Question

a sealed syringe contains 3.555 cubic centimeters of hydrogen gas (h₂) at a pressure of 788.1 torr. the plunger of the syringe is depressed until the gas has a pressure of 808.2 torr. what is the final volume of the h₂ gas in the syringe? assume ideal gas behavior and a constant temperature. write your answer to the correct number of significant figures. round if necessary. cubic centimeters save answer

Explanation:

Step1: Recall Boyle's Law

Boyle's Law states that for a given amount of gas at constant temperature, \( P_1V_1 = P_2V_2 \), where \( P_1 \) and \( V_1 \) are the initial pressure and volume, and \( P_2 \) and \( V_2 \) are the final pressure and volume.

Step2: Identify known values

We know that \( P_1 = 788.1 \) torr, \( V_1 = 3.555 \) \( \text{cm}^3 \), and \( P_2 = 808.2 \) torr. We need to find \( V_2 \).

Step3: Rearrange the formula to solve for \( V_2 \)

From \( P_1V_1 = P_2V_2 \), we can rearrange to get \( V_2=\frac{P_1V_1}{P_2} \).

Step4: Substitute the known values into the formula

Substitute \( P_1 = 788.1 \) torr, \( V_1 = 3.555 \) \( \text{cm}^3 \), and \( P_2 = 808.2 \) torr into the formula:
\( V_2=\frac{788.1\times3.555}{808.2} \)
First, calculate the numerator: \( 788.1\times3.555 = 788.1\times3 + 788.1\times0.555 = 2364.3+437.3955 = 2801.6955 \)
Then, divide by the denominator: \( V_2=\frac{2801.6955}{808.2}\approx3.46 \) (rounded to three decimal places, but we need to consider significant figures. The given values have 4 significant figures for \( V_1 \), 4 for \( P_1 \), and 4 for \( P_2 \), so the result should have 4 significant figures. Wait, let's recalculate more precisely:
\( V_2=\frac{788.1\times3.555}{808.2}=\frac{788.1}{808.2}\times3.555\approx0.97513\times3.555\approx3.459 \) (when calculated more accurately, we get approximately 3.459 cubic centimeters)

Answer:

3.459