Question

a sample of neon gas (ne) is transferred from an 18.9-liter cylinder to an empty 47.8-liter tank. before transfer, the pressure in the 18.9-liter cylinder was 25.3 bar. what is the final pressure of the ne gas inside the tank? assume ideal gas behavior and a constant temperature. write your answer to the correct number of significant figures. round if necessary. bar 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 \( P_1 = 25.3 \) bar, \( V_1 = 18.9 \) L, and \( V_2 = 47.8 \) L. We need to find \( P_2 \).

Step3: Rearrange the formula to solve for \( P_2 \)

From \( P_1V_1 = P_2V_2 \), we can solve for \( P_2 \) by dividing both sides by \( V_2 \): \( P_2=\frac{P_1V_1}{V_2} \)

Step4: Substitute the known values into the formula

Substitute \( P_1 = 25.3 \) bar, \( V_1 = 18.9 \) L, and \( V_2 = 47.8 \) L into the formula: \( P_2=\frac{25.3\times18.9}{47.8} \)

Step5: Calculate the value

First, calculate the numerator: \( 25.3\times18.9 = 478.17 \)
Then, divide by the denominator: \( P_2=\frac{478.17}{47.8}\approx9.87 \) bar (rounded to three significant figures, consistent with the given values)

Answer:

9.87 bar