancel out:

\[\text{V}_2 = \frac{300}{1.5}\]

Now, we can calculate the final volume:

\[\text{V}_2 = 200\text{cm}^3\]

So, the correct answer isOption B: 200cm\(^3\).