Questions: A sample of gas has a volume of 423 mL at a pressure of 3.77 atm. The gas is compressed and now has a pressure of 8.46 atm. Predict whether the new volume is greater or less than the initial volume, and calculate the new volume. Assume temperature is constant and no gas escaped from the container. New volume larger or smaller? New volume = mL

A sample of gas has a volume of 423 mL at a pressure of 3.77 atm. The gas is compressed and now has a pressure of 8.46 atm. Predict whether the new volume is greater or less than the initial volume, and calculate the new volume. Assume temperature is constant and no gas escaped from the container.

New volume larger or smaller?

New volume = mL

Transcript text: TUTOR Boyle's Law A sample of gas has a volume of $\mathbf{4 2 3 \mathrm { mL }}$ at a pressure of $\mathbf{3 . 7 7} \mathrm{atm}$. The gas is compressed and now has a pressure of 8.46 atm . Predict whether the new volume is greater or less than the initial volume, and calculate the new volume. Assume temperature is constant and no gas escaped from the container. New volume larger or smaller? New volume $=$ $\square$ mL Submit Show Approach Show Tutor Steps Submit Answer Try Another Version 10 item attempts remaining

Solution

Solution Steps

Step 1: Understanding Boyle's Law

Boyle's Law states that for a given mass of gas at constant temperature, the volume of the gas is inversely proportional to its pressure. Mathematically, it is expressed as:

\[ P_1 V_1 = P_2 V_2 \]

where:

$ P_1 $ is the initial pressure,
$ V_1 $ is the initial volume,
$ P_2 $ is the final pressure,
$ V_2 $ is the final volume.

Step 2: Identify Given Values

From the problem, we have:

Initial volume, $ V_1 = 423 \, \text{mL} $
Initial pressure, $ P_1 = 3.77 \, \text{atm} $
Final pressure, $ P_2 = 8.46 \, \text{atm} $

Step 3: Predict the New Volume

Since the pressure increases from 3.77 atm to 8.46 atm, according to Boyle's Law, the volume should decrease. Therefore, the new volume will be smaller than the initial volume.

Step 4: Calculate the New Volume

Using Boyle's Law:

\[ P_1 V_1 = P_2 V_2 \]

Rearrange to solve for $ V_2 $:

\[ V_2 = \frac{P_1 V_1}{P_2} \]

Substitute the given values:

\[ V_2 = \frac{3.77 \, \text{atm} \times 423 \, \text{mL}}{8.46 \, \text{atm}} \]

Step 5: Perform the Calculation

\[ V_2 = \frac{1594.71 \, \text{mL} \cdot \text{atm}}{8.46 \, \text{atm}} \approx 188.5 \, \text{mL} \]