Question

The volume of gas in a cylinder is \(1098 \mathrm{~cm}^{3}\). Pressure is increased and the volume changes to \(936 \mathrm{~cm}^{3}\). Calculate the percentage change in the volume of gas.

Short answer

Answer: The percentage change in the volume of the gas after the pressure increase is -14.75%, which indicates that the volume has decreased by 14.75%.

Step-by-step solution

Write down the given information

The initial volume of the gas is \(1098 \mathrm{~cm}^{3}\) and the final volume after the pressure increase is \(936 \mathrm{~cm}^{3}\).

Calculate the change in volume

To find the change in volume, subtract the initial volume from the final volume: Change in volume = Final volume - Initial volume = \(936 \mathrm{~cm}^{3} - 1098 \mathrm{~cm}^{3} = -162 \mathrm{~cm}^{3}\).

Calculate the percentage change in volume

Now, use the formula for percentage change: Percentage change = \(((\text{Change in volume}) / (\text{Initial volume})) * 100\). Plug in the values: Percentage change = \((\)(-162 \mathrm{~cm}^{3}) / (1098 \mathrm{~cm}^{3})\() * 100 = -14.75\%\).

Interpret the result

The percentage change in the volume of the gas is -14.75%. This negative value indicates that the volume of the gas has decreased by 14.75% after the pressure increase.

Key concepts

Volume of Gas

The volume of gas refers to the space that the gas occupies. In our scenario, we're looking at the volume of gas inside a cylinder. When dealing with any gas, understanding the initial and final volumes can help us determine how the gas behaves under different conditions.

Here, the gas initially had a volume of \(1098 \mathrm{~cm}^{3}\). This is a measurement of the space it took up when first put under a given set of conditions, such as specific pressure and temperature. When the pressure was increased, this volume decreased to \(936 \mathrm{~cm}^{3}\).

These changes are essential when studying gas behavior, especially within closed systems like cylinders, where the volume can easily be measured and used to analyze how gasses react to changes in their environment.

Cylinder Calculations

Cylinders often serve as containers for gases due to their streamlined shape, which allows for efficient storage and release of compressed gases. Calculating the volume of gas within a cylinder requires understanding the cylinder's dimensions or understanding the conditions under which the gas was measured.

In this exercise, the volume change is simply measured from the conditions of pressure adjustments, without needing intricacies about the exact cylinder dimensions since the gas volume itself is provided. The key calculation here involves determining changes within the cylinder when the pressure changes, typically using known values like the initial and final volume. These measurements allow students to calculate how much gas volume is adjusted when external factors, like pressure adjustments, come into play.

Pressure and Volume Relationship

Gases have a unique property where their volume can change significantly under varying pressures—a concept explained by Boyle's Law. According to this principle, if the temperature remains constant, the volume of a gas is inversely proportional to the pressure applied: as pressure increases, volume decreases, and vice versa.

In the exercise given, when pressure was increased, the gas volume decreased from \(1098 \mathrm{~cm}^{3}\) to \(936 \mathrm{~cm}^{3}\). This reflects the relationship mentioned, showcasing an inverse relationship between pressure and volume.

To quantify this change, a percentage calculation was applied. This informs us about the relative change compared to the original volume, indicating a \(-14.75\%\) change. This percentage tells us that the gas volume decreased by about 14.75% when the pressure was increased, which is consistent with the gas laws behavior.